MATH 510 — Advanced Number Theory
Number theory, which is one of the most ancient branches of mathematics and continues to be an active area of research, is the study of integers, the most basic structure of mathematics, and many of their fascinating properties. For example, it has a major recent day application in communications and cryptography. Topics include proof by induction, divisibility, primes, uniqueness of factorization, congruencies, Chinese Remainder Theorem, Cryptography, Pythagorean triples and other Diophantine equations, Pells Equation, primarily testing, factoring methods, primitive roots, perfect numbers, rational versus irrational, and continued fractions, quadratic congruencies, and quadratic reciprocity. The required preparation for this course is an undergraduate major in mathematics or mathematics education.