MATH 509 Algebraic Number Theory
The study of number theory using algebraic techniques. Topics include extension fields of rational numbers, algebraic integers, non-uniqueness of factorization of algebraic integers, quadratic and cyclotomic number fields, primes and units in algebraic number fields, integral bases, uniqueness of factorization into prime ideals, class numbers and their relationship to Fermat's last theorem. Prerequisite: 508.