MATH463 GROUP THEORY
| Course Code: | 2360463 |
| 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
This course aims
· to teach the concepts listed in the Catalog Description such as group, group homomorphism, subgroup and quotient group, Isomorphism Theorems, group actions , Sylow Theorems and their applications, solvable groups, nilpotent groups.
· to improve the proficiency in dealing with abstract concepts, and writing down simple proofs.
· to improve the proficiency in giving examples of the abstract concepts.
Course Content
Group, subgroup, normal subgroup, cyclic subgroup, coset, quotient group. Commutator subgroup, center, homomorphism and isomorphism theorems (invariant subgroup, wreath products), Abelian groups. Free abelian group, rank of an abelian group. Divisible abelian group, periodic Abelian group. Sylow Theorems and their applications, soluble groups, nilpotent groups.
Course Learning Outcomes
By the end of the course the students are expected to be able to:
* understand the statements of the theorems, and write the missing arguments for difficult theorems when an outline of a proof is given, also write the proofs of important theorems whose proofs are simple .
* give examples and counterexamples illustrating the mathematical concepts presented in the course.
* use basic theorems of group actions in a given setting.