Unified List of Undergraduate Courses: Διαφορά μεταξύ των αναθεωρήσεων
Χωρίς σύνοψη επεξεργασίας |
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Γραμμή 169: | Γραμμή 169: | ||
==Operator Theory (MAE811)== | ==Operator Theory (MAE811)== | ||
{{:Operator Theory (MAE811)}} | {{:Operator Theory (MAE811)}} | ||
==Qualitative Theory of Partial Differential Equations (MAE815)== | ==Qualitative Theory of Partial Differential Equations (MAE815)== | ||
{{:Qualitative Theory of Partial Differential Equations (MAE815)}} | {{:Qualitative Theory of Partial Differential Equations (MAE815)}} |
Αναθεώρηση της 19:35, 17 Αυγούστου 2024
- Department of Mathematics
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Compulsory Courses
Infinitesimal Calculus I (MAY111)
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General
School | School of Science |
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Academic Unit | Department of Mathematics |
Level of Studies | Undergraduate |
Course Code | MAY111 |
Semester | 1 |
Course Title | Infinitesimal Calculus I |
Independent Teaching Activities | Lectures (Weekly Teaching Hours: 5, Credits: 7.5) |
Course Type | General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations | Language of Instruction (lectures): Greek. Language of Instruction (activities other than lectures): Greek and English Language of Examinations: Greek and English |
Is the Course Offered to Erasmus Students | Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes | Here, the acronym RFooV stands for Real Function of one Variable. Remembering:
Comprehension:
Applying:
Evaluating: Teaching undergraduate courses. |
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General Competences |
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Syllabus
- Real numbers, axiomatic foundation of the set of real numbers (emphasis in the notion of supremum and infimim), natural numbers, induction, classical inequalities.
- Functions, graph of a function, monotone functions, bounded functions, periodic functions. Injective and surjective functions, inverse of a function. Trigonometric functions, inverse trigonometric functions, exponential and logarithmic functions, hyperbolic and inverse hyperbolic functions.
- Sequences of real numbers, convergent sequences, monotone sequences, sequences defined by recursion, limits of monotone sequences, nested intervals. The notion of subsequence, Bolzano Weierstass’ Theorem, Cauchy sequences. Accumulation points of sequences, upper and lower limit of a sequence (limsup, liminf).
- Continuity of functions, accumulation points and isolated points, limits of functions, one sided limits, limits on plus infinity and minus infinity. Continuity of several basic functions, local behaviour of a continuous function. Bolzano Theorem and intermediate value theorem. Characterization of continuity via sequences, properties of continuous functions defined on closed intervals, continuity of inverse functions.
- Derivative of a function, definition and geometric interpretation, examples and applications in sciences. The derivatives of elementary functions, derivation rules, higher order derivation. Rolle’s Theorem, Mean Value Theorem, Darboux’s theorem. Derivative and the monotonicity of a function, extrema of functions, convex and concave functions, inflection points. Derivation of inverse functions. Generalized Mean Value Theorem, De L’ Hospital rule. Study of functions using derivatives.
Teaching and Learning Methods - Evaluation
Delivery |
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Use of Information and Communications Technology |
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Teaching Methods |
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Student Performance Evaluation |
Language of evaluation: Greek and English.
The aforementioned information along with all the required details are available through the course's website. The information is explained in detail at the beginning of the semester, as well as, throughout the semester, during the lectures. Reminders are also posted at the beginning of the semester and throughout the semester, through the course’s website. Upon request, all the information is provided using email or social networks. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
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Fundamental Concepts of Mathematics (MAY112)
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General
School | School of Science |
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Academic Unit | Department of Mathematics |
Level of Studies | Undergraduate |
Course Code | MAY112 |
Semester | 1 |
Course Title | Fundamental Concepts of Mathematics |
Independent Teaching Activities | Lectures (Weekly Teaching Hours: 5, Credits: 7.5) |
Course Type | General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations | Greek |
Is the Course Offered to Erasmus Students | Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
As a first step, the students get familiar with basic tools of logic, set theory (set operations and properties), relations and functions. Emphasis is given to notions such as collections and families (coverings) bounds (max, min, sup, inf) as well as to images and pre-images of sets under functions. Part of the kernel of the course is a detailed axiomatic construction of the real numbers aiming that the students acknowledge this set as result of an axiomatic construction rather than of an empiric approach, yet the value and the significancy of the axiomatic foundation of mathematical structures be apparent.
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General Competences |
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Syllabus
Definition of trigonometric numbers, trigonometric cycle. Trigonometric numbers of the sum of two angles and trigonometric numbers of the double of an arc. Trigonometrical functions. Trigonometrical equations. Transformations of products to sum and of sums to products.
Elements of Logic. Basic set theory, operations and properties, power set, Cartesian products, collections. Relations, properties, equivalence relations, order relations, bounded sets, well ordered sets, principle of infinite reduction, functions, one to one functions, onto functions.
Image and preimage of a set, functions and ordered sets. Families. The set of real numbers: axiomatic approach. The sets of natural numbers, integers. The field of rational numbers. Roots of nonnegative real numbers. The set if irrational numbers.
The axiom of completeness and equivalent statements. Equivalent sets. Finite sets. Infinite sets. Schroder-Bernstein theorem. Numerable sets. At most numerable sets. Denumerable sets. Cantor’ theorem. Axiom of Choice and equivalent statements. A first approach to the necessity of an axiomatic foundation of sets.
Teaching and Learning Methods - Evaluation
Delivery | Face-to-face | ||||||||||
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Use of Information and Communications Technology | Use of ICT (Tex, Mathematica etc.) for presentation of essays and assignments. | ||||||||||
Teaching Methods |
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Student Performance Evaluation | Written examination at the end of the semester including theory and problems-exercises. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- K. G. Binmore, Logic, Sets and Numbers, Cambridge University Press, 1980.
- W. W. Fairchild and C. I. Tulcea, Sets, W. B. Shaunders Co. Philadelphia, 1970.
- S. Lipschutz, Set Theory and Related Topics, Schaum’s Outline Series, New York, 1965.
- D. Van Dalen, H. C. Doets and H. Deswart, Sets: Naïve, Axiomatic and Applied, Pergamon Press, Oxford, 1987.
Linear Algebra I (MAY121)
- Ελληνική Έκδοση
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General
School | School of Science |
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Academic Unit | Department of Mathematics |
Level of Studies | Undergraduate |
Course Code | MAY121 |
Semester | 1 |
Course Title | Linear Algebra I |
Independent Teaching Activities | Lectures (Weekly Teaching Hours: 5, Credits: 7.5) |
Course Type | General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations | Greek |
Is the Course Offered to Erasmus Students | Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
After finishing the course, the students will be able:
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General Competences | The aim of the course is to empower the graduate to analyse and compose basic notions and knowledge of Linear Algebra and advance his creative and productive thinking. |
Syllabus
- The algebra of (m x n) matrices and applications.
- Row echelon forms and reduced row echelon form of a matrix.
- Rank of a matrix. Determinants. Invertible matrices.
- Linear systems and applications.
- Vector spaces. Linear maps.
- The space L(E,F) of linear operations.
- Subspaces. Bases. Dimension. Rank of a linear operation.
- Fundamental equation of dimension and its applications. Matrix of a linear map. Matrix of a change of bases. The isomorphism between linear mapsand matrices. Equivalent matrices. Similar matrices. Determinant of an endomorphism. Sum and direct sum of vector subspaces.
Teaching and Learning Methods - Evaluation
Delivery | Classroom (face-to-face) | ||||||||||
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Use of Information and Communications Technology |
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Teaching Methods |
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Student Performance Evaluation | Final written exam in Greek (in case of Erasmus students, in English) which includes analysis of theoretical topics and resolving application problems. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Introduction to Linear Algebra (Greek), Bozapalidis Symeon, ISBN: 978-960-99293-5-6 (Editor): Charalambos Nik. Aivazis
Number Theory (MAY123)
- Ελληνική Έκδοση
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General
School | School of Science |
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Academic Unit | Department of Mathematics |
Level of Studies | Undergraduate |
Course Code | MAY123 |
Semester | 1 |
Course Title | Number Theory |
Independent Teaching Activities | Lectures (Weekly Teaching Hours: 4, Credits: 7.5) |
Course Type | General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations | Greek, English |
Is the Course Offered to Erasmus Students | Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The main purpose of the course is the study of the structure and basic properties of natural numbers, and more generally of integers. This study is based on the fundamental concept of divisibility of integers, and the (unique) factorization of a natural number into prime factors.
We will formulate and prove several theorems concerning the structure of all integers through the concept of divisibility. During the course will analyse applications of Number Theory to other sciences, and particularly to Cryptography.
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General Competences |
The course aims to enable the undergraduate student to acquire the ability to analyse and synthesize basic knowledge of the theory of numbers, to apply basic examples in other areas, and in particular to solve concrete problems concerning properties of numbers occurring in everyday life. The contact of the undergraduate student with the ideas and concepts of number theory, (a) promotes the creative, analytical and deductive thinking and the ability to work independently, (b) improves his critical thinking and his ability to apply abstract knowledge in various field. |
Syllabus
- Complex numbers.
- Divisibility.
- Congruences mod m.
- Chinese remainder theorem.
- Arithmetical functions and Moebius inversion formula.
- The theorems of Fermat, Euler and Wilson.
- Primitive roots mod p.
- The theory of indices and the Law of quadratic reciprocity.
- Applications to cryptography.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
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Use of Information and Communications Technology |
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Teaching Methods |
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Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students, in English) which includes analysis of theoretical topics and resolving application problems. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Infinitesimal Calculus II (MAY211)
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General
School | School of Science |
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Academic Unit | Department of Mathematics |
Level of Studies | Undergraduate |
Course Code | MAY211 |
Semester | 2 |
Course Title | Infinitesimal Calculus II |
Independent Teaching Activities | Lectures, laboratory exercises (Weekly Teaching Hours: 5, Credits: 7.5) |
Course Type | General Background |
Prerequisite Courses | None (from the typical point of view). Without the knowledge earned from the course “Infinitesimal Calculus I” will be nearly impossible to follow this course. |
Language of Instruction and Examinations | Greek |
Is the Course Offered to Erasmus Students | Yes (exams in English are provided for foreign students) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
This course is the sequel of the course “Infinitesimal Calculus I”. The student will get in contact with more notions and techniques in the branch of Analysis. In this course the students:
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General Competences |
The course provides inductive and analytical thinking, the students evolve their computational skills and they get knowledge necessary for other courses during their undergraduate studies. |
Syllabus
Series, convergence of series and criteria for convergence of series. Dirichlet’s criterion, D’ Alembert’s criterion, Cauchy’s criterion, integral criterion. Series with alternating signs and Leibnitz’s theorem. Absolute convergence and reordering of series, Power series, radius of convergence of power series.
Uniform continuity, definition and properties. Characterization of uniform continuity via sequences. Uniform continuity of continuous functions defined on closed intervals.
Riemann integral, definition for bounded functions defined on closed intervals. Riemann’s criterion, integrability of continuous functions. Indefinite integral and the Fundamental theorem of Calculus. Mean Value theorem of integral calculus, integration by parts, integration by substitution. Integrals of basic functions, integrations of rational functions. Applications of integrals, generalized integrals, relation between generalized integrals and series.
Taylor polynomials, Taylor’s Theorem, forms of the Taylor remainder. Taylor series and expansions of some basic functions as Taylor series.
Teaching and Learning Methods - Evaluation
Delivery |
Due to the theoretical nature of this course the teaching is exclusively given in the blackboard by the teacher. | ||||||||||
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Use of Information and Communications Technology |
The students may contact their teachers by electronic means, i.e. by e-mail. | ||||||||||
Teaching Methods |
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Student Performance Evaluation |
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Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Thomas, Απειροστικός Λογισμός, R.L. Finney, M.D. Weir, F.R.Giordano, Πανεπιστημιακές Εκδόσεις Κρήτης, (Απόδοση στα ελληνικά: Μ. Αντωνογιαννάκης).
Linear Algebra II (MAY221)
- Ελληνική Έκδοση
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General
School | School of Science |
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Academic Unit | Department of Mathematics |
Level of Studies | Undergraduate |
Course Code | MAY221 |
Semester | 2 |
Course Title | Linear Algebra II |
Independent Teaching Activities | Lectures (Weekly Teaching Hours: 5, Credits: 7.5) |
Course Type | General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations | Greek |
Is the Course Offered to Erasmus Students | Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
After finishing the course, the students will be able:
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General Competences |
The aim of the course is to empower the graduate to analyse and compose notions and knowledge of Linear Algebra and advance creative and productive thinking. |
Syllabus
Eigenvalues, Eigenvectors, Eigenspaces, Diagonalisation, Cauley-Hamilton thoerem, Euclidean spaces, Orthogonality, Gram-Schmidt orthogonalization, Orthogonal matrices, Self-adjoint endomorphisms, Symmetric matrices, Spectral theorem, Isometries, Quadratic forms, Principal Axes, Square root of a nonnegative real symmetric matrix. Norms of a matrix.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
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Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
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Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Introduction to Linear Algebra (Greek), Bozapalidis Symeon, ISBN: 978-960-99293-5-6 (Editor): Charalambos Nik. Aivazis
Analytic Geometry (MAY223)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
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Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAY223 |
Semester | 2 |
Course Title |
Analytic Geometry |
Independent Teaching Activities |
Lectures, laboratory exercises (Weekly Teaching Hours: 5, Credits: 7.5) |
Course Type |
General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek, English |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
It is an introductory course on geometry. The aim is to study problems in geometry using rectangular coordinates and tools based on Linear Algebra.
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General Competences |
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Syllabus
Axioms of Euclidean geometry (plane and space) and proofs of basic propositions. Cartesian model, vectors, linear independence, bases, coordinates and applications. Inner product, cross product, area, volume and determinants. Lines and planes. Geometric transformations (parallel transports, rotations, reflections), isometries and the notion of congruence. Transformation of area and volume under linear transformations. Curves and surfaces of 2nd degree and their classification. Curves, surfaces and parametrizations.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
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Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
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Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Introduction to Computer Science (MAY242)
- Ελληνική Έκδοση
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General
School |
School of Science |
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Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAY242 |
Semester | 2 |
Course Title |
Introduction to Computer Science |
Independent Teaching Activities |
Lectures and laboratory exercises (Weekly Teaching Hours: 5, Credits: 7.5) |
Course Type |
General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
This course offers an introduction to the Computer Science. It mainly focuses on how to algorithmically solve simple and complex mathematical problems. It provides basic programming techniques using a high-level programming language such as C/C ++. Moreover, the course analyzes the basic numbering systems, it provides the basic arithmetic operations in different numerical systems and refers to the representation of information on computer systems. Additionally, the course provides basic concepts of mathematical logic, such as Boolean algebra, and principles that govern the semantic and syntactic approach of propositional logic. Upon completion of the course, the students will be able to:
The course includes laboratory exercises in which the participation is obligatory. |
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General Competences |
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Syllabus
- Introduction to Numerical Representation
- Arithmetic operations in numerical systems
- Representations of binary numbers
- Introduction to Mathematical Logic (Boolean Algebra)
- Semantic approach: principles of propositional logic, conjunctive normal form (CNF), complete sets, meta-theorems
- Syntactic approach: axioms, Modus Ponens rule, meta-theorems (abduction, inversion), validity and completeness theorems.
- Basic Programming Techniques with programming language C/C++
- Input/Output data, type of structures and variables
- Flow control if/else
- Loop structures: for, while, do-while
- Defensive Programming
- Arrays (one dimension and multidimensions)
Teaching and Learning Methods - Evaluation
Delivery |
Lectures, labs session | ||||||||||
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Use of Information and Communications Technology |
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Teaching Methods |
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Student Performance Evaluation |
Written final exam (70%)
Laboratory exercises (30%).
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Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Η. Deitel and P. Deitel, C++ Προγραμματισμός 6η Εκδοση, Εκδόσεις Μ. Γκιούρδας, 2013. Κωδικός Ευδ: 12536819.
- Κωδικός Ευδόξου [77106820]: Διακριτά μαθηματικά και εφαρμογές τους, 8η Έκδοση, Kenneth H. Rosen
- Κωδικός Ευδόξου [86055409]: Διακριτά μαθηματικά, Hunter David (Συγγρ.)
- Κωδικός Ευδόξου [77109607]: Εισαγωγή στην πληροφορική, Evans Alan, Martin Kendall, Poatsy Mary Anne.
- Ζάχος, Ε., Παγουρτζής, Α., Σούλιου, Θ., 2015. Θεμελίωση επιστήμης υπολογιστών. [ηλεκτρ. βιβλ.] Αθήνα:Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών. Διαθέσιμο στο: http://hdl.handle.net/11419/545
- [Περιοδικό / Journal] IEEE Transactions on Computers
Infinitesimal Calculus III (MAY311)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
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Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAΥ311 |
Semester | 3 |
Course Title |
Infinitesimal Calculus III |
Independent Teaching Activities |
Lectures, laboratory exercises (Weekly Teaching Hours: 5, Credits: 7.5) |
Course Type |
General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek, English |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The main learning outcomes are the:
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General Competences |
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Syllabus
- Algebraic and topological structure of the Euclidean space R^n and geometric representation of the two- and three-dimensional space. Vector-sequences and their use concerning the topology of R^n.
- Real- and Vector-valued functions of several variables. Limits and continuity of functions.
- Partial derivatives. Partially differentiable and differentiable functions. Directional derivative. Differential operators and curves in R^n.
- Higher order partial derivatives. Taylor Theorem. Local and global extrema of real-valued functions. Implicit Function Theorem. Inverse Function Theorem. Constrained extrema.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
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Use of Information and Communications Technology |
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Teaching Methods |
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Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
Introduction to Probability (MAY331)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΥ331 |
Semester | 3 |
Course Title |
Introduction to Probability |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 5, Credits: 7.5) |
Course Type |
General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English, reading Course) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The aim of this course is to provide with a comprehensive understanding of the basic definitions of probability and the basic principles and laws of probability theory. Further, the introduction to the concepts of the random variable and the distribution function, as well as, their characteristics, such as the mean, variance, moments, moment generating function, etc., is included in the main aims of the course. Special distributions, such as binomial, geometric, Pascal, Poisson, uniform, exponential, gamma, normal distribution, etc. are studied and their use and application is indicated. The course is compulsory, it is of an entry-level and it aims to develop skills that help the students to understand, design and exploit stochastic models to describe real problems. At the end of the course the students is expected to be able to:
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General Competences |
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Syllabus
Basic ideas and laws of probability: Sample space and events. Classical-Statistical and Axiomatic definition of probability. Properties of probability and probabilistic formulas and laws. Elements of combinatorial analysis. Random variables and distribution functions. Discrete and continuous random variables and distribution functions. Standard discrete and continuous distributions: Binomial, Geometric, Pescal, Poisson, Uniform, Exponential, gamma, Normal etc. Characteristics of random variables and probability distributions: Expectation, variance, moments, moment generating function, properties. Transformation of random variables.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
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Use of Information and Communications Technology |
Use of ICT in communication with students | ||||||||||
Teaching Methods |
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Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which concentrates on the solution of problems which are motivated by the main themes of the course. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Ι. Κοντογιάννης, Σ. Τουμπής. Στοιχεία πιθανοτήτων, [Προπτυχιακό εγχειρίδιο]. Κάλλιπος, Ανοικτές Ακαδημαϊκές Εκδόσεις. https://hdl.handle.net/11419/2810.
