Summing It Up

"In Summing It Up, Ash and Gross, with their customary charm and clarity, build an impressive tower from the most basic mathematical story imaginable. They start by adding up finite sequences and whole numbers before journeying to the upper reaches of contemporary developments in number theory."--Jordan Ellenberg, author of How Not to Be Wrong: The Power of Mathematical Thinking"With joy and reflection, Summing It Up encourages readers to work alongside the authors to engage in simple computations with profound implications. It progresses elegantly to an insightful discussion of the ideas behind the classical theory of modular forms. A wonderful book."--Barry Mazur, Harvard University"This book takes general readers on a journey from simple addition to the modern theory of modular forms. Plentiful and accurate references are available for interested readers who want to look up further information."--Xiaoheng Wang, Princeton University"In Summing It Up, Ash and Gross are erudite and meticulous--they write with care and precision. Their book adopts the voice of a wise elder telling math stories to precocious children. It will interest readers of all ages who seek a window into current mathematics."--Kenneth Ribet, University of California, Berkeley"Summing It Up ambitiously presents concepts of number theory, from the elementary to the advanced, for readers with only a knowledge of high school math and some calculus. With a crisp yet conversational style and excellent examples, Ash and Gross explain a great amount of interesting and important math."--James Pommersheim, coauthor of Number Theory: A Lively Introduction with Proofs, Applications, and Stories"A well-motivated and fun introduction to some very deep topics in mathematics, Summing It Up takes readers on a mathematics tour starting with very classical material and building towards some amazing recent work, with many highlights along the way. It can be read by those with many different levels of mathematical background. I thoroughly enjoyed it."--Nathan Kaplan, University of California, Irvine