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

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=== Syllabus ===
=== Syllabus ===


* Representations and characters of groups.
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.
* Groups and homomorphisms.
* FG-modules και group-algebras.
* Schur’s Lemma and Maschke’s Theorem.
* Group-algebras and irreducible modules.
* Conjugacy classes and characters.
* Character tables and orthogonality relations.
* Normal subgroups and lifted characters.
* Elementary examples of characters tables.
* Tensor products. Restricting representations to subgroups.
* Applications.


=== Teaching and Learning Methods - Evaluation ===
=== Teaching and Learning Methods - Evaluation ===

Αναθεώρηση της 13:27, 24 Νοεμβρίου 2022

Graduate Courses Outlines - Department of Mathematics

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
Student's study Hours 78
Exercises: Problem Solving 70.5
Course total 187.5
Student Performance Evaluation

The evaluation is based on the combined performance of the graduate student in:

  • Weekly homeworks,
  • Presentations during the semester,
  • Major Homework at the end of the course,
  • Written examination at the end of the courses in Greek with questions and problems of development of theoretical topics and problem solving.

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.