MATH464 INTRODUCTION TO REPRESENTATION THEORY
| Course Code: | 2360464 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 6.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Prof.Dr. AHMET İRFAN SEVEN |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of this course, the student will learn:
- basic concepts used in representation theory, such as modules, decomposing modules, into irreducibles
- computing character tables
- obtaining information about the group from the character table of the group
Course Content
Group representations, FG-Modules, Machke Theorem, irreducible modules and group algebras, characters, inner products of characters, the number of irreducible characters, character table, induced modules and characters, algebraic integers and real representations.
Course Learning Outcomes
Student, who passed the course satisfactorily will be able to:
- state and use Schur`s Lemma and Maschke`s Thorem
- compute tha character table of some groups
- derive information about the group from its character table
- decompose a given module as a direct sum of irreducible ones
- understand the importance and usefullness of linear algebra
- construct modules over group algebras
- determine irreducibility of a given module
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Can produce innovative thoughts and products. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Has a comprehension of mathematical symbols, concepts together with the interactions among them and can express his/her solutions similarly. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Is responsive to life-long learning, improving his/her skills and abilities | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution