**Student Mathematical Library**

Volume: 68;
2013;
293 pp;
Softcover

MSC: Primary 11;

Print ISBN: 978-1-4704-1048-3

Product Code: STML/68

List Price: $49.00

Individual Price: $39.20

**Electronic ISBN: 978-1-4704-1413-9
Product Code: STML/68.E**

List Price: $49.00

Individual Price: $39.20

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#### Supplemental Materials

# The Joy of Factoring

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*Samuel S. Wagstaff, Jr.*

2014 CHOICE Outstanding Academic Title

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. Most algorithms are described
both in words and in pseudocode to satisfy both number theorists and
computer scientists. Each of the ten chapters begins with a concise
summary of its contents.

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

#### Readership

Undergraduate students, graduate students, and researchers in mathematics and computer science interested in number theory, in particular, methods for factoring integers.

#### Reviews & Endorsements

It is, I think, a fairly safe bet that most students learning about
factoring do not instinctively view the subject as having anything whatsoever
to do with 'joy'. ... [B]y contrast, most people (even many math students)
equate factoring with tedium. Consequently, anybody setting out to write a book
entitled *The Joy of Factoring* is automatically faced with a double
objective. The author must not only teach the reader something about factoring,
but must also explain why anybody should care. The book under review succeeds
on both counts. ... I think a second course in number theory, or senior
seminar, based on this book would be quite interesting. ... The book could also
be used as a text for an upper-level course in computer science for students
with some background in number theory. It also certainly belongs in any good
university library, if only because the material collected in it is not (to my
knowledge at any rate) readily available in the textbook literature.

-- Mark Hunacek, MAA Reviews

This work is a pleasure to read; it is a must for anyone interested in numbers, programming, and codes. The extensive bibliography gives readers direction and the tools to quickly delve deeper into the field. ... Highly recommended.

-- CHOICE

#### Table of Contents

# Table of Contents

## The Joy of Factoring

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface ix10 free
- Why factor integers? 116 free
- Number theory review 1328
- Number theory relevant to factoring 4156
- How are factors used? 7590
- Simple factoring algorithms 119134
- Continued fractions 143158
- Ellliptic curves 173188
- Sieve algorithms 191206
- Factoring devices 219234
- Theoretical and practical factoring 239254
- Answers and hints for exercises 269284
- Bibliography 273288
- Index 287302 free
- Back Cover Back Cover1311