# Math 499: Introduction to p-adic Numbers

## Wednesday 12:00-1:00, Herman Brown 453

**Description:** This class will explore the different descriptions of p-adic numbers. p-adic numbers appear throughout mathematics, and we will focus on their applications to number theory and geometry. Each class will begin with a short lecture followed by exercises. In the exercise session small groups will work on problems and examples related to the lecture. There will be some problems requiring minimal prerequistes, and others that require a decent amount of algebra. As such, this seminar will be accessible to a wide range of students.

**Some topics we will explore:**
- Descriptions of p-adic numbers
- Finite Fields
- Hensel's Lemma
- Elementary p-adic Analysis
- p-adic Fields
- Hasse Principle

**Optional Textbook:*** p-adic Numbers, * Fernando Gouvea

**Contact Information & Office Hours:**
- Brad Duesler
**Office:** Herman Brown 14 (basement)
**Hours:** MW 3-4
**Phone:** (713)348-4598
**Email:** brd4790@rice.edu
**Webpage:** http://www.ruf.rice.edu/~brd4790