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

Αναθεώρηση της 14:27, 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.

@@ Γραμμή 58: / Γραμμή 58: @@
 === 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 ===