Number Theory – Mathematical Association of America

Featured Resources

Modernizing Undergraduate Mathematics

By David Bressoud @dbressoud As of 2024, new Launchings columns appear on the third Tuesday of the month. The recent New York Times article, “They Spent Years on a Math Problem. Then They Were Scooped by A.I.” is one illustration of how fast and dramatically the mathematical landscape is changing. We do not need a wholesale...

There and Back Again: What will we do with it?

By Lew Ludwig When a student asked whether we should be using AI at all, the answer reframed the question: not whether this technology should have arrived, but what educators will do now that it has. Frodo, deep in the Mines of Moria, has just learned the full weight of what he carries. The Ring....

From Classical L-Functions to Modern Reciprocity Laws

The most elusive and tantalizing problem in all of mathematics is the Riemann Hypothesis: I say this both as an opening salvo to start spats among the readers of this review - and even arguments, to be sure - but also because I think it’s a claim that can be defended (of course, I am...

Topology of Numbers

Roger Howe stated during his MAA invited address, “Everybody knows that mathematics is about miracles, only mathematicians have a name for them: theorems.” Allen Hatcher’s Topology of Numbers is one of those rare texts that takes students on a journey weaving through number theory with skill worthy of the Moirai themselves. The book is an introduction to...

Book cover of Topology of Numbers by Allen Hatcher. The cover is blue with a purple boarder and a smaller white rectangle inside the purple boarder. There is a blue and purple circular design on the inside white rectangle in the center of the book.

Explorations in Number Theory

Anne Rice wrote in the foreword to a collection of Kafka short stories, “Don’t bend; don’t water it down; don’t try to make it logical; don’t edit your own soul according to the fashion. Rather, follow your most intense obsessions mercilessly. Only if you do that can you hope to make the reader feel every...

Book cover of Explorations in Number Theory. Top third of the cover is blue and the bottom two thirds is bright yellow

Multiplicative Number Theory I: Classical Theory

This is an excellent introductory textbook in analytic number theory, aimed at graduate and upper-division undergraduate students. Multiplicative number theory means generally speaking the properties and distribution of the prime numbers, and of functions whose value depends on the prime numbers. Sometimes it is broadened to include all kinds of arithmetic functions (function defined on the positive integers), but the...

Cover of the book 'Multiplicative Number Theory I: Classical Theory' by Hugh L. Montgomery at University of Michigan, Ann Arbor and Robert C. Vaughan at Pennsylvania State University featuring a dark gray cover with a diagonal dark blue-gray strip.

Number Theory Through the Eyes of Sophie Germain

It takes tremendous erudition for an author to fully understand Number Theory Through the Eyes of Sophie Germain, and then lucidly explain it to others in a manner that is both captivating and instructive. David Pengelley has done just that in this unique book that will motivate many students to pursue research in this the most...

Book Cover of "Number Theory Through the Eyes of Sophie Germain" published by the American Mathematical Society

Introduction to Proof Through Number Theory

Introduction to Proof Through Number Theory is a fun book that introduces students to mathematical thinking and proof writing through a deeper understanding of elementary concepts in Number Theory. The book’s informal style with humor, games, puzzles, and connections to popular culture with references to music, art, movies and literature lightens up the material without compromising...

Quadratic Number Fields

Franz Lemmermeyer’s Quadratic Number Fields belongs to a growing genre of undergraduate textbooks that aim to make subjects that have traditionally been considered ‘graduate level’ accessible to broader audiences. The quintessential such book is John Stillwell’s gem Naive Lie Theory, which focuses its attention on matrix Lie groups in order to give its readers the flavor...

Excursions in Number Theory, Algebra, and Analysis

Excursions in Number Theory, Algebra, and Analysis by Kenneth Ireland and Al Cuoco differs from most mathematics text books in two ways: its structure and its breadth. The book is in the series Undergraduate Texts in Mathematics. It contains mostly undergraduate-level material, but the breadth and style would be appropriate for a graduate-level course or an...

Number Theory Revealed: An Introduction

In Number Theory Revealed: An Introduction, Andrew Granville presents a fresh take on the classic structure of a number theory textbook. While it includes the standard topics that one would expect to find in a textbook on elementary number theory, it is also filled throughout with related problems, different approaches to proving key theorems, and interesting...

Primes of the Form x^2 + ny^2: Fermat, Class Field Theory, and Complex Multiplication

Every prime number which surpasses by one a multiple of four is composed of two squares. … Every prime number which surpasses by one of three a multiple of eight is composed of a square and the double of another square.… or, even weirder, The general theorem we reach at the end of chapter 2...

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