- J. Blitzstein, J. Hwang. Introduction to Probability, 2nd edition, CRC Press, 2019.
- R. Dobrow. Probability with Applications and R, Wiley, 2014.
- H. Tijms. Understanding Probability, 3rd edition, Cambridge University Press, 2012.
- H. Tijms. ProbabilityQ a lively introduction, Cambridge University Press, 2018.
- [Περιοδικό / Journal] Annals of Probability (IMS)
- [Περιοδικό / Journal] Electronic Journal of Probability (IMS)
- [Περιοδικό / Journal] Journal of Applied Probability (Cambridge University Press)
Introduction to Numerical Analysis (MAY341)
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑY341 |
Semester | 3 |
Course Title |
Introduction to Numerical Analysis |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 4, Credits: 7.5) |
Course Type |
General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Upon successful completion of this course, students will be able to:
|
---|---|
General Competences |
|
Syllabus
- Error Analysis.
- Numerical solution of nonlinear equations: iterative methods, the fixed-point theorem, Newton’s method, the secant method.
- Numerical solution of linear systems: Matrix norms and conditioning. Direct Methods (Gauss elimination, LU factorization). Iterative methods, convergence, and examples of iterative methods (Jacobi, Gauss-Seidel).
- Polynomial interpolation: Lagrange and Hermite interpolation. Linear splines. Error analysis of interpolation.
- Numerical integration: Newton-Cotes quadrature formula (the trapezoidal rule and Simpson’s rule). Error analysis of numerical integration.
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
| ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Written examination (Weighting 100%, addressing learning outcomes 1-4) |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- “An Introduction to Numerical Analysis”, E. Süli, and D. Mayers, Cambridge University Press, Cambridge, 2003.
Introduction to Programming (MAY343)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAY343 |
Semester | 3 |
Course Title |
Introduction to Programming |
Independent Teaching Activities |
Lectures, laboratory exercises, tutorials, quiz (Weekly Teaching Hours: 5, Credits: 7.5) |
Course Type |
General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
This course aims at analyzing and solving problems using the computer as well as at introducing a high-level programming language (which in this case is C++ and Python). After successfully passing this course, the students will be able to:
|
---|---|
General Competences |
|
Syllabus
- Introduction to programming
- Preprocessing, numerical, boolean and logical operators
- Flow control: if/else, switch, for, while, do-while
- Structuring, locality of parameters, pass by value/reference, variable scope, recursive functions, program stack.
- Arrays, strings, objects
- Input/Output
- Functions, variables’ scope and recursion
- Searching and sorting data
- Elementary data structures.
Teaching and Learning Methods - Evaluation
Delivery |
Lectures, labs session | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
| ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written examination (80%)
Laboratory exercises (20%)
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- L. Jesse, Πλήρες εγχειρίδιο της C++, Εκδόσεις Α. Γκιούρδα, 2006. Κωδικός Ευδ: 12374.
- Βιβλίο [50656350]: Υπολογισμοί και Προγραμματισμός με την Python, John V. Guttag, Κλειδάριθμος, 2015.
- Βιβλίο [59357236]: Εισαγωγή στον Προγραμματισμό με την Python, Schneider David
- Βιβλίο [77119000]: Προγραμματισμός με την Python, Στράτος Καλαφατούδης, Γεώργιος Σταμούλης
- Βιβλίο [320152]: Εισαγωγή στον Προγραμματισμό με αρωγό τη γλώσσα Python [Ηλεκτρονικό Βιβλίο], Γεώργιος Μανής
- Βιβλίο [174838]: Python Scripting for Computational Science [electronic resource], Hans Petter Langtangen
- Βιβλίο [170352]: Beginning Python [electronic resource], Magnus Lie Hetland
- [Περιοδικό / Journal] Science of Computer Programming, ELSEVIER.
- [Περιοδικό / Journal] ACM Transactions on Programming Languages and Systems (TOPLAS)
Infinitesimal Calculus IV (MAY411)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAY411 |
Semester | 4 |
Course Title |
Infinitesimal Calculus IV |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 5, Credits: 7.5) |
Course Type |
General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
|
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Here, the acronym VFomV stands for Vector Function of multiple Variables.
Comprehension:
Applying:
Evaluating: Teaching undergraduate and graduate courses. |
---|---|
General Competences |
|
Syllabus
Definition of multiple integral using lower and upper sums over closed rectangles, set of zero volume, Lebesgue Criterion for Riemann Integrability, Jordan measurable sets and the definition of the integral over such sets, Fubini Theorem, Cavalieri Principle, elementary regions in two and three dimensional spaces, change of variables and their basic applications, evaluation of integrals using the aforementioned methods. Definition of integrals over paths for parametrizes functions an vector fields, definition of path length, parametrizes paths, parametrized transformations, gradient fields and path independent integrals, Green Theorem. Surfaces and parametrization of surface integrals. Definition of surface integral for real functions and for vector fields. Area of surface. Stokes and Gauss Theorems. Uniform convergence of function’s sequences and series. Fourier series.
Teaching and Learning Methods - Evaluation
Delivery |
| ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
| ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Language of evaluation: Greek and English.
The aforementioned information along with all the required details are available through the course’s website. The information is explained in detail at the beginning of the semester, as well as, throughout the semester, during the lectures. Reminders are also posted at the beginning of the semester and throughout the semester, through the course’s website. Upon request, all the information is provided using email or social networks. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Metric Spaces and their Topology (MAY413)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAY413 |
Semester | 4 |
Course Title |
Metric Spaces and their Topology |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 5, Credits: 7.5) |
Course Type |
General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Topology is a powerful tool for research and expression in all branches of Mathematical Science. In the last few years, Topology has been increasingly used in the creation of mathematical models that serve research applied disciplines such as Economics, Meteorology, Insurance Mathematics, Epidemiology in Medicine, etc.
|
---|---|
General Competences |
|
Syllabus
Metric spaces, definition, examples, basic properties. Metrics in vector spaces induced by norms. Diameter of a set, distance of sets. Sequences in metric spaces, subsequences, convergence of sequences. Functions between metric spaces, continuous functions, characterization of continuity via sequences, uniform continuity of functions. Open balls, closed balls, interior, closed hull and boundary, accumulation points and derived set. The topology of a metric space, the concept of a topological space. Basic (or Cauchy) sequences, complete metric spaces. Principle of contraction (Banach's Fixed Point Theorem). Totally bounded metric spaces, compact spaces. Equivalent forms of compactness of metric spaces. Properties of compact spaces. Separable metric spaces. Connectedness in metric spaces, properties of connected sets, connected components.
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Use of ICT for presentation of essays and assignments | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Written examination at the end of the semester including theory and problems-exercises. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- K. W. Anderson and D. W. Hall, Sers, Sequences and Mappings, John Wiley and Sons, Inc. New York 1963.
- V. Arkhangel’skii and V.I. Ponomarev, Fundamentals of General topology, D. Reidel Publishing Company, 1983.
- G. Buskes and A. van Rooij, Topological Spaces, Springer-Verlag, New York, 1197.
- D. C. J. Burgess, Analytical Topology, D. Van Nostrand Co. Ltd., London, 1966.
- N. L. Carothers, Real Analysis, Cambridge University Press, 2000.
- E. Copson, Metric Spaces, Cambridge University Press, 1968.
- J. Diedonne, Foundations of Modern Analysis, Academic Press, New York, 1966.
- J. Dugudji, Topology, Allyn and Bacon Inc., Boston, 1978.
- W. Franz, General Topology, G. Harrap and Co. Ltd. London 1965.
- J. R. Giles, Introduction to the Analysis of Metric Spaces, Cambridge University Press, 1989.
- S.-T. Hu, Introduction to General Topology, Holden-Day Inc. San Francisco, 1966.
- T. Husain, Topology and Maps, Plenum Press, New York, 1977.
- K. D. Joshi, Introduction to General Topology, Wiley Eastern Limited, New Delhi, 1986.
- Ι. Kaplansky, Set Theory and Metric Spaces, Allyn and Bacon Inc., Boston, 1975.
- R. L. Kasriel, Undergraduate Topology, W. B. Saunders Co. Philadelphia, 1971.
- J. L. Kelley, General Topology, D. Van Nostrand Co. Inc., Toronto 1965.
- S. Lipschutz, Theory and Problems of General Topology, Schaum’s Outline Series, New York, 1965.
- Mwndelson, Introduction to Topology, Prentice-Hall Inc. New Jersey, 1975.
- M. G. Murdeshuar, General Topology, Wiley Eastern Limited, New Delhi, 1986.
- M. H. A. Newman, Elements of the Topology of Plane Sets of Points, Cambridge University Press, 1964.
- Α. W. Schurle, Topics in Topology, North Holland, New York, 1979.
- Β. Στάϊκος, Μαθήματα Μαθηματικής Αναλύσεως Μέρος Ι και Μέρος ΙΙ, Ιωάννινα, 1981.
Algebraic Structures I (MAY422)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAY422 |
Semester | 4 |
Course Title |
Algebraic Structures I |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 5, Credits: 7.5) |
Course Type |
General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek, English |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course aims to introduce the students to the study algebraic properties of sets which are equipped with one or more (binary) operations. Such mathematical objects are called algebraic structures. We will mainly deal with two types of algebraic structures:
We will formulate various theorems concerning the structure and basic properties of groups and rings emphasizing the concept of isomorphism of groups or rings. From the perspective of Algebra two algebraic structures which are isomorphic, they have exactly the same algebraic properties. As a direct consequence, results concerning an algebraic structure are valid in any isomorphic algebraic structure. In the course we present several examples illuminating various notions of symmetry. It should be noted that the notion of symmetry is the central theme which underlies the concept of group/ring.
|
---|---|
General Competences |
The course aims to enable the undergraduate student to acquire the ability to analyse and synthesize basic knowledge of the theory of algebraic structures, in particular of the general theory of Groups and Rings, which form an important part of modern algebra. The contact of the undergraduate student with the ideas and concepts of the theory of groups and rings, (a) promotes the creative, analytical and deductive thinking and the ability to work independently, (b) improves his critical thinking and his ability to apply abstract knowledge in various field. |
Syllabus
- Preliminaries: Sets, functions, equivalence relations, partitions, (binary) operations.
- Groups – Permutation groups.
- Cyclic groups – generators.
- Cosets with respect to a subgroup – Lagrange’s Theorem.
- Homomorphisms of groups – Quotient groups.
- Rings and fields - Integral domains.
- The theorems of Fermat and Euler.
- Polynomial rings – Homomorphisms of Rings.
- Quotient rings – Prime and maximal ideals.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face to face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Teaching Material: Teaching material in electronic form available at the home page of the course.
| ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students, in English) which includes analysis of theoretical topics and resolving application problems. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Introduction to Statistics (MAY431)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ431 |
Semester | 4 |
Course Title |
Introduction to Statistics |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 4, Credits: 7.5) |
Course Type |
General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English, reading Course) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
At the end of the course student should be able to:
|
---|---|
General Competences |
|
Syllabus
Descriptive Statistics. Population, Samples & Random Samples. Frequencies, Histograms & Frequencies Statistics. Statistics & Sampling Distributions. χ2, t & F Distributions. Sampling from Normal Populations. Statistical Inference: Parameter Estimation & Tests of Hypotheses. Simple Linear Regression. One-Way & Two-Way Analysis of Variance.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English). |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Mendenhall, W., Scheaffer, R. L. and Wackerly, D. D.(1981). Mathematical Statistics with Applications. 2d ed. ISBN: 0-534-98019-8. Duxbury Press. Boston
Introduction to Ordinary Differential Equations (MAY514)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΥ514 |
Semester | 5 |
Course Title |
Introduction to Ordinary Differential Equations |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 5, Credits: 7.5) |
Course Type |
General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Bloom's Taxonomy. (1) Remembering: The notion of linear and non-linear ODE. The notion of existence of solutions and uniqueness of solutions for a linear and non-linear ODE. The notion of stability for a linear ODE, for a system of linear ODE's and for a vector linear ODE. (2) Comprehension: Study the existence and uniqueness of solutions of a ODE. Methods for finding the formula of the general solution of an linear ODE and studying their stability. Study systems of linear ODE's. (3) Applying: Study related real world problems. (4) Evaluating: Teaching secondary school courses. |
---|---|
General Competences |
Working independently and in groups. Production of free, creative and inductive thinking. Creative, analytic and synthetic thinking. |
Syllabus
Section 1. Introduction: Study specific, not necessarily linear, ODE's (Indicatively first order linear, Bernoulli, Riccati), Existence and uniqueness of solutions for first order, not necessarily linear, ODE's (Indicatively Peano Theorem).
Section 2. Study linear ODE's: Methods of calculating formulas of solutions (Method of undetermined coefficients, method of variation of parameters, power series solutions, Laplace transformation), Phase plane, Stability, Transforming a system of ODE's to a vector ODE.
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face (Lectures) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
The platform “e-course” of the University of Ioannina | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Written Final Examination (Theory and Exercises) 100% |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Χ. Φίλος, Μία Εισαγωγή στις Διαφορικές Εξισώσεις
- R. Agarwal, D. O’Regan, H. Agarwal, Introductory Lectures on Ordinary Differential Equations
- F. Ayres, Differential Equations
Elementary Differential Geometry (MAY522)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAY522 |
Semester | 5 |
Course Title |
Elementary differential geometry |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 5, Credits: 7.5) |
Course Type |
General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
It is an introductory course on differential geometry. The aim is to introduce and study geometric properties of regular curves (both plane and space) and regular surfaces. Fundamental notions of differential geometry of curves and surfaces are introduced and studied. Among them is the notion of curvature. The study requires tools from Linear Algebra and Calculus of several variables.
|
---|---|
General Competences |
|
Syllabus
- Plane curves, arclength, curvature, Frenet frame.
- Space curves, curvature and torsion, Frenet frame, fundamental theorem of curves.
- Surfaces, parametrization, Gauss map, Weingarten map, first and second fundamental form, normal curvature, principal and asymptotic directions, Gaussian and mean curvature, minimal surfaces, Theorema Egregium, Gauss and Weingarten formulas, fundamental theorem of surfaces, developable surfaces.
Teaching and Learning Methods - Evaluation
Delivery |
Direct | ||||||||
---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||
Teaching Methods |
| ||||||||
Student Performance Evaluation |
Written final examination |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Barrett O' Neil, Στοιχειώδης Διαφορική Γεωμετρία, Πανεπιστημιακές Εκδόσεις Κρήτης, 2002
- Manfredo do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976
Complex Functions I (MAY611)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAΥ611 |
Semester | 6 |
Course Title |
Complex Functions I |
Independent Teaching Activities |
Presentations, exercises, lectures (Weekly Teaching Hours: 5, Credits: 7.5) |
Course Type |
General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
It is the most basic introductory course of Mathematical Analysis of the complex space. The student begins to understand the notion of complex numbers and their properties. He/she learns about the use of the complex numbers field in solving some real numbers problems. The student learns about the elementary complex functions and then he/she learns about the line integral as well as the complex integral of such functions. Especially, the advantage of such integrals and their important properties are emphasized. Finally, the student learns the use of complex integrals in computing improper integrals of real functions. |
---|---|
General Competences |
|
Syllabus
The complex plane, Roots, Lines, Topology, Convergence, Riemann sphere, analytic properties of complex functions, Power series, elementary functions (rational, exp, log, trigonometric functions, hyperbolic, functions), line integrals, curves, conformal mappings, homotopic curves, local properties of complex functions, basic theorems, rotation index, General results, singularities, Laurent series, Residuum, Cauchy Theorem, Applications.
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Use of ICT for the presentation and communication for submission of the exercises | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Greek. Written exam (100%) on the theory and solving problems. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Γιαννούλης, Ι. (2024). Μιγαδική Ανάλυση [Προπτυχιακό εγχειρίδιο]. Κάλλιπος, Ανοικτές Ακαδημαϊκές Εκδόσεις. http://dx.doi.org/10.57713/kallipos-408
- R. Remmert. Theory of Complex Functions. Springer, 1998.
- S. Lang. Complex Analysis. Fourth Edition. Springer, 1999.
Classical Mechanics (MAY648)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE648 |
Semester | 6 |
Course Title |
Classical Mechanics |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 4, Credits: 7.5) |
Course Type |
General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course provides an introduction to theoretical physics, and aims to broaden the knowledge of Mechanics already gained even in secondary education, with the basic criterion being the mathematical formalism of physical problems. Therefore, the course introduces the basic concepts of Classical Mechanics and their application to particles, particle systems and continuous media.
|
---|---|
General Competences |
|
Syllabus
Review and connection via physical concepts with the basic tools: areas, mass and density, inertia, center of mass and moments. Review of basic types of differential equations and basic concepts of mechanics (space, time and material point). Newton's axioms and the notion of power. Linear motion, energy and angular momentum. Central forces, many-body systems. Lagrangian and Hamiltonian mechanics.
Teaching and Learning Methods - Evaluation
Delivery |
Face to face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Yes | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final exam |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Κ. Τσίγκανος, Εισαγωγή στη Θεωρητική Μηχανική, Εκδόσεις Σταμούλη, 2004.
Elective Courses
History of Mathematics (MAE501)
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE501 |
Semester | 5 |
Course Title |
History of Mathematics |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
No |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The aim of the course is the Introduction to the History of Mathematics. The course is about the history of Mathematical concepts that are covered in the curriculum of the Elementary school, High school and the first years of the University. There will be also presenations on topics that relate the development of Mathematics with the historical development of other Sciences. |
---|---|
General Competences |
|
Syllabus
- Mathematics in Antiquity.
- Mathematics in Ancient Greece.
- Hellenistic Mathematics.
- Mathematics from 150 BC to the Renaissance in different civilizations.
- Topics on the History of Contemporary Mathematics.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
| ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Language of evaluation: Greek
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Teaching of Mathematics (MAE503) (also MAE602)
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE503 (also MAE602) |
Semester |
5 (also 6) |
Course Title |
Teaching of Mathematics |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students | - |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes | - |
---|---|
General Competences |
|
Syllabus
Education and its scopes. Elements of the History of Mathematics and evolution of Mathematics Education. Genaral scopes of Mathematics Education. Philosophy and learning of Mathematics. Models and methods in the teaching of Mathematics. The teaching of mathematical notions: analysis, algebra, geometry. Planning, preparation, presentation, evaluation. Teaching outcomes: conclusions and aspects. The structure of Mathematics Education in the secondary level. Mathematical journals and competitions.
