Symbolic Computations (ΠΛ5)
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General
| School | School of Science |
|---|---|
| Academic Unit | Department of Mathematics |
| Level of Studies | Graduate |
| Course Code | ΠΛ5 |
| Semester | 2 |
| Course Title | Symbolic Computations |
| Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
| Course Type | Specialization |
| Prerequisite Courses |
Undergraduate courses in Data structures, Design and Analysis of Algorithms, Algebraic Structures, (optionally a course in Discrete Mathematics). |
| 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 purpose of the course is an in-depth study of computer algebra and the algorithms used for the symbolic processing of mathematical expressions. The goal is the understanding of the algorithms and the applications of computer algebra and the training of the students in critical thinking for problem solving as well as the research process. Many basic computer algebra algorithms as well as advanced ones are examined and analyzed. Application of these algorithms is also discussed. With the completion of the course the student:
|
|---|---|
| General Competences |
|
Syllabus
- Introduction to computer algebra
- Symbolic computations compared to numerical computations.
- Basic algebraic structures.
- Representation of numbers, polynomials (one or many variables), rational expressions, functions, series.
- Simplifications of symbolic mathematical expressions.
- Basic algorithms: Greatest common devisor, Chinese remainder algorithm.
- Basic operations and algorithms on integers and polynomials.
- Integer and polynomial factorization.
- Modular algorithms.
- Linear algebra algorithms, solution of equations and systems.
- Gröbner bases and applications.
- Algorithms for symbolic integration and summation.
- Symbolic solution of differential equations.
- Software systems for the symbolic manipulation of mathematical expressions.
- Special topics
Teaching and Learning Methods - Evaluation
| Delivery |
Face to face | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology | Yes | ||||||||||
| Teaching Methods |
| ||||||||||
| Student Performance Evaluation |
Final exam (40%) comprised of:
Exercises - problem solution, programming using computer algebra software (30%). Presentations of related topics (30%). |
Attached Bibliography
- Joel S. Cohen, "Computer Algebra and Symbolic Computation: Elementary Algorithms" Publisher: A K Peters/CRC Press, 2002
- Joel S. Cohen, "Computer Algebra and Symbolic Computation: Mathematical Methods" Publisher: A K Peters/CRC Press, 2003
- Keith O. Geddes, Stephen R. Czapor, George Labahn, “Algorithms for Computer Algebra”, Springer, 1992
- Davenport, J.H. and Siret, Y. and Tournier, E., Copmuter Algebra: Systems and Algorithms for Algebraic Computation, Academic Press, 1988.
- Akritas, A., Elements of Computer Algebra with Applications, Jhon Wiley, 1989,
- Modern Computer Algebra, Second Edition Joachim Von Zur Gathen, Juergen Gerhard Cambridge University Press, Cambridge, 2003.
- Computer algebra handbook. Foundations. Applications. Systems. Edited by Johannes Grabmeier, Erich Kaltofen and Volker Weispfenning. Springer-Verlag, Berlin, 2003.
- http://www.journals.elsevier.com/journal-of-symbolic-computation/