Analytic Number Theory – Mathematical Association of America

Featured Resources

Where do our numbers come from?

By Keith Devlin @KeithDevlin@fediscience.org, @profkeithdevlin.bsky.social The numbers we use every day are so familiar, and so much a part of life, it’s easy to forget that they are a recent invention, having been introduced in the late nineteenth and early twentieth centuries. Sure, humanity has had some form of numbers for at least ten thousand years, and...

Grades are Violent: A Reflection on the Negative Impacts of Grades

By Mallory Dolorfino Since I started undergrad, I have witnessed the harmful effects, the ineffectiveness, and the simultaneous overuse of the grading system in higher education. This year, as a first time graduate teaching assistant, the phrase “grades are violent” has become increasingly resonant. The following is a reflection, based on my own experience as...

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...