Teaching and Learning Methods - Evaluation
Delivery |
Face to face | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||||||
Teaching Methods |
| ||||||||||||||
Student Performance Evaluation |
Public presentation, written work, essay/report, semester examination. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ΜΠΑΜΠΗΣ ΤΟΥΜΑΣΗΣ, Σύγχρονη Διδακτική των Μαθηματικών, Gutenberg, Αθήνα1999
- ΑΘΑΝΑΣΙΟΣ ΓΑΓΑΤΣΗΣ, Θέματα Διδακτικής των Μαθηματικών, Εκδόσεις Κυριακίδη, Θεσσαλονίκη 1993
- MORRIS KLEIN, Γιατί δεν μπορεί να κάνει πρόσθεση ο Γιάννης, Εκδόσεις Βάνιας, Θεσσαλονίκη 1993
- G. POLYA, How to solve it?, Princeton University Press, 1999
- PIERRE VAN HIELE, Structure and Insight: A Theory of Mathematics Education, Academic Press, 1986
- SUE JOHNSTON-WILDER, PETER JOHNSTON-WILDER, DAVID PIMM, CLARE LEE, Learning to Teach Mathematics in the Secondary School, 3 rd Edition, Routledge, 2011 (also MAE602)
Elements of General Topology (MAE513)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE513 |
Semester |
5 |
Course Title |
Elements of General Topology |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The aim of the course is to introduce the student to basic notions of General Topology and, in some way, to generalize already obtained knowledge on metric spaces. It is an optional course for students interested in having a background on pure mathematics. It is also attempted to broaden students horizon to mathematical structures which, even if they seem abstract, they have important applications in several branches of science. |
---|---|
General Competences |
|
Syllabus
The notion of Topology. Topologies from metrics and non-metrizable topologies. Bases and subbases. Fundamental notions (open sets, closed sets, closure, interior, boundary, accumulation points). Neighborhood bases and systems. Convergence of sequences in topological spaces. Nets and convergence of nets. Continuity. Topologies from sequence of functions, product spaces. Spaces of 1 and 2 countability. Separation (T1, T2, T3, T4 spaces). Compactness of topological spaces.
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Use of special software (tex, mathematica, e.t.c.) for presentation of projects and exercises. | ||||||||||||
Teaching Methods |
| ||||||||||||
Student Performance Evaluation |
Greek or English
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- J. L. Kelley, General Topology, D. Van Nostrand Co. Inc., Toronto 1965
- J. Dugudji, Topology, Allyn and Bacon Inc., Boston 1978
- K. D. Joshi, Introduction to General Topology, Wiley Eastern Limited, New Delhi, 1986
Topics in Functions of One Variable (MAE515)
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ515 |
Semester |
5 |
Course Title |
Topics in Functions of One Variable |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The plan of the course is the achievement by the undergraduate student of special theoretical background in the theory of real functions. |
---|---|
General Competences |
The objective of the course is the undergraduate student's ability achievement in analysis and synthesis of the basic background in the theory of real functions. |
Syllabus
Monotone functions - points of continuity, functions of bounded variation, sets of measure zero, Lebesgue's theorem (every monotone function is differentiable almost everywhere), Darboux continuous functions-definitions, properties, equivalent characterizations, convex functions, semicontinuous functions, continuity points of Riemann integrable functions, Baire classes, Borel measurable functions, analytic sets-characterizations, connections with Borel sets-related theory, Lebesgue integral, Stieltjes integral.
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Written examination at the end of the semester. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- A.C.M. Van Rooij, W.H. Schikhof, Α second course on real functions, Cambridge University Press.
Group Theory (MAE525)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE525 |
Semester |
5 |
Course Title |
Group Theory |
Independent Teaching Activities | Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special background, skills development. |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek, English |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Familiarity with: group, abelian group, subgroup, normal subgroup, quotient group, direct product of groups, homomorphism, isomorphism, kernel of a homomorphism. Apply group theory to describe symmetry, describe the elements of symmetry group of the regular n-gon (the dihedral group D2n). Compute with the symmetric group. Know how to show that a subset of a group is a subgroup or a normal subgroup. State and apply Lagrange's theorem. State and prove the isomorphism theorems. Sylow theorems. The classification of finite abelian groups. Normal series, central series, nilpotent groups. Applications in Geometry. |
---|---|
General Competences |
|
Syllabus
- Basic properties in groups.
- Symmetries.
- Subgroups, Direct products, Cosets.
- Symmetric groups.
- Normal Subgroups, Quotient groups.
- Homomorphisms.
- Semidirect product.
- Classification of finite abelian groups.
- Sylow theorems.
- Normal series, Solvable groups. Central series, Nilpotent groups.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Communication with students | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Written Examination, Oral Presentation, written assignments in Greek (in case of Erasmus students in English) which includes resolving application problems. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- An Introduction to the Theory of Groups (Graduate Texts in Mathematics) 4th Edition by Joseph Rotman.
Groebner Bases (MAE526)
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE526 |
Semester |
5 |
Course Title |
Groebner Bases |
Independent Teaching Activities |
Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
YES |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The students will acquire with the successful completion of the course
|
---|---|
General Competences |
The course aim is for the student to acquire the ability in analysis and synthesis of knowledge in Computational Algebra and produces free, creative and inductive thinking. |
Syllabus
Polynomial rings. Hilbert;s basis Theorem. Noetherian rings. Monomial οrders. Division Alghorithm. Groebner bases. S-polynomials and Buchberger;s alghorithm. Irreducible and universal Groebner bases. Nullstellensatz Theorem. Applications of Groebner: bases in elimination, Algebraic Geometry, field extensions, Graph Theory and Integer Programming.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Geometry of Transformations (MAE527)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE527 |
Semester |
5 |
Course Title |
Geometry of Transformations |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses |
Linear Algebra, Analytic Geometry |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course can be viewed as a continuation of Analytic Geometry. The aim is to study geometric transformations of the plane or space. The classification of isometries is provided. Further applications are given, as well the classification of second degree surfaces. Moreover, algebraic curves are studied. Upon completion of the course, the student should be familiar with notions of geometry and geometric transformations that are used in other courses like Calculus of several variables. |
---|---|
General Competences |
|
Syllabus
Geometric transformations of the plane and space. Isometries, applications. Classification of second degree surfaces. Algebraic curves.
Teaching and Learning Methods - Evaluation
Delivery |
Direct | ||||||||
---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||
Teaching Methods |
| ||||||||
Student Performance Evaluation |
Written final examination. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Thomas F. Banchoff και John Wermer, Η Γραμμική Άλγεβρα μέσω Γεωμετρίας, Εκδόσεις Leader Books, Σειρά Πανεπιστημιακά Μαθηματικά Κείμενα, Αθήνα, 2009
Theory of Probability and Statistics (MAE531)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ531 |
Semester |
5 |
Course Title |
Theory of Probability and Statistics |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English, reading Course) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Extension and generalization of concepts taught in MAF331 and MAF43# Creation of a suitable base for deepening the scope of Statistical Science. At the end of the course the student should be able to:
|
---|---|
General Competences |
|
Syllabus
Random vectors-Multivariate distribution function-Joint probability- Joint probability density function. Marginal distributions. Conditional distributions. Special bivariate and multivariate distributions (multinomial, bivariate and multivariate normal etc). Expectation, Variance-Covariance matrix. Moments and Moment generating function of random vector. Distribution of a function of random variables. Order Statistics. Convergence of random variables. Sampling distributions.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English). |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Mood, A. M., Graybill, F. A. and Boes, D. C. (1974). Introduction to the Theory of Statistics. 3d ed. ISBN-13 978007085465# McGraw-Hill. New York.
Stochastic Processes (MAE532)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ532 |
Semester |
5 |
Course Title |
Stochastic Processes |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English, reading Course) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The term "stochastic" is used to describe phenomena in which some randomness inherent. A stochastic process is a probabilistic model that describes the behaviour of a system that randomly evolves over time. Observing the system at discrete points in time (for instance at the end of each day or at the end of a time period, etc.) one gets a discrete time stochastic process. Observing the system continuously through time one gets a continuous time stochastic process. Objectives of the course are:
The student should be able to understand the meaning of the stochastic process, use the Markov processes for modelling systems and become familiar with their application, and be able to make various calculations and appropriate conclusions when the stochastic process describes a specific applied problem. |
---|---|
General Competences |
|
Syllabus
Random Walk: Simple random walk, absorbing barriers, reflecting barriers. Markov Chains: General definitions, classification of states, limit theorems, irreducible chains. Markov Processes: The birth-death process. Applications.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | -
Use of ICT in communication with students | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which concentrates on the solution of problems which are motivated by the main themes of the course. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- R. Dobrow. Introduction to Stochastic Processes with R, Wiley, 2016.
- R. Durret. Essentials of Stochastic Processes, Springer, 3rd edition, 2016.
- V.G. Kulkarni. Modeling and Analysis of Stochastic Systems, 3rd edition, CRC Press, London 2017.
- N. Privault. Understanding Markov Chains [electronic resource] HEAL-Link Springer ebooks, 2013 (Κωδικός Εύδοξου: 73260010).
- M. Pinksy, S. Karlin. An introduction to stochastic modelling, 4th edition, Academic Press, 2011.
- S. Ross. Introduction to probability models, Academic Press, New York, 2014.
- [Περιοδικό / Journal] Stochastic Processes and their Applications (Elsevier)
- [Περιοδικό / Journal] Stochastics (Taylor - Francis)
- [Περιοδικό / Journal] Journal of Applied Probability (Cambridge University Press)
Introduction to Computational Complexity (MAE542)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE542 |
Semester |
5 |
Course Title |
Introduction to Computational Complexity |
Independent Teaching Activities |
Lectures, exercises, tutorials (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
This course aims at introducing to students the concepts of time and space complexities for solving difficult problems. After successfully passing this course the students will be able to:
|
---|---|
General Competences |
|
Syllabus
- ΝΡ and Computational Intractibility
- The class of PSPACE
- Extending the limits of tractability
- Approximation Algorithms
- Local search.
- Randomized algorithms
Teaching and Learning Methods - Evaluation
Delivery |
Lectures | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Use of projector and interactive board during lectures. | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Computational Complexity, Christos Papadimitriou.
- Computers and Intractability, M. R. Garey and D. S. Johnson.
- J. Kleinberg and E. Tardos, Σχεδιασμός Αλγορίθμων, ελληνική έκδοση, Εκδόσεις Κλειδάριθμος, 2008
- T. Cormen, C. Leiserson, R. Rivest, and C. Stein, Εισαγωγή στους Αλγορίθμους, ελληνική έκδοση, Πανεπιστημιακές Εκδόσεις Κρήτης, 2012.
Applied Tensor Analysis (MAE543)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ543 |
Semester |
5 |
Course Title |
Applied Tensor Analysis |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course is an introduction to the concepts of Tensor Analysis. The objectives of the course are:
|
---|---|
General Competences |
The course aims to enable the undergraduate students to develop basic knowledge of Applied Tensor Analysis and in general of Applied Mathematics. The student will be able to cope with problems of Applied Mathematics giving the opportunity to work in an international multidisciplinary environment. |
Syllabus
The tensor concept, Invariance of tensor equations, Curvilinear coordinates, Tensors in generalized curvilinear coordinates, Gauss, Green and Stokes theorems, Scalar and vector fields, Nabla operator and differential operators, Covariant differentiation, Integral theorems, Applications to Fluid Dynamics.
Teaching and Learning Methods - Evaluation
Delivery |
In class | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- A. I. Borisenko and I. E. Taparov, Vector and Tensor Analysis, Edition: 2/2017, Editor: G. C. FOYNTAS (in Greek).
- H. Lass, Vector and Tensor Analysis, Edition: 2/2017, Editor: G. C. FOYNTAS (in Greek).
Logic Programming (MAE544)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE544 |
Semester |
5 |
Course Title |
Logic Programming |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The goal of this course is the deeper understanding of PROLOG. During the course a detailed examination of the following topics are done:
After completing the course the student can handle:
|
---|---|
General Competences |
|
Syllabus
- Introductory concepts of Automata , Computability and Complexity as well as basic definitions, basic theorems and inductive proofs
- Finite State Machines and Languages, Finite Automata (Deterministic FA, Nondeterministic FA, FA with Epsilon-Transitions) and their applications, Regular Expressions and Languages, derivation trees. Removing Nondeterminism . Equivalence NFA and NFA with ε-moves. Minimization of DFA, Pumping Lemma
- FA and Grammars. Grammars of Chomsky Hierarchy. Regular Sets (RS). Properties of Regular Languages. RS and FA. Finding a correspondence Regular Expression of a FA. Abilities and disabilities of FA.
- Context-Free Grammars and Languages, Pushdown Automata (Deterministic PDA, Acceptance by Final State, Acceptance by Empty Stack) , Properties of Context-Free Languages. Correspondence PDA and Context-Free Languages.
- Introduction of Turing Machines. Standard TM, useful techniques for TM constructions. Modification of TM. TM as procedure.
- Unsolvability. The Church-Turing Thesis. The Universal TM. The Halting Problem for TM. Computational Complexity. NP-complete problems.
Teaching and Learning Methods - Evaluation
Delivery |
Face to face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Yes, Use of Natural Language and Mathematical Problems Processing Laboratory | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final test |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Π. Σταματόπουλος, "Λογικός και Συναρτησιακός Προγραμματισμός", Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών, http://hdl.handle.net/11419/3587 (με διορθωμένα παροράματα εδώ)
- Η. Σακελλαρίου, Ν. Βασιλειάδης, Π. Κεφαλάς, Δ. Σταμάτης, "Τεχνικές Λογικού Προγραμματισμού", Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών, http://hdl.handle.net/11419/777
- I. Bratko, "Prolog Programming for Artificial Intelligence", Third Edition, Addison-Wesley, 2000.
- L. Sterling, E. Shapiro, "The Art of Prolog", The MIT Press, 1994.
- J. W. Lloyd, "Foundations of Logic Programming", Springer Verlag, 1993
Biomathematics (MAE546A)
- Ελληνική Έκδοση
- Undergraduate Courses Outlines
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ546A |
Semester |
5 |
Course Title |
Biomathematics |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
This course is an introduction to the basic concepts of Biomathematics. Upon successful completion of the course, the student will be able to:
|
---|---|
General Competences |
The course aims to enable the student to analyze and synthesize basic knowledge of Biomathematics and Applied Mathematics.
|
Syllabus
- Short introduction of Algebra, Analysis and Differential Equations
- Differential equations of biofluids motion
- Applications of mathematical modeling of biofluids in the human body and in the arterial system
- Analytical and numerical techniques for solving the differential equations describing biofluids flows
- Algbraic statistics for Computational Biology: Algebraic varieties and Groebner bases, Toric ideals and varieties, Linear and toric models
- Markov bases, Markov bases for hierarchical models, Contigency tables, Phylogenetic Models.
Teaching and Learning Methods - Evaluation
Delivery |
In class | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
| ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Algebraic Statistics for Computational Biology, L. Pachter, B. Sturmfels, 2005, Editor: Cambridge University Press
- Cardiovascular Mathematics, Modeling and simulation of the circulatory system, Formaggia L., Quarteroni A., Veneziani A., 2009, Editor: Springer
Design and Analysis of Algorithms (MAE581)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE581 |
Semester |
5 |
Course Title |
Design and Analysis of Algorithms |
Independent Teaching Activities |
Lectures, laboratory exercises, tutorials, quiz (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
This course aims at introducing to students the philosophy of fundamental algorithmic background and techniques. After successfully passing this course the students will be able to:
|
---|---|
General Competences |
|
Syllabus
- Fundamental concepts of design and analysis of algorithms
- Analysis of algorithms, Asymptotical growing functions
- Typical running times and data structures (lists, arrays, queues, stacks)
- Stable matching, correctness, priority queue
- «Divide & Conquer» technique, sorting, recursive formulations
- Graph algorithms: BFS, DFS, connectedness, topological ordering
- Greedy algorithms: interval scheduling & shortest paths (Dijkstra)
- Minimum spanning trees(Prim & Kruskal algorithms), Huffman coding
- Dynamic programming: maximum flow, interval scheduling, and Knapsack
- Further Topics: computational complexity and ΝΡ-completeness.
Teaching and Learning Methods - Evaluation
Delivery |
Lectures | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
| ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written examination (70%)
Exercises (30%)
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Approximation Theory (MAE585)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ585 |
Semester |
5 |
Course Title |
Approximation Theory |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
After successful end of this course, students will be able to:
|
---|---|
General Competences |
|
Syllabus
Introduction to Approximation Theory in Spaces of Functions (Existence - Uniqueness). Polynomial Approximation of Functions: Weierstrass Theorem. Best Uniform Approximation. Least Squares Approximation. Hermite Polynomial Interpolation. Cubic Splines Polynomial Interpolation.
Teaching and Learning Methods - Evaluation
Delivery |
In the class | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Written examination |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- "Approximation Theory". Noutsos D., University of Ioannina.
Integral Equations (MAE613)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE613 |
Semester |
6 |
Course Title |
Integral Equations |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course aims to an introduction to the area of Integral Equations. Students are expected to obtain basic knowledge on standard types of integral equations, learn how to solve certain linear integral equations, also study existence and uniqueness of solutions by the use of fixed point theorems. |
---|---|
General Competences |
|
Syllabus
An introduction with historical notes. Classification of Integral Equations. Problems leading to integral equations. Laplace transformations and their use to solving integral equations. Other integral transformations. Volterra integral equations: Neumann series, successive approximations, Laplace transformation and the convolution kernel. Fredholm integral equations: Symmetric kernels, separated kernels, Fredholm Alternative, classical Fredholm theory. Green functions for second order boundary value problems. Existence and uniqueness of solutions: Banach spaces, contractions and applications to integral equations. Existence of solutions by Schauder's theorem.
Teaching and Learning Methods - Evaluation
Delivery |
Lectures. Presentations in class. | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Use of the platform “E-course” of the University of Ioannina | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Students choose evaluation by one or both of the following:
In case that a student participates to both, the final grade is the maximum of the two grades. Evaluation criteria and all steps of the evaluation procedure are accessible to students through the platform “E-course” of the University of Ioannina. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Σ. Ντούγια, Ολοκληρωτικές Εξισώσεις
- C. Corduneanu, Principles of Differential and Integral Equations
Ordinary Differential Equations I (MAE614)
- Ελληνική Έκδοση
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- Outline Modification (available only for faculty members)
- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE614 |
Semester |
6 |
Course Title |
Differential Equations I |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Language of Instruction (lectures): Greek
|
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Bloom's Taxonomy. (1) Remembering: The notion of fixed point, of maximum domain of solutions and of the stability of not necessarily linear ODE's. (2) Comprehension: Study fixed point theorems and Topological Degree Theory, with applications to not necessarily linear ODE's. Study the maximum domain of solutions of not necessarily linear ODE's. Linearization of ODE's. (3) Applying: Study related real world problems. (4) Evaluating: Teaching secondary school courses. |
---|---|
General Competences |
Working independently and in groups. Production of free, creative and inductive thinking. Creative, analytic and synthetic thinking. |
Syllabus
Study of not necessarily linear ODE's: Existence of solutions using fixed point theorems and topological degree theory (i.e. Brouwer degree), Maximum domain for solutions, Stability using the Lyapunov method, Linearization.
Teaching and Learning Methods - Evaluation
Delivery |
| ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
| ||||||||||||
Teaching Methods |
| ||||||||||||
Student Performance Evaluation |
Language of evaluation: Greek and English. Methods of evaluation:
In any case, all students can participate in written exams at the end of the semester, during the exams period. The aforementioned information along with all the required details are available through the course's website. The information is explained in detail at the beginning of the semester, as well as, throughout the semester, during the lectures. Reminders are also posted at the beginning of the semester and throughout the semester, through the course's website. Upon request, all the information is provided using email or social networks. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Topics in Real Analysis (MAE615)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE615 |
Semester |
6 |
Course Title |
Topics in Real Analysis |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The plan of the course is the achievement by the undergraduate student of the introductory background in the theory of metric spaces. |
---|---|
General Competences |
The objective of the course is the undergraduate student's ability achievement in analysis and synthesis of the basic background in Real Analysis. |
Syllabus
Baire spaces, the theorem of Cantor, characterization of complete metric spaces, compact metric spaces, Lebesgue's lemma, uniform continuous functions and extensions of them, completetion of a metric space and uniqueness up to isometry, oscillation of a function, continuity sets of a function which is the pointwise limit of a sequence of continuous functions, uniform convergence of a sequence of functions and related topics, Dini's theorem.
