MATH267 ABSTRACT ALGEBRA I
| Course Code: | 2360267 |
| METU Credit (Theoretical-Laboratory hours/week): | 4 (3.00 - 2.00) |
| ECTS Credit: | 7.5 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
At the end of the course students are expected to learn the fundemental notions of abstract algebra. The student is expected to understand and process the basics of algebraic structures, specifically basics of group theory. Objectives include the ability to follow and understand proofs of standard theorems of abstract algebra.
Course Content
Binary Operations, Groups, Subgroups, Subgroups generated by a set, Cyclic groups (generators and subgroups), Cosets and Lagrange?s Theorem. Normal Subgroups and Quotient groups, Homomorphisms and Isomorphisms, Permutation groups, Finite symmetric groups, Group actions, The orbit Stabilizer Theorem, Cayley?s Theorem, Conjugacy classes and the class equation, Cauchy?s theorem, Sylow theorems, Direct products, The fundamental theorem of finite abelian groups.
Course Learning Outcomes
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