Number Theory

by Jamie Pommersheim, Tim K. Marks, Erica Flapan

"Number Theory: A Lively Introduction with Proofs, Applications, and Stories," is a new book that provides a rigorous yet accessible introduction to elementary number theory along with relevant applications.

Readable discussions motivate new concepts and theorems before their formal definitions and statements are presented. Many theorems are preceded by "Numerical Proof Previews," which are numerical examples that will help give students a concrete understanding of both the statements of the theorems and the ideas behind their proofs, before the statement and proof are formalized in more abstract terms. In addition, many applications of number theory are explained in detail throughout the text, including some that have rarely (if ever) appeared in textbooks.

A unique feature of the book is that every chapter includes a "math myth," a fictional story that introduces an important number theory topic in a friendly, inviting manner. Many of the exercise sets include in-depth "Explorations," in which a series of exercises develop a topic that is related to the material in the section.

Genres: Mathematics, Reference, Textbooks

784 pages, Hardcover

First published February 4, 2009

Reviews

[Greg Boyle · Rating 4 out of 5]

I actually used this textbook for an online Number Theory Class taken through SUNY Empire State College. Originally, I thought the concept of the book was foolish. The authors start most chapters in the book with an introductory biography of a famous mathematician. They then concoct a seemingly silly story using the highlighted person and some of the material covered in that chapter. As I progressed through the course, I began to realize the utility of this method. I gained a deeper understanding of the concepts in the course based on the stories. I guess they piqued my curiosity and facilitated better retention of the material. I also found the exercises in the book challenging and interesting. I liked the book so much that I completed the material from chapter 10 onward as a self-study. I would have given this book a higher rating, but the book does contain a few errors in every chapter. Luckily, this is a first edition so an errata should be issued soon.