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Written examination at the end of the semester. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Charalambos D. Aliprantis, Owen Burkinshaw, Principles of Real Analysis, Academic Press.
Measure Theory (MAE616)
- Ελληνική Έκδοση
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- Outline Modification (available only for faculty members)
- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE616 |
Semester |
6 |
Course Title |
Measure Theory |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special background |
Prerequisite Courses |
None (from the typical point of view). In order to be able to follow this course, the knowledge from the following courses are required: Infinetisimal Calculus I, Introduction to Topology. |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (exams in English are provided for foreign students) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
After completing this course the students will
|
---|---|
General Competences |
The course promotes inductive and creative thinking and aims to provide the student with the theoretical background and skills to use measure theory and integration. |
Syllabus
Algebras, σ-algebras, measures, outer measures, Caratheodory's Theorem (concerning the construction of a measure from an outer measure). Lebesgue measure, definition and properties. Measurable functions. Lebesgue integral, Lebesgue's Monotone Convergernce Theorem, Lebesgue's Dominated Convergence Theorem. Comparison between Riemann integral and Lebesgue integral for functions defined on closed bounded integrals of the set of reals.
Teaching and Learning Methods - Evaluation
Delivery |
Teaching on the blackboard by the teacher. | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Communication with the teacher by electronic means (i.e. e-mail). | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Exams in the end of the semester (mandatory), potential intermediate exams (optional), assignments of exercises during the semester (optional). |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Measure Theory, Donald Cohn, Birkhauser.
Real Analysis (MAE617)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code | MAE617 |
Semester |
6 |
Course Title |
Real Analysis |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course aims in presenting topics concerning real valued functions defined on a metric space. Pointwise and uniform convergence of a sequence of functions are discussed as so as topics like Ascoli-Arzela theorem and Stone-Weirstrass theorem. Applications of the above are also given. |
---|---|
General Competences |
|
Syllabus
Function spaces on a metric space (X,d), pointwise and uniform convergence of sequence of functions, the space B(X) of real bounded functions on X-, the space C(X) of continuous functions on X – equicontinuous subsets of C(X), Ascoli-Arzela theorem and applications, Dini's theorem, Stone-Weierstrass theorem and applications, separable metric spaces, Lindelof's theorem on Euclidean spaces, the Cantor set, the Cantor function-applications.
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Use of ICT for the presentation and communication for submission of the exercises | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Written examination at the end of the semester. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Charalambos D. Aliprantis, Owen Burkinshaw, Principles of Real Analysis, Academic Press.
- Michael O Searcoid, Metric Spaces, Springer Undergraduate Mathematics Series.
Seminar in Analysis I (MAE618)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ618 |
Semester |
6 |
Course Title |
Seminar in Analysis I |
Independent Teaching Activities |
Lectures (Weekly Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | None. However it is desirable to have a strong knowledge of basic notions of differential equations. |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
No |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The report can be, but not required to be, original. Further details can be determined by the teaching professor. |
---|---|
General Competences |
Further details can be determined by the teaching professor. |
Syllabus
In depth study in a scientific subject related to mathematical analysis. Further details can be determined by the teaching professor.
Teaching and Learning Methods - Evaluation
Delivery |
Details will be determined by the teaching professor. Methods include presentations contacted by the students. | ||||||||
---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Details will be determined by the teaching professor. | ||||||||
Teaching Methods |
| ||||||||
Student Performance Evaluation |
Other means of evaluation can be determined by the teaching professor. |
Attached Bibliography
Bibliography is suggested by the teaching professor, depending on the subject under study.
Differentiable Manifolds (MAE622)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE622 |
Semester |
6 |
Course Title |
Differentiable Manifolds |
Independent Teaching Activities |
Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek, English |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
In this lecture, the fundamental concept of a differentiable manifold will be developed. In particular, this lecture is a basic prerequisite for the upcoming class of Riemannian geometry. After a quick review of basic facts from general topology we will introduce the notions of a smooth manifold, tangent bundle, vector field, submanifold, connection, geodesic curve, parallel transport and Riemannian metric. On the completion of this course we expect that the students fully understand these important concepts and the main theorems that will be presented in the lectures. |
---|---|
General Competences |
|
Syllabus
Review of basic facts from general topology, smooth manifolds, tangent bundle, vector fields, immersions and embeddings, Lie bracket, Frobenius' theorem, Whitney's embedding theorem, connections and parallel transport, Riemannian metrics.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Weekly exercises and homeworks, presentations, final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- M. do Carmo, Riemannian Geometry, Birkhaüser Boston, Inc., Boston, MA, 1992.
- V. Guillemin & A. Pollack, Differentiable Topology, Prentice-Hall, Inc, Englewood Cliffs, 1974.
- J. Lee, Introduction to Smooth Manifolds, Graduate Texts in Mathematics, 218, 2013.
- J. Milnor, Topology From the Differentiable Viewpoint, Princeton University Press, NJ, 1997.
- L. Tu, An Introduction to Manifolds, Universitext. Springer, New York, 2011.
- Δ. Κουτρουφιώτης, Διαφορική Γεωμετρία, Πανεπιστήμιο Ιωαννίνων, 1994.
Elementary Global Differential Geometry (MAE624)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE624 |
Semester |
6 |
Course Title |
Elementary Global Differential Geometry |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
It is an introductory course on global differential geometry. The aim is to study global geometric properties of regular plane curves and regular surfaces. The study requires tools from Linear Algebra, Calculus of several variables, Topology and elementary differential geometry. On completion of the course the student should be familiar with the interplay between local and global properties of curves and surfaces. |
---|---|
General Competences |
|
Syllabus
Convex curves, Hopf's Umlaufsatz, Four vertex theorem, isoperimetric inequality. Surfaces, vector fields, covariant derivative, parallel transport, geodesic curvature, geodesics, exponential map, surfaces of constant Gaussian curvature, Gauss Bonnet Theorem, Liebmann Theorem.
Teaching and Learning Methods - Evaluation
Delivery |
Direct | ||||||||
---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||
Teaching Methods |
| ||||||||
Student Performance Evaluation |
Written final examination |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Barrett O' Neil, Στοιχειώδης Διαφορική Γεωμετρία, Πανεπιστημιακές Εκδόσεις Κρήτης, 2002
- Manfredo do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976
Algebraic Curves (MAE627)
Rings, Modules and Applications (MAE628)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE628 |
Semester |
6 |
Course Title |
Rings, Modules and Applications |
Independent Teaching Activities |
Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The principal aim of the course is to introduce the students to the main tools and methods of the theory of modules and rings. At the end of the course we expect the student to have understood the definitions and basic theorems which are discussed in the course, to have understood how they are applied in discrete examples, to be able to apply the material in order to extract new elementary conclusions, and finally to perform some (no so obvious) calculations. |
---|---|
General Competences |
The contact of the undergraduate student with the ideas and concepts of the theory of modules and rings, (a) promotes the creative, analytical and deductive thinking and the ability to work independently, (b) improves his critical thinking and his ability to apply abstract knowledge in various field. |
Syllabus
- Elementary Ring Theory.
- Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains.
- Module Theory.
- Modules over polynomial rings.
- Finitely generated and free modules.
- Modules over Principal Ideal Domains.
- Decomposition Theorems.
- Applications to Linear Algebra and Abelian groups.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Μ. Μαλιάκας: «Εισαγωγή στη Μεταθετική Άλγεβρα», Εκδόσεις Σοφία.
- N. Jacobson: “Basic Algebra I”, Dover Publications (1985).
- S. Lang: «Άλγεβρα», Εκδόσεις Πολιτεία (2010).
Linear Programming (MAE631K)
- Ελληνική Έκδοση
- Undergraduate Courses Outlines
- Outline Modification (available only for faculty members)
- Department of Mathematics
- Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)
General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ631K |
Semester |
6 |
Course Title |
Linear Programming |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course learning outcomes are: the introduction of the students to linear programming formulation, the comprehension of the mathematical properties of linear programming problems, the understanding of the theory underlying the simplex algorithm, the understanding of the dual theory and its interpretation, the use of LINDO software package to solve linear programming problems. Upon successful completion of the course the student will be able to:
|
---|---|
General Competences |
|
Syllabus
- Linear programming problems formulation
- Graphical solution
- The Simplex Method
- The Big M method
- The Two-Phase Simplex Method
- Dual theory
- Sensitivity analysis
- Transportation problem
- Assignment problem
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Lindo Software, Email, class web | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
LANGUAGE OF EVALUATION: Greek
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Βασιλείου Β. και Τσαντας Ν., Εισαγωγή Στην Επιχειρησιακή Έρευνα, Εκδόσεις Ζητη 2000.
- Κολετσος Κ., Στογιαννης Δ. Επιχειρησιακή Έρευνα Θεωρία, Αλγόριθμοι Και Εφαρμογές, Εκδόσεις, Συμεών, 2021.
- Κουνιας Σ. και Φακινος Φ., Γραμμικός Προγραμματισμός, Εκδόσεις Ζητη, Θεσσαλονίκη 1999.
- Παπαρριζος Π., Γραμμικός Προγραμματισμός. Εκδόσεις Ζυγός, Θεσσαλονίκη 1999.
- Σισκος Γ., Γραμμικός Προγραμματισμός, Εκδόσεις Νέων Τεχνολογιών, Αθήνα 1998.
- Υψηλαντης Π. Μέθοδοι και Τεχνικές Λήψης Αποφάσεων, Εκδόσεις Προπομπός, 2015.
- Φακινου Δ. Και Οικονομου Α., Εισαγωγή Στην Επιχειρησιακή Έρευνα- Θεωρία Και Ασκήσεις, Αθήνα 2003.
- Βertsimas D. And J. N. Τsitsiklis Introduction to Linear Optimization, Athena Scientific, 1997.
- Κουνετάς, Κ., Χατζησταμούλου, Ν., 2015. Εισαγωγή Στην Επιχειρησιακή Έρευνα Και Στον Γραμμικό Προγραμματισμό. Λύσεις Προβλημάτων Με Το Πρόγραμμα R. [Ηλεκτρ. Βιβλ.] Αθήνα: Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών. Διαθέσιμο Στο: Http://Hdl.Handle.Net/11419/5699.
- Gass S. Linear Programming Methods and Applications, Mcgraw-Hill 1985.
- Hadley G. Linear Programming, Addison-Wesley Publishing Company, Inc, 1965.
- Hillier F. S. And G. J. Lieberman Introduction Operations Research. The Mcgraw-Hill Companies, 2001.
- RardinL. R. Βελτιστοποίηση στην Επιχειρησιακή Έρευνα, ΕκδοσειςΚλειδαριθμος, 2022.
- TahaH., Εισαγωγή Στην Επιχειρησιακή Έρευνα, 10η Έκδοση, Eκδόσεις Α. Τζιολα & YιοιA.E., 2017.
- Winston W. L., Operations Research (Applications And Algorithms). Duxbury Press (International Thomson Publishing) 1994.
- [Περιοδικό / Journal] Mathematical Programming Journal, Series A and Series B.
- [Περιοδικό / Journal] INFORMS Transactions on Education (ITE).
Statistical Inference (MAE633)
- Ελληνική Έκδοση
- Undergraduate Courses Outlines
- Outline Modification (available only for faculty members)
- Department of Mathematics
- Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)
General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ633 |
Semester |
6 |
Course Title |
Statistical Inference |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English, reading Course) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The aim of the course is to present and study techniques and methods of parametric statistical inference. In particular, the interest is mainly focused on the theoretical development of the field of parameter estimation (point and interval) and the development of the theory of statistical tests for testing statistical hypotheses. Moreover, this course aims to provide the necessary tools and methods which help students to be able to draw statistical conclusions on the basis of experimental data and by utilizing these methods. At the end of the course students will have acquired the theoretical background of the parametric statistical inference methodologies. |
---|---|
General Competences |
|
Syllabus
Point estimation: unbiased, sufficient and efficient estimators, unbiased estimators with minimum variance, the Cramer-Rao lower bound for the variance, Lehmann-Scheffe theory, asymptotic properties of estimators, methods of estimation (method of maximum likelihood and method of moments). Interval estimation. Confidence intervals. Testing Statistical Hypothesis: the Neyman- Pearson lemma, simple and composite hypotheses, uniformly most powerful tests, likelihood ratio tests. Large sample tests. Applications.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Use of ICT in communication with students | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which concentrates on the solution of problems which are motivated by the main themes of the course. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Casella, G. and Berger, R. (2002). Statistical Inference. 2 Edition. Duxbury Advanced Series.
- Hogg, R. V., McKean, J. W. and Craig, A. T. (2005). Introduction to Mathematical Statistics. Pearson Education, Inc.
- Mood, A., Graybill, F. and Boes, D. (1974). Introduction to the Theory of Statistics. McGrawHill.
- Roussas, G. (2003). An Introduction to Probability and Statistical Inference. Academic Press.
- Κουρούκλης, Σ. (2007). Στατιστική Ι. Πανεπιστήμιο Πατρών.
Queueing Theory (MAE634)
- Ελληνική Έκδοση
- Undergraduate Courses Outlines
- Outline Modification (available only for faculty members)
- Department of Mathematics
- Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)
General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE634 |
Semester |
6 |
Course Title |
Queueing Theory |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course learning outcomes are: the study and development models that describe and analyse the behaviour and performance of queueing systems and their applications for optimal decision making. Upon successful completion of the course the student will be able to:
|
---|---|
General Competences |
|
Syllabus
Introduction. Birth death process. Transforms. Markovian Queueing Systems (Μ/Μ/1/∞, Μ/Μ/m/k, Μ/Μ/m/m, Μ/Μ/∞/∞). Queue with group arrival, Queue with group services, M/G/1/∞. Applications for optimal decision making.
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | -
Software for the calculation of queueing systems performance measures, Email, class web | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
LANGUAGE OF EVALUATION: Greek
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Δ. Φακίνος. Ουρές Αναμονής. 2η Έκδοση, Εκδόσεις Συμμετρία, 2008 (Κωδ. Εύδοξου: 45392).
- Α. Οικονόμου. Θεωρία Ουρών Αναμονής [Προπτυχιακό εγχειρίδιο]. Κάλλιπος, Ανοικτές Ακαδημαϊκές Εκδόσεις, 2023. https://dx.doi.org/10.57713/kallipos-182(Κωδ. Εύδοξου: 121051698).
- Α. Σταφυλοπάτης, Γ. Σιόλας. Ανάλυση Επίδοσης Υπολογιστικών Συστημάτων [Προπτυχιακό εγχειρίδιο]. Κάλλιπος, Ανοικτές Ακαδημαϊκές Εκδόσεις, 2015.https://dx.doi.org/10.57713/kallipos-453(Κωδ. Εύδοξου: 59303597).
- I. Adan, J. Resing. Queueing Theory. Eindhoven. Notes available online https://www.win.tue.nl/jadan/queueing.pdf , 2001.
- J. Medhi. Stochastic Models in Queueing Theory, Academic Press, New York, 2003.
- P. Phuoc Tran-Gia, T. Hosfeld. Performance Modeling and Analysis of Communication Networks, 2017.
- [Περιοδικό / Journal] Queuing Systems (Springer)
- [Περιοδικό / Journal] Stochastic Models (Taylor - Francis)
- [Περιοδικό / Journal] European Journal of Operational Research (Elsevier)
Numerical Analysis (MAE642)
- Ελληνική Έκδοση
- Undergraduate Courses Outlines
- Outline Modification (available only for faculty members)
- Department of Mathematics
- Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)
General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ642 |
Semester |
6 |
Course Title |
Numerical Analysis |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
After successful end of this course, students will be able to:
|
---|---|
General Competences |
|
Syllabus
Sets of Orthogonal Polynomials: Legendre, Chebyshev. Numerical Integration: Newton-Cotes, Chebyshev, Gauss-Legendre, Gauss-Chebyshev. Numerical Solution of Equations: Newton's Method, Secant Method, Aitken-Steffensen Methods. Numerical Solution of Nonlinear Systems: Newton's Method.
Teaching and Learning Methods - Evaluation
Delivery |
In the class | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Written examination |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- "Introduction to Numerical Analysis". Akrivis G.D., Dougalis B.A, Crete University Press, 4th Edition, 2010.
Introduction to Symbolic Mathematics (MAE644)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE644 |
Semester |
6 |
Course Title |
Introduction to Symbolic Mathematics |
Independent Teaching Activities |
Lectures and laboratory exercises (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course is an introduction to symbolic mathematical computations (computer algebra) and programming using a language for processing symbolic mathematical expressions, such as Mathematica. The course examines basic concepts in symbolic algebraic computations and emphases is given on finding the solution of a problem in closed form (exact solution) as opposed to a numerical solution (approximate solution). Using a symbolic language the course examines tools / commands to solve problems from different areas of Mathematics (Calculus, Algebra, Geometry, Statistics, etc.) and how to graphically show the results of solving a problem. Also programming methods are examined which can be used for the solution of a problem in addition to using just ready commands. Much of the course is to present the possibilities and tools available in a programming language for symbolic processing of mathematical expressions. After completing the course the student:
|
---|---|
General Competences |
|
Syllabus
- Symbolic mathematical manipulation systems
- Introduction to Mathematica
- Representation of symbolic mathematical expressions
- Numerical computations
- Symbolic computations
- Symbolic manipulation of mathematical expressions
- Basic functions of Mathematica
- Lists
- Patterns and transformation rules
- Input / Output and Files
- Functions
- Structures for program flow control (assignment, selection, loops, etc)
- Programming with Mathematica
- Graphics
- Factorization
- Solving equations and systems
- Differentiation
- Integration
- Series
- Linear algebra
- Basic algorithms in symbolic mathematics
Teaching and Learning Methods - Evaluation
Delivery |
Face to face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Yes | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Written final exam (70%) comprising:
Term project (teams) (30%)
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- SCHAUM'S MATHEMATICA, EUGENE DON, 2006, Publicer KLEIDARITHMOS (translation)
- Mathematics and programming with Mathematica, Karampetakis Nikolaos, Stamatakis Stylianos, Psomopoulos Evangelos, 2004, Publicer Ziti Pelagia & Co.
- Wolfram, S., The Mathematica Book, 5 Edition, Wolfram Media.
- Abell, M., Braselton, J., Mathematica by Example, 2d Edition, Academic Press, 1997.
- Gaylord, R., Kamin, S., Wellin, P., An Introduction to Programming with Mathematica, 2d Edition, Telos Springer-Verlag, 1996.
- Gray, J., Mastering Mathematica - Programming Methods and Applications, 2d Edition, Academic Press, 1998.
