"The Joy of Factoring" by Samuel S. Wagstaff, Jr.

This book is about the theory and practice of integer factorization presented in a historic perspective. It describes about twenty algorithms for factoring and a dozen other number theory algorithms that support the factoring algorithms. This book is written for readers who want to learn more about the best methods of factoring integers, many reasons for factoring, and some history of this fascinating subject.

The book starts with a general explanation of why factoring integers is important.
The next two chapters present number theory results that are relevant to factoring.
Further on there is a chapter discussing, in particular, mechanical and electronic devices for factoring, as well as factoring using quantum physics and DNA molecules.
Another chapter applies factoring to breaking certain cryptographic algorithms. Yet another chapter is devoted to practical vs. theoretical aspects of factoring.
The book contains more than 100 examples illustrating various algorithms and theorems. It also contains more than 100 interesting exercises to test the reader's understanding.
Hints or answers are given for about a third of the exercises.
The book concludes with a dozen suggestions of possible new methods for factoring integers.

This book can be read by anyone who has taken a first course in number theory.

Brief Contents
Preface
1 Why factor integers?
2 Number theory review
3 Number theory relevant to factoring
4 How are factors used?
5 Simple factoring algorithms
6 Continued fractions
7 Ellliptic curves
8 Sieve algorithms
9 Factoring devices
10 Theoretical and practical factoring
Appendix: Answers and hints for exercises
Bibliography
Index