Mathematics 409 - The p-Adic Numbers

The p-adic numbers provide an alternative completion of the rational numbers, one for each prime p, and play a central role in modern number theory. While they share formal similarities with the real numbers, p-adic fields exhibit fundamentally different algebraic, analytic, and topological behavior. This course develops the theory of p-adic numbers from first principles, emphasizing rigorous proofs and the interaction between algebraic structure and analysis. Topics include the construction of p-adic fields, their basic analytic properties, and key structural results that distinguish the p-adic setting from the classical real case.

Fall semester. Professor Daniels.

How to handle overenrollment: Priority determined by seniority.

Students who enroll in this course will likely encounter and be expected to engage in the following intellectual skills, modes of learning, and assessment: May include problem sets, in-class quizzes or exams, take-home exams, and final projects.