- http://www.wolfram.com/
- http://library.wolfram.com/
Techniques of Mathematical Modelling (MAE646)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE646 |
Semester |
6 |
Course Title |
Techniques of Mathematical Modelling |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course is a first introduction to the basic methods of applied mathematics and particularly in perturbation theory. There are many situations in mathematics where one finds expressions that cannot be calculated with absolute precision, or where exact answers are too complicated to provide useful information. In many of these cases, it is possible to find a relatively simple expression which, in practice, is just as good as the complete, exact solution. The asymptotic analysis deals with methods for finding such approximations and has a wide range of applications, both in the fields of pure mathematics such as combinatorics, probability, number theory and applied mathematics and computer science, for example, the analysis of runtime algorithms. The goal of this course is to introduce some of the basic techniques and to apply these methods to a variety of problems. Upon completion of this course students will be able to:
|
---|---|
General Competences |
|
Syllabus
Introduction and notation of perturbation theory. Regular and singular perturbations. Asymptotic expansions of integrals. Asymptotic solutions of linear and nonlinear differential equations. Laplace and Fourier transforms (if time permits).
Teaching and Learning Methods - Evaluation
Delivery |
Face to face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Yes | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- C. M. Bender, S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory, Springer, 1999.
- E. J. Hinch, Perturbation Methods, Cambridge University Press, 1991.
- A. H. Nayfeh, Perturbation Methods, Wiley-Interscience, 1973.
Object Oriented Programming (MAE647)
- Ελληνική Έκδοση
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- Outline Modification (available only for faculty members)
- Department of Mathematics
- Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)
General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE647 |
Semester |
6 |
Course Title |
Object Oriented Programming |
Independent Teaching Activities |
Lectures, laboratory exercises, tutorials, quiz (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
This course aims at introducing to students basic concepts and techniques related to object oriented programming. Introduction to object oriented programming, the notions of classes and objects in programming, Abstraction, Encapsulation, Modularity, Hierarchy. After successfully passing this course the students will be able to:
|
---|---|
General Competences |
|
Syllabus
- Introduction to object oriented programming
- Classes and objects in programming
- Properties and methods
- Simple and multiple inheritance
- Abstraction
- Encapsulation
- Modularity
- Hierarchy and Composition
Teaching and Learning Methods - Evaluation
Delivery |
Lectures | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
| ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Software Engineering - Theory & Practice, S. L. Pfleeger, ISBN 978-960-461-477-6
- Software Engineering, I. Sommerville, ISBN 978-960-461-220-8
- Βασικές Αρχές Γλωσσών Προγραμματισμού, Ellis Horowitz, Εκδόσεις Κλειδάριθμος
ICT in Education (MAE649)
- Ελληνική Έκδοση
- Undergraduate Courses Outlines
- Outline Modification (available only for faculty members)
- Department of Mathematics
- Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)
General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE649 |
Semester |
6 |
Course Title |
ICT in education |
Independent Teaching Activities |
Lectures, laboratory exercises, tutorials, quiz (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes | - |
---|---|
General Competences |
|
Syllabus
ICT as a teaching and learning tool. Basic concepts and didactic tools of Informatics, Internet and educational applications (HTML, JavaScript), Learning Management Systems and tools (LMS, OBS studio-Twitch TV, Jitsi, Zoom), interactive educational technologies (MIT scratch), Multimedia applications programming for educational purposes (Adobe Flash), computational educational tools, educational tools for Mathematics (Geogebra, MathML, Maxima), mobile, IoT and werable educational technologies (BLE, Wi-Fi, Beacons, NFC, touchpad, Android studio, tinkercad, circuits simulator-3D printing), mathematical word processing tools (LateX), image and video processing tools (Gimp, Audacity, SynFig Studio, Blender, Tupitube), programming of mobile educational, tactile, remote surveillance and feedback applications using Blynk.
Teaching and Learning Methods - Evaluation
Delivery |
Lectures | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Data Structures (MAE681)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE681 |
Semester |
6 |
Course Title |
Data Structures |
Independent Teaching Activities |
Lectures and laboratory exercises (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course is an introduction to basic data structures such as strings, arrays, lists, stacks, queues, trees, graphs. It studies properties and implementation issues as well as basic properties on the data structures and their complexity. It also examines basic applications of the above data structures. The main purpose is the design and use of appropriate data structures for storing and retrieving the data of a problem in order for a most efficient processing during the problem solving process. After completing the course the student:
|
---|---|
General Competences |
|
Syllabus
- Elements Of Analysis Of Algorithms
- Abstract Data Types
- Strings
- Arrays
- Algorithms for Searching, Sorting, Selection
- Lists (Single Linked Lists, Doubly Linked Lists, Circular Lists, Generalised Lists)
- Stacks
- Queues, DeQueues, Priority Queues
- Trees (General Trees, Binary Trees, Binary Search Trees, Threaded Trees)
- Heaps
- AVL-Trees, 2-3 Trees, 2-3-4 Trees, B Trees
- Directed Graphs, Undirected Graphs
- Set Manipulation
- Hashing
- Dynamic Memory Management
Teaching and Learning Methods - Evaluation
Delivery |
Face to face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Yes | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Written final exam (70%) comprised of:
Laboratory exercises / midterm (30%) |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Data structures, algorithms and applications using c ++, Sahnii Sartaj, Publicer A. Tziola (Greek translation)
- Algorithms in C ++, parts 1-4: fundamental concepts, data structures, sorting, searching, Robert Sedgewick, Prentice Hall (Greek translation)
- Algorithms in C, parts 1-4: fundamental concepts, data structures, sorting, searching, Robert Sedgewick, Prentice Hall (Greek translation)
- Data Structures with C, Nicholas Misirlis (Greek)
- Data Structures, Bozanis Panagiotis, Publicer A. Tziola (Greek)
- Michael T. Goodrich, Roberto Tamassia, and David M. Mount, Data Structures and Algorithms in C ++, John Wiley & Sons
- Michael Goodrich, Roberto Tamassia, Data Structures and Algorithms in Java, Publicer DIAYLOS
- Cormen, Leiserson and Rivest, Introduction to Algorithms, MIT Press, 1990. (there is also a translation from the University of Crete)
- Mark Allen Weiss, Data Structures & Algorithm Analysis in Java, Addison-Wesley
- Clifford A. Shaffer, Data Structures and Algorithm Analysis, ebook, http://people.cs.vt.edu/shaffer/Book/
- http://opendatastructures.org/
Numerical Linear Algebra (MAE685)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ685 |
Semester |
6 |
Course Title |
Numerical Linear Algebra |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Upon successful completion of this course, students will be able to:
|
---|---|
General Competences |
|
Syllabus
- Introduction to matrix theory. Singular Value Decomposition (SVD). Matrix condition number and conditioning of linear systems.
- The linear least squares problem, QR method, Householder transformations.
- Direct methods (LU Factorization, Cholesky Factorization).
- Iterative methods: Jacobi, Gauss-Seidel, SOR method, steepest descent method, conjugate gradient method.
- Computation of eigenvalues and eigenvectors.
- Applications (PageRank Google search algorithm, image processing, etc.)
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
| ||||||||||||
Teaching Methods |
| ||||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- “Αριθμητική Γραμμική Άλγεβρα”, Β. Δουγαλής, Δ. Νούτσος, & Α. Χατζηδήμος, Τυπογραφείο Πανεπιστημίου Ιωαννίνων.
- “Numerical Linear Algebra”, L. Trefethen, & D. Bau, SIAM, 1997.
- “Matrix Computations”, G. Golub, C. Van Loan, 3rd edition, Johns Hopkins Univ. Press 1996.
- “Iterative Methods for Sparse Linear Systems”, Y. Saad, PWS Publishing, 1996.
- “Linear Algebra and Learning from Data”, G. Strang, Wellesley-Cambridge Press, 2019.
- “Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control”, S. Brunton, & J. Kutz, Cambridge: Cambridge University Press, 2019. doi:10.1017/9781108380690.
Complex Functions II (MAE712)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ754 |
Semester |
7 |
Course Title |
Seminar in Analysis II |
Independent Teaching Activities |
Lectures (Weekly Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | None. However it is desirable to have a strong knowledge of basic notions of differential equations. |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
No |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The report can be, but not required to be, original. Further details can be determined by the teaching professor. |
---|---|
General Competences |
Further details can be determined by the teaching professor. |
Syllabus
In depth study in a scientific subject related to mathematical analysis. Further details can be determined by the teaching professor.
Teaching and Learning Methods - Evaluation
Delivery |
Details will be determined by the teaching professor. Methods include presentations contacted by the students. | ||||||||
---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Details will be determined by the teaching professor. | ||||||||
Teaching Methods |
| ||||||||
Student Performance Evaluation |
Other means of evaluation can be determined by the teaching professor. |
Attached Bibliography
Bibliography is suggested by the teaching professor, depending on the subject under study.
Partial Differential Equations (MAE713)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE713 |
Semester |
7 |
Course Title |
Partial Differential Equations |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek, English |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The aim of the course is an introduction to Partial Differential Equations. By this course the students become familiar with a broad area of Analysis that has many applications to other sciences. The course highlights the wealth of problems that arise and proposes methods to overcome them. These are presented exemplarily and aim to teach ways of transcending and generalizing known methods and solutions. The students learn to analyze methodically externally given problems, taking into account relevant informations and aims, and to try to apply knowledge from other areas of Pure Mathematics in order to solve these problems. Moreover, the students learn to interpret the obtained mathematical results. On the level of content, the students learn about, mainly linear, Partial Differential Equations of first and second order for functions of two variables with respect to both, their explicit solution and their qualitative behavior, and obtain an elementary overview of further problems. |
---|---|
General Competences |
|
Syllabus
- Overview of Partial Differential Equations (PDE) and Systems: classification with respect to their (non-)linearity, description of the arising problems and of the various kinds of solutions (classical and weak, general and with boundary values).
(In the following the focus is given on two independent variables.)
- First order PDE (linear, semi-linear, quasi-linear): geometric and algebraic observations concerning their qualitative behavior, initial value problems and method of characteristics, discussion of the Burgers equation, shock waves and weak solutions, Rankine-Hugoniot condition.
- Second order PDE: classification, characteristic directions and characteristic curves, wave equation on the line (homogeneous and inhomogeneous), separation of variables for the Laplace and heat equations, Poisson formula.
(Alternatively: instead of the discussion of the (non-linear) Burgers equation and of weak solutions an introduction to the Fourier transform may be given and the heat equation on the line may be discussed.)
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
The students may contact the lecturer by e-mail | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Δάσιος, Γ., Κυριάκη, Κ., & Βαφέας, Π. (2023). Μερικές Διαφορικές Εξισώσεις [Προπτυχιακό εγχειρίδιο]. Κάλλιπος, Ανοικτές Ακαδημαϊκές Εκδόσεις. http://dx.doi.org/10.57713/kallipos-317
- L. C. Evans. Partial Differential Equations. Second edition. AMS, 2010.
- G. B. Folland. Introduction to Partial Differential Equations. Princeton University Press, 1995.
Set Theory (MAE714)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE714 |
Semester |
7 |
Course Title |
Set Theory |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The plan of the course is an introduction to Axiomatic Set Theory. |
---|---|
General Competences |
|
Syllabus
The construction of the sets of numbers (Natural, Rational and Real numbers), Axioms for the Zermelo-Fraenkel theory, the Axiom of Choice, Zorn's Lemma, Well ordered sets, Ordinal and Cardinal Numbers and arithmetic of them.
Teaching and Learning Methods - Evaluation
Delivery |
Lectures\ Presentations in class | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Written examination at the end of the semester. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Derek Goldrei, Classical Set Theory
- Γ. Μοσχοβάκη, Θεωρία Συνόλων
- R. Vaught, Set Theory, An Introduction
- Paul Halmos, Naïve Set Theory
Ordinary Differential Equations II (MAE716)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE716 |
Semester |
7 |
Course Title |
Differential Equations I |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Language of Instruction (lectures): Greek
|
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Bloom's Taxonomy. (1) Remembering: The notion of functional differential equation, of integral equation, of integral-differential equation and of difference equation. The notion of solutions of such equations, of uniqueness of such solutions and of stability of such solutions. The notion of solutions of systems of difference equations. (2) Comprehension: Study of solutions of functional ODE's, of integral equations and of difference equations. Methods of finding such solutions and of studying their stability. Study of systems of such equations. (3) Applying: Study related real world problems. (4) Evaluating: Teaching secondary school courses. |
---|---|
General Competences |
Working independently and in groups. Production of free, creative and inductive thinking. Creative, analytic and synthetic thinking. |
Syllabus
Section 1. Functional differential equations: Reasons of existence of such equations, Existence and uniqueness of their solutions, Finding solutions, Stability, Linear and non-linear systems. Section 2. Integral equations: Reasons of existence of such equations, Fredholm equations, Volterra equations, Integral-difference equations, Abel problem, Non-linear integral equations. Section 3. Difference equations: Reasons of existence of such equations, Finding the formula of solutions for linear difference equations, Linearization, Systems of difference equations, Stability using the Lyapunov method.
Teaching and Learning Methods - Evaluation
Delivery |
| ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
| ||||||||||||
Teaching Methods |
| ||||||||||||
Student Performance Evaluation |
Language of evaluation: Greek and English. Methods of evaluation:
In any case, all students can participate in written exams at the end of the semester, during the exams period. The aforementioned information along with all the required details are available through the course's website. The information is explained in detail at the beginning of the semester, as well as, throughout the semester, during the lectures. Reminders are also posted at the beginning of the semester and throughout the semester, through the course's website. Upon request, all the information is provided using email or social networks. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Harmonic Analysis (MAE718)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE718 |
Semester |
7 |
Course Title |
Harmonic Analysis |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (In English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The aim of the course is the achievement by the undergraduate student of the theoretical background in the theory of Fourier series |
---|---|
General Competences |
The objective of the course is the undergraduate student's ability achievement in analysis and synthesis of the basic background in Harmonic Analysis. |
Syllabus
Trigonometric polynomials, partial sums of the Fourier series of a function, Bessel's inequality, Lemma Riemann-Lebesgue, Parseval's identity for Riemann integrable functions, complex Riemann integrable functions defined on an interval, Fourier coefficients and Fourier series, the Dirichlet kernel, criteria for uniform convergence of the Fourier series, convolution of functions and approximations to the identity, Fejer kernel, theorem of Fejer, Poisson kernel, Abel summability of the Fourier series, applications.
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Written examination at the end of the semester. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Yitzhak Katznelson, An Introduction to Harmonic Analysis, Dover Edition.
- Elias M. Stein, Rami Shakarchi, Fourier Analysis, An Introduction, Princeton University Press.
Functional Analysis (MAE719)
- Ελληνική Έκδοση
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE719 |
Semester | 7 |
Course Title |
Functional Analysis |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes ( in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The goal of this course is: To familiarize the student with the notions, the basic theorems and the techniques concerning normed vector spaces, Banach spaces, Hilbert spaces, bounded linear operators between them and the dual spaces. After completing this course the student will be able to recognize if a given normed linear space is a Banach space, to compute the norm of a bounded linear operator, to use the basic theorems of Functional analysis (Hahn-Banach theorem and its consequences, Open mapping theorem, Closed graph theorem, Banach-Steinhaus theorem, Uniform Boundedness Principle). |
---|---|
General Competences |
|
Syllabus
Linear spaces and algebraic bases (Hamel bases). Linear operators. Normed linear spaces. Banach spaces and classical examples. Finite dimensional spaces. Bounded linear operators, bounded linear functionals and computation of their norm. Dual space. Conjugate operators. Hahn Banach theorem and its consequences. The second dual space. Reflexive spaces. Baire's category theorem and some of its consequences in Functional Analysis (Open Mapping Theorem, Closed graph Theorem, Uniform Boundedness Principle, Banach-Steinhaus Theorem). Elements from Hilbert spaces.
Teaching and Learning Methods - Evaluation
Delivery |
Teaching on the blackboard from the teacher | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Exams in the end of the semester (mandatory), intermediate exams (optional), assignments of exercises during the semester (optional). |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Special Topics in Algebra (MAE723)
- Ελληνική Έκδοση
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE723 |
Semester |
7 |
Course Title |
Special Topics in Algebra |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The principal aim of the course is to introduce the students to the main ideas and methods of Commutative Algebra. |
---|---|
General Competences |
The course promotes inductive and creative thinking and aims to provide the student with the theoretical background and skills of commutative rings. |
Syllabus
- Polynomial Rings
- Hilbert's Basis Theorem
- Localization
- Integral dependence
- Hilbert Series
- Dimension
- Groebner Bases
- Hilbert's Nullstellensatz Theorem
Teaching and Learning Methods - Evaluation
Delivery |
Teaching on the blackboard by the teacher. | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Communication with the teacher by electronic means (i.e. e-mail). | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- J.Beachy, Introductory Lectures on Rings and Modules, LMS, Cambridge University Press, (1999).
- D.Dummit, R.M.Foote, Abstract Algebra, 3 edition, Prentice Hall, (2003).
- N.Jacobson, Basic Algebra I & II, W. H. Freeman and Company, (1985 & 1989).
- S.Lang, Algebra, Graduate Texts in Mathematics, Springer (2002).
- L.Rowen, Ring Theory, Academic Press, 2 edition (1991).
- Μαλιάκας. Ταλέλλη, Πρότυπα πάνω από Περιοχές Κυρίων Ιδεωδών και Εφαρμογές, Εκδ. Σοφία (2009).
- Α. Μπεληγιάννης, Μια Εισαγωγή στη Βασική Άλγεβρα, Εκδ. Κάλλιπος (2015).
Algebraic Structures II (MAE724)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE724 |
Semester |
7 |
Course Title |
Algebraic Structures II |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The students will acquire with the successful completion of the course
|
---|---|
General Competences |
The course aim is for the student to acquire the ability in analysis and synthesis of knowledge in Field Theory and produces free, creative and inductive thinking. |
Syllabus
- Rings
- Integral Domains, Fields, Homomorphisms and Ideals
- Quotient Rings
- Polynomial Rings over fields
- Prime and Maximal Ideals
- Irreducible Polynomials
- The classical methods of solving polynomial equations
- Splitting fields
- The Galois Group
- Roots of unity
- Solvability by Radicals
- Independence of characters
- Galois extensions
- The Fundamental Theorem of Galois Theory
- Discriminants
- Polynomials of degree less than 4 and Galois Groups
- Ruler and Compass constructions
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- M. Holz: "Repetition in Algebra", Greek Edition, Symmetria Publishing Company, (2015).
- Th. Theochari-Apostolidou and C. M. A. Charalambous: "Galois Theory", (Greek), Kallipos Publishing (2015).
Ring Theory (MAE725)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE725 |
Semester |
7 |
Course Title |
Ring Theory |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek, English |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The principal aim of the course is to introduce the students to the main tools and methods of the theory of non-commutative rings, where by non-commutative ring is meant an associative ring with unit, which is not necessarily commutative.
|
---|---|
General Competences |
The course aims to enable the undergraduate student to acquire the ability to analyse and synthesize basic knowledge of the Theory of Rings, which is an important part of modern algebra. The contact of the undergraduate student with the ideas and concepts of the theory of rings, (a) promotes the creative, analytical and deductive thinking and the ability to work independently, (b) improves his critical thinking and his ability to apply abstract knowledge in various field. |
Syllabus
Rings - Homomorphisms - Ideals - Quotient Rings - Modules - Rings arising from various constructions - Algebras - Group algebras - Modules over group algebras - Module homomorphisms - The bicommutator - Simple faithful modules and primitive rings - Artin rings - Simple finite dimensional algebras over algebraically closed fields - Artinian modules - Noetherian rings and modules - Jacobson radical.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face to face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
| ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Combination of: Weekly homework, presentations in the class by the students, written work, and, at the end of the semester, written final exams in Greek (in case of Erasmus students, in English) which includes analysis of theoretical topics and resolving application problems. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Nathan Jacobson: "Basic Algebra I & II", W. H. Freeman and Company, (1985 & 1989).
