Course Language:

English

Course Objectives:

To teach as much about rings and fields as one can in a first course to constitute a firm foundation for more specialized work and to provide valuable experience for any further axiomatic study of mathematics.

Course Content:

Rings. Integral domains. Fermat's and Euler's theorems. Quotient field of an integral domain. Rings of polynomials. Factorization of polynomials over a field. Noncommutative rings. Ring homomorphisms and factor rings. Prime and maximal ideals. Unique factorization domains. Field extensions. Algebraic extensions. Geometric constructions. Finite fields.

Course Methodology:

1: Lecture, 2: Problem Solving

Course Evaluation Methods:

A: Written examination, B: Homework