MATH268 ABSTRACT ALGEBRA II
| Course Code: | 2360268 |
| 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 fundamental notions of abstract algebra. The student is expected to understand and process the basics of algebraic structures, specifically basics of rings and fields. Objectives include the ability to follow and understand proofs of standard theorems of abstract algebra.
Course Content
Rings, integral domains, fields. Subrings and ideals. Quotient rings. Ring homomorphisms. Prime and maximal ideals. Field of fractions. Principal ideal domains, Euclidean domains, Unique factorization domains. Polynomial rings: Factorization in polynomial rings, Euclidean algorithm in polynomial rings over fields. Field Extensions, extension degrees, algebraic and transcendental elements. Geometric constructions. Finite Fields.