- I.N. Herstein: "Non-commutative Rings", AMS, Carus Mathematical Monographs 85, (1971).
- Luis Rowen: "Ring Theory (student edition)", Academic Press, Second Edition, (1991).
- T.Y. Lam: "A First Course in Noncommutative Rings", GTM 131, Springer, (2001).
- P. M. Cohn: "Introduction to Ring Theory", Springer (2000).
- Y. Drozd and V. Kirichenko: "Finite Dimensional Algebras", Springer (1994).
Euclidean and Non Euclidean Geometries (MAE727)
- Ελληνική Έκδοση
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- Department of Mathematics
- Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)
General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE727 |
Semester |
7 |
Course Title |
Euclidean and Non Euclidean Geometries |
Independent Teaching Activities |
Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek, English |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
This is an introductory course on non Euclidean geometries. The aim is to study how the attempt to prove Euclid's fifth postulate led the way to non Euclidean geometries. On completion of the course the student should be familiar with the foundations of Euclidean and non Euclidean geometries. |
---|---|
General Competences |
|
Syllabus
Euclid's geometry, Hilbert's system of axioms, the fifth postulate, compatibility of axioms, neutral geometry, independence of the fifth postulate, hyperbolic geometry, Poincarẻ model, spherical geometry, Platonic solids.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
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Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Π. Πάμφιλου, Γεωμετρία, Εκδόσεις Τροχαλία, 1989.
- M.J. Greenberg, Euclidean and non-Euclidean Geometry-Development and History, W.H. Freedmann and Company, 1973.
- R. Hartshorne, Geometry: Euclid and beyond, Springer, 2000.
- H. Meschkowski, Noneuclidean Geometry, Academic Press, 1964.
Differentiable Manifolds (MAE728)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE728 |
Semester |
7 |
Course Title |
Differentiable Manifolds |
Independent Teaching Activities |
Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek, English |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
In this lecture we introduce basic notions of modern Differential Geometry. More precisely, we introduce among others the notions of manifold, tangent bundle, connection, parallel transport and Riemannian metric. |
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General Competences |
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Syllabus
- Smooth manifolds.
- Smooth maps.
- Tangent vectors.
- Vector fields.
- Regular values and Sard's Theorem.
- Homotopy and Isotopy.
- Lie bracket.
- Frobenius' Theorem.
- Connections and parallel transport.
- Riemannian metrics.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||
---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||
Teaching Methods |
| ||||||||
Student Performance Evaluation |
Weakly homeworks and written final examination. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- M. do Carmo, Riemannian Geometry, Birkhaüser Boston, Inc., Boston, MA, 1992.
- V. Guillemin & A. Pollack, Differentiable Topology, Prentice-Hall, Inc, Englewood Cliffs, 1974.
- J. Lee, Introduction to Smooth Manifolds, Graduate Texts in Mathematics, 218, 2013.
- J. Milnor, Topology From the Differentiable Viewpoint, Princeton University Press, NJ, 1997.
- L. Tu, An Introduction to Manifolds, Universitext. Springer, New York, 2011.
- Δ. Κουτρουφιώτης, Διαφορική Γεωμετρία, Πανεπιστήμιο Ιωαννίνων, 1994.
Decision Theory - Bayesian Theory (MAE731A)
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ731A |
Semester |
7 |
Course Title |
Decision Theory - Bayesian Theory |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English, reading Course) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
This course consists of two modules: the Decision Theory and Bayes Theory. The Decision Theory deals with problems of decision-making. Object of Statistical Decision Theory is decisions about unknown numerical quantities (parameters) by utilizing the presence of statistical knowledge. The aim of the course is the evaluation of the performance of the estimators subject to properties such as the unbiasedness, sufficiency, consistency etc.
|
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General Competences |
|
Syllabus
Decision Theory: decision function, loss function, risk function, admissible and minimax estimators; Bayesian inference: Bayes estimators, Bayes confidence intervals, minimax and Bayes tests.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Use of ICT in communication with students | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which concentrates on the solution of problems which are motivated by the main themes of the course. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Berger, J.O. (1985) Statistical decision theory and Bayesian analysis. Springer.
- Bernardo J. M. & Smith A. F. M., (1994). Bayesian Theory, Wiley, London.
- Congdon, P. (2007), Bayesian Statistical Modelling, Willey.
- Κ. Φερεντίνος (2005). Εκθετική οικογένεια κατανομών Θεωρία Bayes, Πανεπιστημιακές Παραδόσεις.
Topics in Operations Research (MAE732A)
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- Department of Mathematics
- Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)
General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE732A |
Semester |
7 |
Course Title |
Topics in Operations Research |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course learning outcomes are: the introduction of the students to integer programming formulations, the introduction of the students to the dynamic programming methodology, the introduction of the students to techniques and tools for decision-making under uncertainty. Upon successful completion of the course the student will be able to:
|
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General Competences |
|
Syllabus
Integer linear programming (integer and mixed integer problems formulation, integer programming algorithms). Dynamic programming (Bellman principle of optimality, finite and infinite horizon problems, Applications on: Routing problems, Equipment-Replacement Problem, inventory problems, etc). Decision analysis (General characteristics of decision problems, decisions under uncertainty, decision trees, risk analysis).
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Lindo/Lingo Software, Email, class web | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
LANGUAGE OF EVALUATION: Greek
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Bellman, R.E.. Dynamic Programming, Princeton University Press, 1957, Princeton, NJ. Republished 2003
- Bertsekas D. P. Dynamic Programming and Optimal Control, Vols. I and II, Athena Scientific, 1995, (3 Edition Vol. I, 2005, 4th Edition Vol. II, 2012),
- BERTSIMAS D. and J. N. TSITSIKLIS Introduction to Linear Optimization, Athena Scientific 1997
- HADLEY G. Linear Programming, Addison-Wesley Publishing Company, INC, 1965
- HILLIER F. S. and G. J. Lieberman. Introduction Operations research. The McGraw-Hill Companies, 2001
- WINSTON W. L., Operations research (Applications and algorithms). Duxbury Press (International Thomson Publishing) 1994.
- [Περιοδικό / Journal] Mathematical Programming Journal, Series A and Series B
- [Περιοδικό / Journal] INFORMS Transactions on Education (ITE)
Regression and Analysis of Variance (MAE733)
- Ελληνική Έκδοση
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- Department of Mathematics
- Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)
General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ733 |
Semester |
7 |
Course Title |
Regression and Analysis of Variance |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English, reading Course) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The aim of the course is the presentation, study and application of linear models and more precisely the simple and multiple linear regression models and analysis of variance of one or more factors, as well. The general linear model is presented to unify the above mentioned regression and analysis of variance models. This course is focused on the theory of linear models and their applications in modelling statistical data. At the end of the course, students understand the aforementioned issues of the theory of linear models and it is, moreover, expected that they will be able to apply the theory of linear models for the analysis of real statistical data. |
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General Competences |
|
Syllabus
Theory of linear models. Simple linear regression. Multiple linear regression. One-and multi-way analysis of variance. Multiple comparisons. Applications.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Use of ICT in communication with students | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which concentrates on the solution of problems which are motivated by the main themes of the course. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Kutner, M. H., Nachtsheim, Ch., Neter, J. and Li. W. (2004). Applied Linear Statistical Models. 5 Edition, McGraw-Hill.
- Montgomery, D. C., Peck, E. A. και Vining, G. G. (2006). Introduction to linear regression analysis. 4th Edition, Wiley.
- Rencher, A. C. (2000). Linear models in statistics. Wiley.
- Sahai, H. and Ageel, M. (2000). The Analysis of Variance. Birkhauser.
- Καρακώστας, Κ. (2002). Γραµµικά Μοντέλα: Παλινδρόµηση και Ανάλυση ∆ιακύµανσης. Πανεπιστήµιο Ιωαννίνων.
Database Systems and Web Applications Development (MAE741)
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE741 |
Semester |
7 |
Course Title |
Database Systems and Web applications development |
Independent Teaching Activities |
Lectures-Laboratory (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Students knowledge acquisition of design, implementation procedures and methodologies using Relational DataBase Management Systems (RDBMS), as well as familiarity with the development of Internet programming applications using PHP, JavaScript, jQuery and AngularJS.
|
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General Competences |
|
Syllabus
- Data models with emphasis on relational model. Introduction to relational algebra and relational calculus. Conceptual Models: Entity-Associations Model. Theory of dependencies. Form normalization (1NF, 2NF, 3NF, BCNF). Database design. Introduction to Database Management Systems.
- SQL language with practical application using MariaDB. Create tables, modify fields, add records to a table, Database tables management.
- Create basic SQL queries in MariaDB tables.
- SQL joins, SQL table associations-relations, foreign keys, stored procedures, triggers.
- Introduction to the web and its capabilities. Web page development. Basic HTML content formatting commands, Add images, create tables, lists and frames, HTML layers, divs HTML 5 additional commands.
- HTML and content formatting using Cascading Style Sheets (CSS). Advanced ways of responsive formatting using the Bootstrap library.
- Introduction to JavaScript, ways to import JavaScript into HTML, JavaScript DOM, functions and classes.
- Introduction to PHP, basic language capabilities, input output, data types, conditions, repetitive loops.
- Create forms in HTML and retrieve form information using PHP and JavaScript (AJAX), using GET, POST methods.
- Use of PHP and MySQL, presentation of PHP input functions and retrieval of information from DB tables. (mysqli-PDO api). Creating dynamic web pages.
- Mathematical extensions of PHP, PHP and data processing from DB to solve linear equation problems, presentation of the PHP-LAPACK class.
- Mathematical extensions of PHP, PHP and statistical data processing from DB, presentation of PHP statistical functions.
- Asynchronous communication with DB, PHP and AJAX, using the jQuery library and JSON configuration. Presentation and use of AngularJS and NodeJS frameworks.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Use of Micro-computers Laboratory | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- PHP 6 AND MYSQL 5 FOR DYNAMIC WEB SITES, 5 Edition, LARRY ULLMAN, ISBN-13: 978-0134301846, 2018.
- JAVASCRIPT & JQUERY interactive front-end web development, Jon Duckett, ISBN-13: 978-1118531648, 2017.
Introduction to Computational Mathematics (MAE742A)
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE742A |
Semester |
7 |
Course Title |
Introduction to Computational Mathematics |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Science is based on two major pillars, both theoretical and experimental. However, over the last few decades scientific computing has emerged and recognized as the third pillar of science. Now, in most scientific disciplines, theoretical and experimental studies are linked to computer analysis. In order for the graduate student to be able to stand with claims in the modern scientific and work environment, knowledge in computational techniques is considered a necessary qualification.
|
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General Competences |
The course aims to enable the student to:
|
Syllabus
- Vector and matrix definition and calculations
- Basic commands and functions
- Graphic representation of the numerical results
- Polynomial interpolation: Lagrange Method, Newton's Method
- Numerical integration: Simple and generalized types of numerical integration, rectangular rule, trapezoid rule, Simpson rule, Gauss integration
- Numerical solution of non-linear equations: iterative methods, bisection method, fixed point method, Newton's method
- Numerical solution of linear systems - Direct methods: Gauss elimination, LU decomposition.
Teaching and Learning Methods - Evaluation
Delivery |
In the laboratory | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Use of scientific computing software packages | ||||||||||||
Teaching Methods |
| ||||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Introduction to Numerical Analysis, G.D. Akrivis, V.A. Dougalis, 2010 (in Greek).
- Numerical Linear Algebra, V. Dougalis, D. Noutsos, A. (in Greek).
- A Primer on Scientific Programming with Python, H. P. Langtangen, Springer-Verlag Berlin Heidelberg, 5 Edition, 2016.
- Programming for Computations- MATLAB/Octave, S. Linge, H. P. Langtangen, Springer International Publishing, 2016 (in Greek).
Introduction to Mathematical Physics (MAE743)
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ743 |
Semester |
7 |
Course Title |
Introduction to Mathematical Physics |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course is an introduction to the basic analytic and numerical methods of Mathematical Physics. The objectives of the course are:
|
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General Competences |
The course aims to enable the undergraduate students to develop basic knowledge of Mathematical Physics and in general of Applied Mathematics. The student will be able to cope with problems of Applied Mathematics giving the opportunity to work in an international multidisciplinary environment. |
Syllabus
Short introduction of linear vector spaces, Vector spaces of infinite dimensions, The Sturm-Liouville problem, Orthogonal polynomials and special functions, Multi-dimensional problems, Operator Theory, Applications in modern Physics.
Teaching and Learning Methods - Evaluation
Delivery |
In class | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Use of computer (Mechanics) lab | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Numerical Solution of Ordinary Differential Equations (MAE744)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE744 |
Semester |
7 |
Course Title |
Numerical Solution of Ordinary Differential Equations |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special background, skills development. |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Upon successful completion of the course, students will be able to:
|
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General Competences |
|
Syllabus
- Initial Value Problems
- Explicit Euler and Implicit Euler.
- Consistency, stability, and convergence of Runge-Kutta methods.
- Consistency, stability, and convergence of multistep methods.
- Applications to ODEs systems arising from Physics and Biology.
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face. | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
| ||||||||||||
Teaching Methods |
| ||||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- “Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations”, E. Hairer, & C. Lubich, Springer, 2010.
- “Numerical Methods for Ordinary Differential Equations: Initial Value Problems”, D.F. Griffiths, & D. J. Higham, Springer, 2010.
Theory of Computation (MAE745)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE745 |
Semester |
7 |
Course Title |
Theory of Computation |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The goal of this course is the deeper understanding of Automata Theory and Languages. During the course a detailed examination of the following topics are done:
Upon completion of the course, the students will be able to:
which are related to Finite Automata, Pushdown Automata, and Turing Machines as well as to Unsolvability , to Computational Complexity and to NP-complete problems. |
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General Competences |
|
Syllabus
- Introduction and related concepts.
- Finite automata and regular expressions, regular languages, closure properties, pumping lemma, algorithms.
- Determinism, non-determinism.
- Pushdown automata and context-free grammars, context-free languages, closure properties, pumping lemma, algorithms.
- Chomsky normal form.
- Turing machines, equivalence of different models.
- Recursive and recursively enumerable languages.
- Church-Turing thesis.
- Undecidability, the halting problem, Post’s correspondence problem.
- Classes P and NP.
Teaching and Learning Methods - Evaluation
Delivery |
Face to face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
| ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final test |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- [11776]: Στοιχεία θεωρίας υπολογισμού, Lewis Harry R.,Παπαδημητρίου Χρίστος Χ.
- [257]: ΕΙΣΑΓΩΓΗ ΣΤΗ ΘΕΩΡΙΑ ΥΠΟΛΟΓΙΣΜΟΥ, SIPSER MICHAEL.
Graph Theory (MAE746)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE746 |
Semester |
7 |
Course Title |
Graph Theory |
Independent Teaching Activities |
Lectures, laboratory exercises, tutorials, quiz (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Introduction to fundamental concepts of graph theory and understanding of algorithmic techniques of graph problems. Basic definitions and concepts, Connectivity and Biconnectivity, Trees, Spanning Trees and Rooted trees, Eulerian and Hamiltonian graphs, Otpimization problems on graphs, Planar graphs, Graphs, connectivity, spanning trees, Eulerian & Hamiltonian graphs, Graph coloring, Clique, Independent set, Vertex cover, Planar graphs. |
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General Competences |
|
Syllabus
- Introduction to basic graph concepts
- Connectivity and biconnectivity
- Trees
- Eulerian & Hamiltonian graphs
- Graph optimization problems
- Planar graphs
Teaching and Learning Methods - Evaluation
Delivery |
Lectures | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
| ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Γ. Μανωλόπουλος, Μαθήματα Θεωρίας Γράφων . Κωδικός Βιβλίου στον Εύδοξο: 3472
- Σημειώσεις στη Θεωρία Γραφημάτων, Χάρης Παπαδόπουλος, Πανεπιστήμιο Ιωαννίνων, 2012.
- Θεωρία γραφημάτων με παραδείγματα κ ασκήσεις, Κωδικός Βιβλίου στον Εύδοξο: 31528, Συγγραφείς: ΠΑΠΑΙΩΑΝΝΟΥ ΑΛΕΞΑΝΔΡΟΣ, Διαθέτης (Εκδότης): ΑΡΗΣ ΣΥΜΕΩΝ.
Linear and Nonlinear Waves (MAE747)
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE747 |
Semester |
7 |
Course Title |
Linear and Nonlinear Waves |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The study of nonlinear systems has quietly and steadily revolutionized the realm of science over recent years. It is known that for nonlinear systems new structures emerge that have their features and peculiar ways of interacting. Examples of such structures abound in nature and include, amongst others: vortices (like tornadoes), solitons (bits of information used in optical fiber communications, water waves, tsunamis, etc), and chemical reactions. This course is intended as an introduction to the theory and of Nonlinear Waves and their applications. By the end of the course students will be able to:
|
---|---|
General Competences |
|
Syllabus
The linear wave theory, Burgers' equation, the Korteweg-de Vries (KdV) equation, travelling waves and the scattering problem for the KdV equation, the inverse scattering transform and solitons, the nonlinear Schrödinger equation, applications to water waves and optics.
Teaching and Learning Methods - Evaluation
Delivery |
Face to face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Yes | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Solitons: an Introduction, P. G. Drazin and R. S. Johnson, Cambridge University Press, 1989.
- Γ. Δ. Ακρίβης και Ν .Δ. Αλικάκος, Μερικές Διαφορικές Εξισώσεις, Σύγχρονη Εκδοτική, 2012.
- Εφαρμοσμένα Μαθηματικά, D. J. Logan, Πανεπιστημιακές Εκδόσεις Κρήτης, 2010.
Efficient Algorithms (MAE748)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE748 |
Semester |
7 |
Course Title |
Efficient Algorithms |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course is introducing advanced algorithmic concepts and techniques. Several optimization problems are examined and solved using algorithmic techniques. Upon a successful completion of the course, the student will be able to:
|
---|---|
General Competences |
|
Syllabus
Basics: Algorithm analysis (correctness, time and space complexity), asymptotic analysis (worst and average care), recursive algorithms (Strassen’s algorithm for the matrix multiplication problem), lower bounds (comparison-based sorting, the convex-hull problem). Amortized analysis: The accounting, aggregate and potential methods. Minimum spanning trees: The greedy algorithms by Tarjan, Prin and Kruskal. Minimum cuts: The algorithm by Stoer and Wagner. Maximum flows: Basis terminology (flow network, augmenting path, residual network) the max-flow min-cut theorem, the algorithms by Ford και Fulkerson, Edmonds και Karp, and Dinitz. Planar graphs: Basic terns, Euler’s formula, Kurantowski Theorem, the 5-color theorem, drawings of planar graphs: the algorithm by de Fraysseix, Pach and Pollack, the crossing Lemma. Approximation algorithms: simple algorithms of constant approximation factor, Christofides’ algorithm for the traveling salesman problem, approximation schemes for knapsack and bin packing. Randomized algorithms: simple randomized algorithms for verifying polynomial identities and 2-SAT, random walks.
