MATH708 ADVANCED LINEAR ALGEBRA
| Course Code: | 2360708 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. GÜLİN ERCAN |
| Offered Semester: | Fall Semesters. |
Course Objectives
This course is a thorough introduction to linear algebra for the graduate or advanced undergraduate students. We discuss modules, emphasize a comparison between the properties of modules and those of vector spaces, and provide more on modules. One of the main goals is to prove that any two bases of a free module have the same cardinality and to introduce noetherian modules. We also introduce the theory of modules over a principal ideal domain, establishing the cyclic decomposition theorem for finitely generated modules. This theorem is the key to the structure theorems for finite dimensional linear operators. The rest of the course is devoted to metric vector spaces, where we describe the structure of symplectic and orthogonal geometries, and a brief intruction to tensor products.
Course Content
Courses not listed in catalogue. Contents vary from year to year according to interest of students and instructor in charge. Typical contents include contemporary developments in Algebra, Analysis, Geometry, Topology, Applied Mathematics.
Course Learning Outcomes
At the end of the course, students are expected to understand:
- the theory of modules over a principal ideal domain
- the structure of symplectic and orthogonal geometries over various base fields
- the universal property of tensor products
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 | Gains academic maturity through self-study. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Carries out parts of a mathematical research program independently. | ✔ | |||
| 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 | Gets exposed to academic culture through interaction with others. | ✔ | |||
| 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