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Undergraduate Seminar (395-0-71)

Instructors

Nir Avni
847 4915575
Lunt Hall Rm. 213

Meeting Info

Lunt Hall 103: Mon, Wed, Fri 1:00PM - 1:50PM

Overview of class

Title: "The Arithmetic of Quadratic Forms"

Description:
A quadratic form over a commutative ring R is a homogeneous polynomial of degree 2 in R[x_1,...,x_n]. One of the main goals of this course will be a classification of quadratic forms over Q, originally due to Minkowski. Along the way, we will introduce fundamental concepts like the p-adic numbers, quadratic reciprocity, and the Riemann zeta function and prove other number theoretic results such as Lagrange's four-square theorem and Dirichlet's theorem on primes in arithmetic progressions. Other topics can be covered depending on student interests (for example, we could go further with analytic methods).

Prerequisites: Math 331-3. No previous experience with number theory is assumed.

Class Materials (Required)

No textbook required

Class Materials (Suggested)

No materials suggested.

Enrollment Requirements

Enrollment Requirements: Registration in this course is reserved for students who are majoring or minoring in Mathematics. Registration in this course is reserved for students who are majoring or minoring in Mathematics.