Algebra II (ΑΛ2)
Graduate Courses Outlines - Department of Mathematics
General
| School | School of Science |
|---|---|
| Academic Unit | Department of Mathematics |
| Level of Studies | Graduate |
| Course Code | ΑΛ2 |
| Semester | 2 |
| Course Title | Algebra II |
| Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, 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 main purpose of the course is to introduce the main concepts, tools and methods of Commutative Algebra, and to indicate some of its direct applications to various areas of Mathematics, most notably in Algebraic Geometry, and related sciences. 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 of algebraic and geometric origin, to be able to apply them to derive new elementary consequences in various related fields, and finally to be able to perform some (not so obvious) calculations related to the thematic core of the course. |
|---|---|
| General Competences |
The course aims at enabling the graduate to acquire the ability to analyse and synthesize basic knowledge of Commutative Algebra, which is an important part of modern Mathematics, in particular of contemporary Algebra and Geometry. When the graduate comes in for the first time in connection with the basic notions of Commutative Algebra and its applications to Algebraic Geometry, (s)he strengthens her/his creative, analytical and inductive thinking, and her/his ability to apply abstract knowledge in related fields. |
Syllabus
- Introduction to Algebraic Geometry.
- Dimension.
- Krull’s Principal Ideal Theorem.
- Regular sequences.
- Depth.
- Cohen-Macaulay rings.
- Gorenstein rings.
- Free resolutions.
- Hilbert functions.
Teaching and Learning Methods - Evaluation
| Delivery |
Face to face | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology | - | ||||||||||
| Teaching Methods |
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| Student Performance Evaluation |
The evaluation is based on the combined performance of the graduate student in:
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Attached Bibliography
- J.P. Serre: “Linear Representations of Finite Groups”, Springer-Verlag, (1977).
- B. Steinberg: “Representation Theory of Finite Groups: An Introductory Approach”, Springer, (2012).
- C.W. Curtis and V. Reiner: “Methods of Representation Theory: With Applications to Finite Groups and Orders”, Wiley, (1981).
- P. Etingof et al: “Introduction to Representation Theory”, Student Mathematical Library 59, AMS, (2011).
- J.L. Alperin and R.B. Bell: “Groups and Representations”, Springer (1995).
- M. Burrow: “Representation Theory of Finite Groups”, Academic Press, (1965).
- M. Liebeck and G. James: “Representations and Characters of Groups”, CUP, (2001).