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Specialized Topics in Algebra (ΑΛ6): Διαφορά μεταξύ των αναθεωρήσεων

Specialized Topics in Algebra (ΑΛ6): Διαφορά μεταξύ των αναθεωρήσεων

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[[Graduate Courses Outlines]] - [https://math.uoi.gr  Department of Mathematics]
* [[Ειδικά Θέματα Άλγεβρας (ΑΛ6)|Ελληνική Έκδοση]]
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=== General ===
=== General ===
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! Course Type
! Course Type
| General Background
| Special Background
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! Prerequisite Courses
! Prerequisite Courses
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! Learning outcomes
! Learning outcomes
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The main purpose of the course is to introduce the student to the basic concepts, results, tools and methods of the Representation Theory of Finite Groups and its applications to other areas of Mathematics, mainly in Group Theory, and other related sciences, e.g. in Physics.
The aim of the course is for the postgraduate student to reach a good level of theoretical background on topics related to the theory of commutative rings.
 
At the end of the course, we expect the student to understand the basic concepts and the main theorems that are analysed in the course, to understand how these are applied to concrete examples arising from different thematic areas of Mathematics and related sciences, to be able to apply them to derive new elementary consequences in various fields, and finally to be able to perform some (not so obvious) calculations related to several problems arising in Group Theory.  
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! General Competences
! General Competences
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The course aims at enabling the graduate student to acquire the ability to analyse and synthesize basic knowledge of the basic Representation Theory of Finite Groups, which is an important part of modern Mathematics with numerous applications to other sciences, for instance in Physics.  When the graduate student comes in for the first time in connection with the basic notions of representation theory and its applications to group theory, (s)he strengthens her/his creative, analytical and inductive thinking, and her/his ability to apply abstract knowledge in different areas of central interest in Mathematics and related sciences.
The aim of the course is to empower the postgraduate student to analyse and compose basic notions of Commutative Algebra.
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=== Syllabus ===
=== Syllabus ===


ΧΧΧ
Topics of Commutative and Combinatorial Algebra:  Hilbert's Basis theorem, Primary Decomposition, Localization, Dimension, Hilbert Series, Groebner Bases, Simplicial complexes and homology, Stanley-Reisner ideals, Hilbert's Nullstellensatz theorem.


=== Teaching and Learning Methods - Evaluation ===
=== Teaching and Learning Methods - Evaluation ===
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! Delivery
! Delivery
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Face to face
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! Use of Information and Communications Technology
! Use of Information and Communications Technology
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! Teaching Methods
! Teaching Methods
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| ΧΧΧ
| Study of theory
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| ΧΧΧ
| Solving of Exercises
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| 70.5
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| Course total  
| Course total  
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! Student Performance Evaluation
! Student Performance Evaluation
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Written exam at the end of semester (obligatory), problem solving or/and intermediate exams (optional)
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Τελευταία αναθεώρηση της 16:28, 15 Ιουνίου 2023

General

School School of Science
Academic Unit Department of Mathematics
Level of Studies Graduate
Course Code ΑΛ6
Semester 2
Course Title Specialized Topics in Algebra
Independent Teaching Activities Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
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 for the postgraduate student to reach a good level of theoretical background on topics related to the theory of commutative rings.

General Competences

The aim of the course is to empower the postgraduate student to analyse and compose basic notions of Commutative Algebra.

Syllabus

Topics of Commutative and Combinatorial Algebra: Hilbert's Basis theorem, Primary Decomposition, Localization, Dimension, Hilbert Series, Groebner Bases, Simplicial complexes and homology, Stanley-Reisner ideals, Hilbert's Nullstellensatz theorem.

Teaching and Learning Methods - Evaluation

Delivery

Face to face

Use of Information and Communications Technology -
Teaching Methods
Activity Semester Workload
Lectures 39
Study of theory 78
Solving of Exercises 70.5
Course total 187.5
Student Performance Evaluation

Written exam at the end of semester (obligatory), problem solving or/and intermediate exams (optional)

Attached Bibliography

  • Μαλιάκας Μιχάλης, Εισαγωγή στην Μεταθετική Άλεβρα, Εκδόσεις Σοφία, 2008
  • Atiyah, M. F.; Macdonald, I. G., Introduction to commutative algebra. Addison-Wesley Publishing Co., 1969 ix+128 pp.
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