MA 403 - Introduction to Modern Algebra
Fall 2003


Text: A Concrete Introduction to Higher Algebra, 2nd edition by Lindsay N. Childs


Week 1 - Numbers, Induction and Euclid Algorithm

Week 2 - Bezout's Identity, Unique Factorization and the Fundamental Theorem of Arithmetic

Week 3 - Primes, Exponential Notation and Infinity of Primes

Week 4 - Clock Arithmetic, Congruences and Basic Properties of Congruence Modulo M.

Week 5 - Congruence Classes, Arithmetic Modulo M. Complete Sets of Representatives and Units, Application of Congruences.

Week 6 - Fiends and Rings

Week 7 - Homomorphisms

Week 8 - Fermat's and Euler's Theorems

Week 9 - Application of Fermat's and Euler's Theorems

Week 10 - Groups, agrange's Theorem, Some Non-Abelian groups.

Week 11 - The Chinese remainder Theorem, Product of Rings and Euler's O - function

Week 12 - Polynomials

Week 13 - Division Theorem, Primitive Roots, Factorization Into Irreducible Polynomials

Week 14 - The Fundamental Theorem of Algebra Irreducible Polynomials over the Ring of Integers

Week 15 - Irreducible Polynomials over a Finite Field. Every Finite Field has the order pn for some prime p and a positive integer n.