Analytic Number Theory – Mathematical Association of America

Featured Resources

Calculus for Teachers: Complex Integration

By David Bressoud @dbressoud As of 2024, new Launchings columns appear on the third Tuesday of the month. Once we get into complex integration, the theorems become much more technical, so in most cases I will simply state the result, possibly with some indication of why it makes sense that it would be true. For anyone...

Low Stakes, High Rewards: How a Corequisite Course Improved Student Performance in Intro to Proofs

By Ekaterina Yurasovskaya With its highly abstract material and proof-writing that students encounter for the first time, Introduction to Proofs often turns into a gatekeeper to a mathematics major. At the Mathematics Department at Seattle University, we achieved significant results by creating a lecture-free, problem-solving ungraded co-requisite course called Mathematical Communication and Reasoning (MCR). The new...

An Introduction to the Circle Method

The circle method is a technique, originated by Ramanujan, to estimate the coefficients in a generating function by expressing the coefficient in terms of an integral of the function around the unit circle in the complex plane and estimating the integral. It has been successfully applied to many problems in additive number theory, including Waring’s Problem and the ternary Goldbach Conjecture...

Analytic Number Theory for Beginners

Analytic Number Theory for Beginners by Prapanpong Pongsriiam covers a lot of material in under 400 pages. It is primarily a graduate textbook. It could be used as an undergraduate text: roughly speaking the first third of the book is undergraduate material and the remaining two thirds is graduate-level material, but the writing is a bit terse for an undergraduate text....

Steps into Analytic Number Theory

This book is full of interesting problems and results, most of them not found in books. It is structured as a problem book, with problems in the front and solutions in the back. It excludes complex-variable methods (except a little bit in Dirichlet’s Theorem). Only real-analysis methods are used (and really nothing past calculus), so there is an emphasis...