Almost your entire mathematical life has been spent on the real line and in real space working with real numbers. Some have dipped into complex numbers, which are just the real numbers after you throw in i. Are these the only numbers that can be built from the rationals? The answer is no. There are entire parallel universes of number that are totally unrelated to the real and complex numbers. Welcome to the world of p-adic analysis-where arithmetic replaces the tape measure and numbers take on a whole new look. Here we will explore this new notion of number and discover its impact on arithmetic, geometry, and calculus. It turns out that p-adic analysis not only dramatically simplifies many mathematical areas but also provides a powerful tool for analyzing number theoretic issues. Format: lecture/seminar. Evaluation will be based primarily on homework, examinations, and class participation. Prerequisites: Mathematics 312 and either Mathematics 301 or Mathematics 305; or permission of instructor, no number theory background is required. No enrollment limit (expected: 20).