Number Theory A Lively Introduction with Proofs, Applications, and Stories

Number Theory: A Lively Introduction with Proofs, Applications,and Stories, is a new book that provides a rigorous yetaccessible introduction to elementary number theory along withrelevant applications. Readable discussions motivate new concepts and theorems beforetheir formal definitions and statements are presented.

Can learning math actually be fun?

Number Theory: A Lively Introduction with Proofs, Applications, and Stories proves it can!

Number Theory: A Lively Introduction with Proofs, Applications, and Stories will introduce you to elementary number theory, helping you develop your proof writing skills while learning the core concepts in number theory as well as advanced topics used in modern applications.

To help you succeed, you'll learn "math myths"—fictional stories starring famous mathematicians that illustrate important number theory topics in a friendly, inviting manner that's easy to understand and remember. "Numerical Proof Previews" give you a concrete way to understand the key ideas of a proof. Illustrations throughout the text add to the fun and your understanding.

As accessible as the book is, it does not skimp on the serious mathematics. You'll explore:

• Methods of proof and the basic properties of the integers, including mathematical induction
• Central concepts and theorems in elementary number theory using a developmental approach, including basic divisibility properties, prime numbers, the Euclidean Algorithm, modular arithmetic (including applications), Fermat's Little Theorem, Euler's Theorem, and RSA (public-key) encryption
• Primitive roots, primality testing, quadratic reciprocity, Gaussian integers, Fermat's Two Squares Theorem, continued fractions, Pell's Equation, and Fermat's Last Theorem, and much more
• Ideal for first-timers in number theory as well as math majors and math education majors, Number Theory: A Lively Introduction with Proofs, Applications, and Stories makes learning number theory a joy!

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.