Teaching and Learning Methods - Evaluation
Delivery |
Face to face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Yes | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Convex Analysis (MAE753)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑE753 |
Semester |
7 |
Course Title |
Convex Analysis |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course aims to an introduction to convex analysis at undergraduate level. It is desired for students to understand convex sets with respect to some of their qualitative (from a geometric/combinatorial point of view) and quantitative (e.g. volume, surface area) properties together with the study of the corresponding convex functions. |
---|---|
General Competences |
|
Syllabus
Basic notions. Convex functions and convex sets. Polytopes. Gauge functions and support functions. The Caratheodory. Radon's and Helly's theorems. Minkowski's First theorem. The Brunn-Minkowski inequality. Mixed volumes. Inequalities of isoperimetric type (e.g. the classical isoperimetric inequality and the Blaschke-Santalo inequality). F. John's Theorem. The reverse isoperimetric inequality.
Teaching and Learning Methods - Evaluation
Delivery |
Lectures/ Class presentations | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Use of the platform “E-course” of the University of Ioannina | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Students' evaluation by the following:
Evaluation criteria and all steps of the evaluation procedure will be accessible to students through the platform "E-course" of the University of Ioannina. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- R. J. Gardner, Geometric tomography. Second edition. Cambridge University Press, 2006.
- R. Tyrel Rockafellar, Convex Analysis. Princeton University Press, 1970.
- R. Schneider, Convex bodies: the Brunn-Minkowski theory. Second expanded edition. Cambridge University Press, 2014.
- A. C. Thompson, Minkowski Geometry. Cambridge University Press, 1996.
- R. Webster, Convexity. Oxford University Press, 1970.
Seminar in Analysis II (MAE754)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ754 |
Semester |
7 |
Course Title |
Seminar in Analysis II |
Independent Teaching Activities |
Lectures (Weekly Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | None. However it is desirable to have a strong knowledge of basic notions of differential equations. |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
No |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The report can be, but not required to be, original. Further details can be determined by the teaching professor. |
---|---|
General Competences |
Further details can be determined by the teaching professor. |
Syllabus
In depth study in a scientific subject related to mathematical analysis. Further details can be determined by the teaching professor.
Teaching and Learning Methods - Evaluation
Delivery |
Details will be determined by the teaching professor. Methods include presentations contacted by the students. | ||||||||
---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Details will be determined by the teaching professor. | ||||||||
Teaching Methods |
| ||||||||
Student Performance Evaluation |
Other means of evaluation can be determined by the teaching professor. |
Attached Bibliography
Bibliography is suggested by the teaching professor, depending on the subject under study.
Astronomy (MAE801)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE801 |
Semester |
8 |
Course Title |
Astronomy |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course introduces students to the basic principles of astronomy. Upon successful completion of this course students should be able to:
|
---|---|
General Competences |
|
Syllabus
Mechanisms of emission and absorption of radiation. Radiative transfer in stellar atmospheres. Stellar magnitudes and distances. Stellar spectra and classification, Hertzsprung‐Russell diagram. Internal structure, formation and evolution of stars. Final stages of stars: white dwarfs, neutron stars and black holes. The Sun and the solar system. Variable and peculiar stars. Stellar groups and clusters. Interstellar matter. The Milky Way Galaxy. Other galaxies. Cosmology.
Teaching and Learning Methods - Evaluation
Delivery |
Face to face teaching | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
The Moodle e‐learning platform is used for the delivery of lecture notes and exercises to the students. | ||||||||||||
Teaching Methods |
| ||||||||||||
Student Performance Evaluation |
Written examination at the end of semester. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- "Αstrophysics, volume Ι", F. Shu, Crete University Press, ISBN: 978-960-7309-16-7 (in Greek).
- "Αstrophysics, volume ΙI", F. Shu, Crete University Press, ISBN: 978-960-7309-17-4 (in Greek).
Meteorology (MAE802)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE802 |
Semester |
8 |
Course Title |
Meteorology |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The aim of the course is to give students the opportunity to be familiar with the basic principles of Meteorology and realize if they are interested in working, studying or doing research on this scientific field in the future. Specifically, after the successful completion of the course, the students will be able to:
|
---|---|
General Competences |
|
Syllabus
Weather and climate. Composition and vertical structure of the atmosphere. Solar radiation and mechanisms of heat transfer in the atmosphere. Air temperature. Atmospheric pressure. Wind. Large-scale and small-scale circulations in the atmosphere. Atmospheric humidity. Atmospheric stability. Clouds, fog, dew and frost. Precipitation (rain, snow, etc.). Fronts. Atmospheric disturbances. Measurement techniques and meteorological instruments. Fundamental elements of weather analysis and forecasting. Educational visit to the Laboratory of Meteorology of the Physics department and the university meteorological station.
Teaching and Learning Methods - Evaluation
Delivery |
Face to face | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Asynchronous online learning via Moodle is used for providing the lecture slides and the communication with the students. | ||||||||||||
Teaching Methods |
| ||||||||||||
Student Performance Evaluation |
Written examinations at the end of semester, comprising questions of knowledge and understanding of the course content. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Ahrens CD, Henson Ρ. 2018: Meteorology Today: An Introduction to Weather, Climate and the Environment 12th Edition, Cengage Learning.
Operator Theory (MAE811)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE811 |
Semester | 8 |
Course Title |
Operator Theory |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes ( in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The goal of the course is the study of inner product and Hilbert spaces (which in the case of finite dimensional spaces are the well-known Euclidean spaces) and the study of bounded, but also of non-bounded, linear maps (linear operators) between them. These operators appear in many branches of theoretical and applied mathematics. For example, they appear in Differential and Integral equations, in Fourier analysis, in quantum mechanics and in quantum information theory. The aim is to transform these operators (where it is possible) into diagonal operators with respect to appropriate "bases". Classes of operators will be studied for which this result is achieved. |
---|---|
General Competences |
|
Syllabus
Spaces with inner product, Hilbert spaces, basic properties. Orthonormal sets and orthonormal bases in Hilbert spaces. Bounded operators, adjoint operators, orthogonal projections. Finite-order operators, compact operators, Fredholm's Alternative. Operator diagonalization, the spectral theorem for compact normal and in particular self-adjoint operators. Unbounded linear operators.
Teaching and Learning Methods - Evaluation
Delivery |
Teaching on the blackboard from the teacher | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Exams in the end of the semester (mandatory), intermediate exams (optional), assignments of exercises during the semester (optional). |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Qualitative Theory of Partial Differential Equations (MAE815)
Qualitative Theory of Partial Differential Equations (MAE815)
Difference Equations - Discrete Models (MAE816)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE816 |
Semester |
8 |
Course Title |
Difference Equations - Discrete Models |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Language of Instruction (lectures): Greek
|
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Remembering:
Comprehension:
Applying:
Evaluating: Teaching undergraduate and graduate courses. |
---|---|
General Competences |
|
Syllabus
The Difference Calculus, Linear difference equations, Stability theory, Asymptotic methods, The Sturm-Liouville problem, Boundary value problems for non-linear difference equations, Partial difference equations.
Teaching and Learning Methods - Evaluation
Delivery |
| ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | -
| ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
The aforementioned information along with all the required details are available through the course's website. The information is explained in detail at the beginning of the semester, as well as, throughout the semester, during the lectures. Reminders are also posted at the beginning of the semester and throughout the semester, through the course's website. Upon request, all the information is provided using email or social networks. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Special Topics in Geometry (MAE822)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE822 |
Semester |
8 |
Course Title |
Special Topics in Geometry |
Independent Teaching Activities |
Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek, English |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
This course introduces the notion of differential forms. The aim of the course is to prove Stokes theorem for manifolds with boundary and to provide applications in differential geometry as well as in other areas of mathematics. The course requires tools from linear algebra, calculus of several variables, topology and elementary differential geometry. On completion of the course the student should be familiar with differential forms and the meaning of Stokes theorem. |
---|---|
General Competences |
|
Syllabus
Differential forms in Euclidean space, line integrals, differentiable manifolds (with or without boundary), integration of differential forms on manifolds, theorem of Stokes and applications, Poincare lemma, differential geometry of surfaces, structure equations.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- M. do Carmo, Διαφορικές Μορφές, Θεωρία και Εφαρμογές, Prentice-Hall, Πανεπιστημιακές Εκδόσεις Κρήτης, 2010.
Riemannian Geometry (MAE825)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE825 |
Semester |
8 |
Course Title |
Riemannian Geometry |
Independent Teaching Activities |
Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek, English |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The main task is to present the fundamental concepts of Riemannian geometry, i.e., the concepts of curvatures and differential form on manifolds with boundary. Moreover, we will introduce the notions of Riemannian submanifold and will investigate the Gauss-Codazzi-Ricci equations. The lecture will be completed with the presentation of the sphere theorem, a deep and important result that connects geometry with topology. On the completion of the course we expect that the student fully understand the main theorems that were presented during the lectures. |
---|---|
General Competences |
|
Syllabus
Riemannian metrics, curvature operator, Schur's theorem, differential forms, integration on manifolds, Stokes' theorem, Riemannian submanifolds, sphere theorem.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Weekly exercises and homeworks, presentations, final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- M. do Carmo, Riemannian Geometry, Birkhaüser Boston, Inc., Boston, MA, 1992.
- J. Eschenburg, Comparison Theorems in Riemannian Geometry, Universität Augsburg, 1994.
- J. Jost, Riemannian Geometry and Geometric Analysis, Universitext, Springer, 2017.
- J. Lee, Riemannian manifolds: An Introduction to Curvature, Vol. 176, Springer, 1997.
- P. Petersen, Riemannian Geometry, Graduate Texts in Mathematics, 171, Springer, 2016.
- Δ. Κουτρουφιώτης, Διαφορική Γεωμετρία, Πανεπιστήμιο Ιωαννίνων, 1994.
Topological Matrix Groups (MAE826)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE826 |
Semester |
8 |
Course Title |
Topological Matrix Groups |
Independent Teaching Activities |
Interactive, Presentations (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background, skills development |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek, English |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The aim of the course is to provide an introduction to Lie theory through matrix groups. The main subject of study is the closed subgroups of the general linear group. Our study is extended from real to complex and quaternion numbers. The corresponding linear groups are in fact topological groups and an introduction of basic properties of topological group is also provided. The Lie algebra of a matrix group is defined. The special orthogonal, unitary and symplectic groups provide important example of Lie algebras. Lie algebras are studied using the exponential map. Finally Lie groups are defined. |
---|---|
General Competences |
|
Syllabus
- General linear groups
- Real and Complex algebras, Quaternions. Matrix algebras
- Inner product, orthogonal, unitary and symplectic groups
- Homomorphisms
- Differential curves, tangent vectors. Dimension of a matrix group
- Differential homomorphisms
- Expontential and logarithmic funcions. Lie algebras
- Special orthogonal and symplectic groups
- Topological groups, manifolds
- Maximal tori
- Differential manifolds, Lie groups.
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face, Distance learning | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Communication with students | ||||||||||||||
Teaching Methods |
| ||||||||||||||
Student Performance Evaluation |
Written Examination, Oral Presentation, written assignments. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- J. F. Adams, Lectures on Lie groups, University of Chicago Press, 1969.
- M. L. Curtis, Matrix Groups, Springer-Verlag, 1979.
- R. Howe. Very basic Lie theory, American math. monthly,90, 1983.
Statistical Data Analysis (MAE832)
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ832 |
Semester |
8 |
Course Title |
Statistical Data Analysis |
Independent Teaching Activities |
Lectures-Laboratory (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English, reading Course) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
In this course, various statistical methodologies are applied with the help of the computer and the use of statistical programs (SPSS, JASP, R). Emphasis is placed on choosing the appropriate statistical methodology and examining whether the assumptions of its application are met. |
---|---|
General Competences |
|
Syllabus
In this course, various statistical methodologies are applied with the help of the computer and the use of statistical programs (SPSS, JASP, R).
Upon completion of the course, the student will be able to:
- enter data into the computer
- conduct descriptive statistical analysis, that is to summarize the available data,
- conduct basic data analyzes (testing hypotheses concerning the mean of a population, the means of two populations with dependent and independent samples, one way analysis of variance etc.,)
- fits simple-multiple linear regression models, binomial logistic regression models, checking whether the assumptions of their application are violated
- applies basic methodologies of multidimensional analysis (clustering, factor analysis)
- present the results of the above analyzes (reference report).
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Use of ICT in communication with students | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which concentrates on the solution of problems which are motivated by the main themes of the course. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Andy Field. Η Διερεύνηση της Στατιστικής με τη χρήση του SPSS της IBM. Εκδόσεις Προπομπός
- Julie Pallant. SPSS Οδηγός ανάλυσης δεδομένων με το ΙΒΜ SPSS. Εκδόσεις Κλειδάριθμος ΕΠΕ.
- Δ. Φουσκάκης. Ανάλυση Δεδομένων με χρήση της R. Εκδόσεις Τσότρας Αν. Αθανάσιος
- Joaquim P. Marques de Sá. Applied Statistics Using SPSS, STATISTICA, MATLAB and R. Springer Berlin Heidelberg Διαθέτης (Εκδότης) HEAL-Link Springer ebooks
- Μαλεφάκη, Σ., Μπατσίδης, Α., & Οικονόμου, Π. (2023). Στατιστική Ανάλυση Δεδομένων [Προπτυχιακό εγχειρίδιο]. Κάλλιπος, Ανοικτές Ακαδημαϊκές Εκδόσεις.
Inventory Control and Production Planning (MAE833)
- Ελληνική Έκδοση
- Undergraduate Courses Outlines
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE833 |
Semester |
8 |
Course Title |
Inventory Control and Production Planning |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Upon successful completion of the course, students will:
|
---|---|
General Competences |
|
Syllabus
Introduction. Forecasting (Classical Demand Forecasting Methods, Forecast Accuracy, Machine Learning in Demand Forecasting, Demand Modeling Techniques). Deterministic Inventory Models (Continuous Review: Economic Order Quantity (EOQ) model, EOQ Model with Discounts, EOQ Model with shortages, Economic Production Quantity (EPQ) Model, Periodic review: Wagner-Whitin Algorithm). Stochastic Inventory Models (Continuous Review: Exact (r,Q) policy with Continuous Demand Distribution, Exact (r,Q) policy with Discrete Demand Distribution. Periodic Review with Zero Fixed Costs: Base Stock Policies, Periodic Review with Nonzero Fixed Costs: (s, S) Policies, Policy Optimality). Materials requirement planning (MRP)
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
eCourse | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
LANGUAGE OF EVALUATION: Greek
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Ιωάννου, Γ., Διοίκηση Παραγωγής και Υπηρεσιών, Εκδόσεις Α. Σταμούλης, Αθήνα-Πειραιάς, 2005.
- Ξανθόπουλος Αλ., Κουλουριώτης Δημ., Διοίκηση παραγωγής και επιχειρησιακών λειτουργιών: σχεδιασμός, προγραμματισμός και έλεγχος σε συστήματα παραγωγής και υπηρεσιών, Εκδόσεις Τζιολα, 2019.
- Muckstadt, J. A., A. Sapra. Principles of Inventory Management When You Are Down to Four, Order More. Springer, 2010
- Nahmias, S., Production and Operations Analysis, McGraw-Hill: Series in Operations and Decision Sciences, 2009.
- Shenoy D. and R. Rosas. Problems & Solutions in Inventory Management. Springer, 2018
- Shim, J.K. and Siegel, J.G., Διοίκηση Εκμετάλλευσης (μεταφρ.), Εκδόσεις Κλειδάριθμος: Σειρά Οικονομία και Επιχείρηση, Αθήνα, 2002.
- Silver, E. A., D. F. Pike, and R. Peterson. Inventory Management and Production Planning and Scheduling, 3rd ed. Hoboken, NJ: Wiley, 1998.
- Snyder, L. V. and Z-J. M. Shen. Fundamentals of Supply Chain Theory, 2rd ed. John Wiley & Sons, Inc., 2019
- Tersine R. J. Διαχείριση υλικών και συστήματα αποθεμάτων (μεταφρ.), Εκδόσεις Παπαζηση ΑΕΒΕ, 1984
- Zipkin, P. Foundations of Inventory Management. McGraw-Hill/Irwin. 2000.
- Tersine R. J. Διαχείριση υλικών και συστήματα αποθεμάτων (μεταφρ.), Εκδόσεις Παπαζηση ΑΕΒΕ, 1984
- [Περιοδικό / Journal] Production and Operations Management
- [Περιοδικό / Journal] Production Planning and Control.
Non Parametric Statistics - Categorical Data Analysis (MAE835)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ835 |
Semester |
8 |
Course Title |
Non Parametric Statistics- Categorical Data Analysis |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English, reading Course) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The aim of this course is to introduce students to the methods of Non parametric techniques (goodness-of-fit tests, ranks etc) as well as their application to real practical problems. At the end of the course the student should have understood the basic methods of Non-Parametric Statistics and Categorical Data, knowing when to adopt and how to apply them for analyzing data. |
---|---|
General Competences |
|
Syllabus
Empirical distribution function, Goodness of fit tests: Kolmogorov-Smirnov test, Chi-square, Runs test, Sign tests, Wilcoxon - Mann - Whitney test, Kruskal - Wallis test. Correlation coefficients. Categorical Variables. Statistical inference for binomial and multinomial parameters, Contingency Tables, Comparing two proportions, Testing: independence, Symmetry, Homogeneity. 2 x 2 Tables (Exact Fisher's test, McNemar's test). Applications. Loglinear models.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English). |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Agresti, A. (2007). An Introduction to Categorical Data Analysis. 2 ed. ISBN: 978- 0-470-38800-# Wiley
- Conover, W. J. (1999). Practical Nonparametric Statistics. 3 ed. ISBN: 978-0-471- 16068-# John Wiley & Sons
- Ζωγράφος, Κ. (2009). Κατηγορικά Δεδομένα. Πανεπιστήμιο Ιωαννίνων.
- Μπατσίδης, Α. (2010). Εισαγωγή στη Μη Παραμετρική Στατιστική. Πανεπιστήμιο Ιωαννίνων
Computational Statistics (MAE836)
- Ελληνική Έκδοση
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- Department of Mathematics
- Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)
General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ836 |
Semester |
8 |
Course Title |
Computational Statistics |
Independent Teaching Activities |
Lectures-Laboratory (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English, reading Course) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Students completing this course should be able to:
|
---|---|
General Competences |
|
Syllabus
Using R the following topics will be discussed: Generation of random numbers from discrete and continuous distributions. Monte Carlo integration. Using simulation techniques to visualize classical results of statistical inference via simulated data (asymptotic normality of mean, power of a test etc). Density Estimation and Applications (Kernel density estimation). Methods of Resampling ς (Jackknife και Bootstrap). Numerical maximization techniques (Newton-Raphson, Fisher scoring, expectation-maximization [EM]).
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which concentrates on the solution of problems which are motivated by the main themes of the course. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Davison, A. C., Hinkley, D. V., Bootstrap methods and their application. Cambridge University Press 1997.
- Rizzo, M. L., Statistical computing with R. Chapman & Hall/CRC 2007.
