Summing It Up: From One Plus One to Modern Number Theory

Description

We use addition on a daily basis--yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems. Mathemat

Avner Ash is professor of mathematics at Boston College. Robert Gross is associate professor of mathematics at Boston College. They are the coauthors of Elliptic Tales: Curves, Counting, and Number Theory and Fearless Symmetry: Exposing the Hidden Patterns of Numbers (both Princeton).

"Offers a clear and beautiful progression from addition to modern number theory."--Math-Blog "The authors did a remarkable job in making some aspects of modern number theory very accessible to readers with only a minimal knowledge of mathematics, say a student who had a first calculus course. However, also mathematicians who do not have number theory as their main focus will enjoy this book."--Adhemar Bultheel, European Mathematical Society "Ash and Gross do a masterful job of leading students from finite sums to modular forms and to the forefront of modern number theory... This is an excellent piece of mathematical writing."--Choice "[A]n accessible and fun introduction to modular forms... [Summing It Up] is engaging and conversational, without losing accuracy or essential rigor."--Dominic Lanphier, American Mathematical Monthly