Undergraduate Seminar (395-0-1)

Instructors

Maria Nastasescu

Meeting Info

Lunt Hall 104: Mon, Wed, Fri 12:00PM - 12:50PM

Overview of class

Title: The Distribution of Primes

Prime numbers appear irregularly distributed among the integers, yet collectively they obey remarkably precise asymptotic laws. This seminar surveys analytic and sieve methods for studying the primes. We will familiarize ourselves with some classical results, such as the Prime Number Theorem and its connection to the Riemann Hypothesis and get a glimpse of combinatorial tools behind modern work on primes in intervals and twin primes. Students will present selected topics, and those with a more advanced background will have the opportunity to explore special topics, if desired.

The study of prime numbers connects many areas of mathematics, including real analysis, complex analysis, harmonic analysis, combinatorics, and probability theory. The course assumes no knowledge beyond basic real analysis.

Prerequisite: Math 320-1 and experience with proofs, or instructor's permission.

Class Materials (Required)

No required materials. See suggested materials.

Class Materials (Suggested)

Introduction to Analytic Number Theory
Tom M. Apostol
Springer
978-0387901633

Analytic Number Theory Revealed - A first guide to prime numbers
Andrew Granville
AMS
978-1470481520

Class Attributes

Advanced Expression
SoC Additional Distro

Enrollment Requirements

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