**Student Mathematical Library**

Volume: 67;
2013;
298 pp;
Softcover

MSC: Primary 05; 11; 20; 51;

Print ISBN: 978-0-8218-9176-6

Product Code: STML/67

List Price: $49.00

Individual Price: $39.20

**Electronic ISBN: 978-1-4704-0973-9
Product Code: STML/67.E**

List Price: $49.00

Individual Price: $39.20

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#### Supplemental Materials

# Difference Sets: Connecting Algebra, Combinatorics, and Geometry

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*Emily H. Moore; Harriet S. Pollatsek*

Difference sets belong both to group theory
and to combinatorics. Studying them requires tools from geometry,
number theory, and representation theory. This book lays a foundation
for these topics, including a primer on representations and characters
of finite groups. It makes the research literature on difference sets
accessible to students who have studied linear algebra and abstract
algebra, and it prepares them to do their own research.

This text is suitable for an undergraduate capstone course, since
it illuminates the many links among topics that the students have
already studied. To this end, almost every chapter ends with a coda
highlighting the main ideas and emphasizing mathematical
connections. This book can also be used for self-study by anyone
interested in these connections and concrete examples.

An abundance of exercises, varying from straightforward to
challenging, invites the reader to solve puzzles, construct proofs,
and investigate problems—by hand or on a computer. Hints and
solutions are provided for selected exercises, and there is an
extensive bibliography. The last chapter introduces a number of
applications to real-world problems and offers suggestions for further
reading.

Both authors are experienced teachers who have successfully
supervised undergraduate research on difference sets.

#### Readership

Undergraduate students, graduate students, and research mathematicians interested in algebra and combinatorics.

#### Reviews & Endorsements

It is a welcome addition to all undergraduate libraries.

#### Table of Contents

# Table of Contents

## Difference Sets: Connecting Algebra, Combinatorics, and Geometry

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface xi12 free
- Introduction 116 free
- Designs 1126 free
- Automorphisms of designs 3752
- Introducing difference sets 4560
- Bruck-Ryser-Chowla theorem 7186
- Multipliers 87102
- Necessary group conditions 103118
- Difference sets from geometry 121136
- Families from Hadamard matrices 135150
- Representation theory 167182
- Group characters 197212
- Using algebraic number theory 233248
- Applications 253268
- Background 267282
- Notation 273288
- Hints and solutions to selected exercises 277292
- Bibliography 287302
- Index 293308 free
- Index of parameters 297312 free
- Back Cover Back Cover1314