MAT 444-01 - Senior Seminar: Introduction to p-Ardic Numbers

4 credits (Spring)

In the late 19th century, mathematicians discovered the bizarre field of so-called “p-adic numbers”. In contrast to the fields of real and complex numbers, the structure of the p-adic field — and the way analysis works within it — is intimately related to the primes. Since their discovery, p-adic numbers have played key roles in major advances in number theory, including the proof of Fermat’s Last Theorem and the ongoing attempts to prove the Riemann Hypothesis. In this course we will construct the p-adic numbers, investigate the striking relationships between their algebraic and topological structures, and compare/contrast p-adic analysis with real analysis. This course will heavily rely on the MAT 316 and MAT 321 course material, involve presentations, and conclude with projects that further explore the applications and strange features of p-adic numbers.

Prerequisite: MAT 321 with grade S, c, or better. MAT 316 highly recommended.
Note: Plus-2 option available.
Instructor: Webster