Modern Algebra. (3-0) 3 Credit Hours

Catalog description

Prerequisite: MAT 3003 . An introduction to modern algebra building up from concrete examples in elementary algebra and number theory which lead to the abstract theory of groups, rings, and fields. Topics include arithmetic congruences in the ring of integers; residue rings modulo n; finite fields; the group of units; cyclic groups; the Chinese Remainder Theorem, Fermat’s and Euler’s theorems; polynomial rings; the Fundamental Theorem of Algebra; irreducible polynomials and factorization in polynomial rings; and quotient rings and construction of the Galois fields. This course has Differential Tuition.