- Robert, C. P., Casella, G., Introducing Monte Carlo methods with R. Springer Verlag 2009
Special Topics in Statistics (MAE837)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ837 |
Semester |
8 |
Course Title |
Special Topics in Statistics |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English, reading Course) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Students will become familiar with the themes in question and develop knowledge of statistical methods, and will also learn how the methodology becomes relevant in certain application areas. Students will learn a specialized field of statistics not covered by any ordinary course. |
---|---|
General Competences |
|
Syllabus
The precise contents of this course may vary from occasion to occasion, but will consist of selected themes of contemporary research interest in statistics methodology, depending on both demands from students and the availability of appropriate course leaders. Examples include parametric lifetime modeling, experimental design, extreme value statistics, advanced stochastic simulation, graphical modeling, statistics quality control etc. The course will be of interest to students who want to develop their basic knowledge of statistics methodology. See the specific semester page for a more detailed description of the course.
For the next academic year the syllabus of the course is the following: Multivariate distributions: basic properties. Multivariate normal distribution: properties and estimation. Brief review of multivariate methods of statistical analysis: Principal Components, Factor Analysis, MANOVA, Discriminant Analysis.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom (face-to-face) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final written exam in Greek (in case of Erasmus students in English) which concentrates on the solution of problems which are motivated by the main themes of the course. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Σημειώσεις διδάσκοντα
- Everitt, B., Hothorn, T. (2011) An introduction to Applied Multivariate Analysis with R. Springer.
- Hastie, Tibshirani and Friedman (2009) Elements of Statistical Learning, 2nd edition, Springer.
- James, Witten, Hastie and Tibshirani (2011) Introduction to Statistical Learning with applications in R. Springer.
- B.S. Everitt, S. Landau, M. Leese and D. Stahl (2011) Cluster Analysis, 5th Edition, Wiley.
Special Topics in Probability (MAE838)
Special Topics in Probability (MAE838)
Parallel Algorithms and Systems (MAE840)
- Ελληνική Έκδοση
- Undergraduate Courses Outlines
- Outline Modification (available only for faculty members)
- Department of Mathematics
- Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)
General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE840 |
Semester |
8 |
Course Title |
Parallel Algorithms and Systems |
Independent Teaching Activities |
Lectures-Laboratory (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses |
Introduction to programming, Introduction to Computers, Database Systems and Web applications development |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes(in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Students knowledge acquisition of:
|
---|---|
General Competences |
|
Syllabus
- Historical review of parallel and distributed processing.
- Von Neumann model. Flynn categorization. Tubing. Multiprocessors, Multi-computers.
- Distributed and Shared Memory Systems. Memory architectures for single and non-unified access time.
- Performance calculations and metrics. System scalability, partitioning and optimization. Parallel computer interface networks.
- Law of Grosch, of Amdahl, of Gustafson Barsis. Design of parallel applications.
- Program parallelization - MPI. Synchronization. Dependency charts, shared resources and racing conditions. Scheduling. Shared Memory Affinity. MESI. Parallel Processing using parallella FPGA cores.
- Models and process communication mechanisms. Vector Processing. Arrays and computational grid. Examples of application parallelization. Synchronization issues
Course laboratory part
- Introductory programming concepts using gcc. Pointers, classes, dynamic structures. Creating processes in Linux, separating user-space and kernel-space concepts, parenting processes and parent-child relationships, Process Management.
- Containers, Templates, STL (C++ standard templates library).
- Introduction to Boost and advanced C ++ aspects.
- Introduction to C ++ Armadilo
- Process intercommunication. Static memory areas, pipelines, shared memory areas, process signalling.
- Threads creation and thread management. shared thread memory areas, critical areas, producer-consumer model, threads signalling.
- Thread Management and Synchronization, critical areas protection using mutex locks and semaphores. Presentation of conditional execution threads and sync barriers.
- Introduction to MPI, MPI settings, MPI key features presentation, preliminary MPI programs.
- Presentation of basic modern methods of sending and receiving messages in MPI. Presentation of asynchronous upload methods. Examples.
- Using Gather-Scatter-Reduce-Broadcast Collective Methods and Examples.
- Basic structures for organizing distributed programs. Examples of distributed calculations. Advanced data types using MPI. Creating # Complex Data Structures with MPI And Sending Data Structure Messages.
- Parallel programming OpenMP and Epiphany-SDK, BSP.
Teaching and Learning Methods - Evaluation
Delivery |
Classroom | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Use of Micro-computers Laboratory | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Parallel Scientific Computing in C++ and MPI: A Seamless Approach to Parallel Algorithms and their Implementation, G.M. Karniadakis and R.M. Kirby, 2003, Cambridge University press, ISBN: 0-521-81754-4
- Using OpenMP, Portable Shared Memory Parallel Programming., B. Chapman, G. Jost and R. Pas, 2008, MIT press, ISBN: 9780262533027
- Learning Boost C++ libraries, A. Mukherjee, 2015, PACKT, ISBN:978-1-78355-121-7
- Boost C++ Application Development Cookbook - Second Edition: Recipes to simplify your application development, 2 Edition, A. Polukhin, 2017, PACKT, ISBN:978-1-78728-224-7
- C++17 STL Cookbook, J. Galowicz, PACKT,978-1-78712-049-5, 2017
Special Topics in Computer Science (MAE841)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE841 |
Semester |
8 |
Course Title |
Special Topics in Computer Science |
Independent Teaching Activities |
Lectures, exercises, tutorials (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The aim of the course is to specialize in areas covered by Computer Science in applied fields. It provides background in data and information management. The specialization covers cognitive domains such as Databases, Machine Learning, Artificial Intelligence, Data Mining, etc. It also addresses all issues related to the design and optimization of computer hardware and software. This includes cognitive areas such as Programming Languages and their Implementation, Compilers, Hardware Design, Computer Architecture, Operating Systems, Distributed Systems, and more.
|
---|---|
General Competences |
|
Syllabus
The main objective of the course is to specialize in areas covered by Computer Science in applied fields such as:
- Data Mining
- Artificial Intelligence
- Database Systems
- Security of Information Systems
- Distributed Systems
- Mobile and Wireless Networks
- Pattern Recognition
- Machine Learning
- Signal Processing
The specialized subject will be adapted and specialized according to the necessary developments and requirements.
Teaching and Learning Methods - Evaluation
Delivery |
Lectures | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Use of projector and interactive board during lectures. | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Παπαδόπουλος, Α., Μανωλόπουλος, Ι., Τσίχλας, Κ. 20# Εισαγωγή στην Ανάκτηση Πληροφορίας, Αποθετήριο «Κάλλιπος», 2015.
- Παρασκευάς, Μιχαήλ, Ειδικά θέματα εφαρμογών της Κοινωνίας της Πληροφορίας, Αποθετήριο «Κάλλιπος», 20#
- Δημακόπουλος, Β. Εισαγωγή: Παράλληλα Συστήματα και Προγραμματισμός, Αποθετήριο «Κάλλιπος», 2015.
Special Topics in Numerical Analysis (MAE842)
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ842 |
Semester |
8 |
Course Title |
Special Topics in Numerical Analysis |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
After successful end of this course, students will be able to:
|
---|---|
General Competences |
|
Syllabus
Special subjects of Numerical Linear Algebra coming from Applications. Special subjects of Numerical Solution of Differential Equations coming from Applications.
Teaching and Learning Methods - Evaluation
Delivery |
In the class | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Written examination, Project. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Special Topics in Applied Mathematics (MAE843)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE843 |
Semester |
8 |
Course Title |
Special Topics in Applied Mathematics |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Introduction to computational or theoretical research on acceptable applied mathematics problems and supervision of reading on topics not covered by regular courses of instruction. |
---|---|
General Competences |
|
Syllabus
Depending on the students interests and Instructor availability.
Teaching and Learning Methods - Evaluation
Delivery |
Face to face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Use of computer (Mechanics) lab | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Algorithm Engineering (MAE844)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE844 |
Semester |
8 |
Course Title |
Algorithm Engineering |
Independent Teaching Activities |
Lectures, laboratory exercises, tutorials, quiz (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
This course aims at introducing to students the concepts , techniques, properties, developments and applications of basic and advanced algorithms and data structures.
|
---|---|
General Competences |
|
Syllabus
- Introduction to algorithm engineering
- Methodology of Algorithm Engineering: motivation, applications, software systems
- System checking
- Software reliability and correctness
- STL and Generalized programming
- Experimental evaluation of algorithms
Teaching and Learning Methods - Evaluation
Delivery |
Lectures | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
| ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- K. Mehlhorn and S. Naeher, LEDA: A platform for combinatorial and geometric computing, Cambridge University Press, 1999.
- M. Mueller-Hannemanni and S. Schirra, Algorithm Engineering - Bridging the Gap between Algorithm Theory and Practice, Springer 2010.
- C.C. McGeoch, A Guide to Experimental Algorithmics, Cambridge University Press, 2012.
- J. Siek, L.Q. Lee, and A. Lumsdaine, The Boost Graph Library, Addison-Wesley, 2002.
- M.A. Weiss, Data structures and problem solving with C++, 2 Edition, Addison-Wesley, 2000.
Introduction to Natural Languages Processing (MAE845)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE845 |
Semester |
8 |
Course Title |
Introduction to Natural Language Processing |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The goal of this course is the deeper understanding of Natural Language Processing (NLP). During the course a detailed examination of the following topics are done:
After completing the course the student can handle:
which related to NLP different topics. |
---|---|
General Competences |
|
Syllabus
- A historical retrospection of Language Technology evolution
- The goal of NLP and its Applications
- The NLP levels. Language Processors such as recognition machines, transducers, parsers and generators
- The language as a rule based system. Language Understanding as process
- NLP Resources for parsing, such as Data Base, Knowledge Base, Data Structure, Algorithms and Expert Systems
- Fundamental parsing strategies concerning context free grammars.
- Fundamental Methods of Computational Morphology, Computational Semantics and NLP. Implementations-Applications
Teaching and Learning Methods - Evaluation
Delivery |
Face to face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Yes , Use of Natural Language and Mathematical Problems Processing Laboratory | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final test |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Mitkov Ruslan, The Oxford Handbook of Computational Linguistics. ISBN 0-19-823882
- Jurafsky Daniel & Martin H. James, Speech and Language Processing - An Introduction to Ntural Language Proocessing, Computational Linguistics and Speech Recognition. ISBN 0-13-095069-6
- Allen James, Natural Language Understanding. ISBN 0-8053-0334-0,
- Natural Language Generation ed. by Gerard Kempen. ISBN 90-247-3558-0
- Professor's Notes.
Introduction to Expert Systems (MAE846)
- Ελληνική Έκδοση
- Undergraduate Courses Outlines
- Outline Modification (available only for faculty members)
- Department of Mathematics
- Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)
General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE846 |
Semester |
8 |
Course Title |
Introduction to Expert Systems |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses |
Logic Programming, Data Structure |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The goal of this course is the deeper understanding of PROLOG. During the course a detailed examination of the following topics are done:
After completing the course the student can handle:
|
---|---|
General Competences |
|
Syllabus
- Ιntroduction to Expert Systems
- Main Features of Expert Systems, classic examples
- Knowledge acquisition and verification, knowledge representation, inference and interpretation, consistency and uncertainties.
- Inference techniques
- Rule-based forward chaining Expert Systems
- Rule-based backward chaining Expert Systems
- Rule-based Expert Systems
- Expert Systems tools
- Users Interface
- Machine learning, decision making machines, Expert Systems examples.
Teaching and Learning Methods - Evaluation
Delivery |
Face to face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Yes , Use of Natural Language and Mathematical Problems Processing Laboratory | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Final test |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Γεώργιος Ι. Δουκίδης, Μάριος Κ. Αγγελίδης, "Έμπειρα συστήματα, τεχνητή νοημοσύνη και LISP", ISBN 960-08-0004-9, ISBN-13 978-960-08-0004-3
- Σπύρος Τζαφέστας, "ΕΜΠΕΙΡΑ ΣΥΣΤΗΜΑΤΑ ΚΑΙ ΕΦΑΡΜΟΓΕΣ", ISBN: - (Κωδικός Βιβλίου στον Εύδοξο: 89871)
- Παναγιωτόπουλος Ιωάννης - Χρήστος Π., "Νέες Μορφές Τεχνολογίας - Γενικευμένα Αυτόματα Συστήματα - Έμπειρα Συστήματα Turbo Prolog"
Fluid Mechanics (MAE847)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ847 |
Semester |
8 |
Course Title |
Fluid Mechanics |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
This course is an introduction to the basic concepts of Fluid Mechanics. Upon successful completion of the course, the student will be able to:
|
---|---|
General Competences |
The course aims to enable the student to be able analyze and synthesize basic knowledge of Fluid Mechanics and Applied Mathematics.
|
Syllabus
- Physical properties of fluids
- Static of fluids
- Kinematics of fluids
- Conservation of mass - continuity equation and Stream function
- Differential equations of motion for ideal fluids - Euler equations, Differential equations of motion for viscous fluids - Navier-Stokes equations
- Applications of Fluid Mechanics.
Teaching and Learning Methods - Evaluation
Delivery |
| ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Use of computer (Mechanics) lab | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- ---
Scientific Computing (MAE848A)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE848A |
Semester |
8 |
Course Title |
Scientific Computing |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
In most scientific disciplines, the integration of computers has defined new directions to perform research and has offered unprecedented potential to solve complicated problems. Combined with theory and experimentation, computational analysis is nowadays considered an integral part of science and research.
|
---|---|
General Competences |
The course aims to enable the student to:
|
Syllabus
- Initial Value Problems
- Boundary Value Problems
- Finite Difference method
- Equations of Difference
- Shooting methods and Method of undetermined coefficients
- One-step Methods (Euler, Taylor, Runge-Kutta)
- Multi-step Methods (Adams-Bashforth, Adams-Moulton, Predictor-Corrector)
- Finite Element Method (Galerkin).
Teaching and Learning Methods - Evaluation
Delivery |
In the laboratory | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Use of scientific computing software packages | ||||||||||||
Teaching Methods |
| ||||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Numerical Methods for Ordinary Differential Equations, 2 Edition, G.D. Akrivis, V.A. Dougalis, 2012 (in Greek).
- A Primer on Scientific Programming with Python, H. P. Langtangen, Springer-Verlag Berlin Heidelberg, 5 Edition, 2016.
- Programming for Computations- MATLAB/Octave, S. Linge, H. P. Langtangen, Springer International Publishing, 2016 (in Greek).
- The Mathematical Theory of Finite Element Method, S. C. Brenner, L. R. Scott, Springer-Verlag, New York, 2008.
- Automated Solution of Differential Equations by the Finite Element Method, A. Logg, K.-A. Mardal, G. N. Wells, Springer-Verlag Berlin Heidelberg, 2012.
Calculus of Variations (MAE849)
- Ελληνική Έκδοση
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- Department of Mathematics
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE849 |
Semester |
8 |
Course Title |
Calculus of Variations |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses |
Classical Mechanics |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Calculus of Variations deals with optimisation problems where the variables, instead of being finite dimensional as in ordinary calculus, are functions. This course treats the foundations of calculus of variations and gives examples on some (classical and modern) physical applications. After successfully completing the course, the students should be able to:
|
---|---|
General Competences |
|
Syllabus
The Euler-Lagrange equation. The brachistochrone problem. Minimal surfaces of revolution. The isoperimetric problem. Fermat's principle (geometric optics). Hamilton's principle. The principle of least action. The Euler-Lagrange equation for several independent variables. Applications: Minimal surfaces, vibrating strings and membranes, eigenfunction expansions, Quantum mechanics: the Schrödinger equation, Noether's theorem, Ritz optimization, the maximum principle.
Teaching and Learning Methods - Evaluation
Delivery |
Face to face | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | Yes | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- Calculus of Variations, I. M. Gelfand and S. V. Fomin, Dover Publications, 2000.
- Εφαρμοσμένα Μαθηματικά, D. J. Logan, Πανεπιστημιακές Εκδόσεις Κρήτης, 2010.
- Θεωρητική Μηχανική, Π. Ιωάννου και Θ. Αποστολάτος, ΕΚΠΑ, 2007.
Seminar in Differential Equations (MAE852)
- Ελληνική Έκδοση
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- Outline Modification (available only for faculty members)
- Department of Mathematics
- Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)
General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ852 |
Semester |
8 |
Course Title |
Seminar in Differential Equations |
Independent Teaching Activities |
Lectures (Weekly Hours: 3, Credits: 6) |
Course Type |
Special Background |
Prerequisite Courses | None. However it is desirable to have a strong knowledge of basic notions of differential equations. |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
No |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The report can be, but not required to be, original. Further details can be determined by the teaching professor. |
---|---|
General Competences |
Further details can be determined by the teaching professor. |
Syllabus
In depth study in a scientific subject related to differential equations, ordinary or partial or stochastic. For example, subjects related to existence and uniqueness of solutions, qualitative theory, methods of finding solutions, tools and theory from other fields of mathematics which can be used to study differential equations, and applications. Further details can be determined by the teaching professor.
Teaching and Learning Methods - Evaluation
Delivery |
Details will be determined by the teaching professor. Methods include presentations contacted by the students. | ||||||||
---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Details will be determined by the teaching professor. | ||||||||
Teaching Methods |
| ||||||||
Student Performance Evaluation |
Other means of evaluation can be determined by the teaching professor. |
Attached Bibliography
Bibliography is suggested by the teaching professor, depending on the subject under study.
Numerical Solution of Partial Differential Equations (MAE882)
- Ελληνική Έκδοση
- Undergraduate Courses Outlines
- Outline Modification (available only for faculty members)
- Department of Mathematics
- Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)
General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE882 |
Semester |
8 |
Course Title |
Numerical Solution of Partial Differential Equations |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special background, skills development. |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
Upon successful completion of the course, students will be able to:
|
---|---|
General Competences |
|
Syllabus
- Finite difference approximations to derivatives.
- The two-point boundary value problem. Boundary conditions of type Dirichlet, Neumann, and Robin.
- Finite differences schemes for the two-point boundary value problem. Consistency and stability. The energy method. Order of accuracy and convergence.
- The Finite Element Method (FEM) for the two-point boundary value problem. A priori and a posteriori estimates. Implementation of FEM.
- Finite differences and Finite element methods for the Heat Equation in 1D. Explicit- and implicit Euler, the Crank-Nicolson method. Consistency and stability.
- The finite element method for elliptic and parabolic equations in higher dimensions.
Teaching and Learning Methods - Evaluation
Delivery |
Face-to-face. | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
| ||||||||||||
Teaching Methods |
| ||||||||||||
Student Performance Evaluation |
|
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- “Αριθμητική επίλυση μερικών διαφορικών εξισώσεων”, Π. Χατζηπαντελίδης, & Μ. Πλεξουσάκης, Κάλλιπος, (2015). http://hdl.handle.net/11419/665
- “Αριθμητικές Μέθοδοι για Συνήθεις Διαφορικές Εξισώσεις”, Γ. Δ. Ακρίβης, & Β. Α. Δουγαλής., Πανεπιστημιακές Εκδόσεις Κρήτης, Ηράκλειο, 2η έκδοση, 2013.
- “The mathematical theory of finite element methods”, S. C. Brenner & L. R. Scott (Third ed., Vol. 15), Springer, New York, 2008.
- “Partial differential equations with numerical methods”, S. Larsson, & V. Thomée, Springer-Verlag, Berlin, 2009.