Softcover ISBN:  9780821891766 
Product Code:  STML/67 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470409739 
Product Code:  STML/67.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9780821891766 
eBook: ISBN:  9781470409739 
Product Code:  STML/67.B 
List Price:  $108.00 $83.50 
Softcover ISBN:  9780821891766 
Product Code:  STML/67 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470409739 
Product Code:  STML/67.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9780821891766 
eBook ISBN:  9781470409739 
Product Code:  STML/67.B 
List Price:  $108.00 $83.50 

Book DetailsStudent Mathematical LibraryVolume: 67; 2013; 298 ppMSC: Primary 05; 11; 20; 51
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 selfstudy 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 realworld problems and offers suggestions for further reading.
Both authors are experienced teachers who have successfully supervised undergraduate research on difference sets.
Ancillaries:
ReadershipUndergraduate students, graduate students, and research mathematicians interested in algebra and combinatorics.

Table of Contents

Chapters

Chapter 1. Introduction

Chapter 2. Designs

Chapter 3. Automorphisms of designs

Chapter 4. Introducing difference sets

Chapter 5. BruckRyserChowla theorem

Chapter 6. Multipliers

Chapter 7. Necessary group conditions

Chapter 8. Difference sets from geometry

Chapter 9. Families from Hadamard matrices

Chapter 10. Representation theory

Chapter 11. Group characters

Chapter 12. Using algebraic number theory

Chapter 13. Applications

Appendix A. Background

Appendix B. Notation

Appendix C. Hints and solutions to selected exercises


Additional Material

Reviews

This is one among the beautiful books on the subject of difference sets that I came across in the field of mathematics and especially in combinatorics because of its lucid style and simplicity...The present book overviews these subjects if not exhaustively but impressively with required theorems sometimes with full proofs and sometimes with comprehensive explanations and required examples. By the study of this book, one gains an opportunity to further explore the subject with confidence in different angles enriching one's vision for further research with the orientation of applications in the reallife situations as the authors mention such lines as well...This book lays a good foundation for the study of difference sets together with the subjects related to it and prepares the students for further extensive research.
Ratnakaram Nava Mohan, Zentralblatt MATH 
It is a welcome addition to all undergraduate libraries.
CHOICE 
This book would seem tailormade as a text for a senior seminar or capstone course. It is clearly written, emphasizes motivation, contains lots of examples, has a good bibliography and contains a respectable number of exercises at the end of each chapter. ... Reading this book taught me some nice mathematics that I didn't know before, and it did so in an interesting, enjoyable way.
MAA Reviews


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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 selfstudy 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 realworld problems and offers suggestions for further reading.
Both authors are experienced teachers who have successfully supervised undergraduate research on difference sets.
Ancillaries:
Undergraduate students, graduate students, and research mathematicians interested in algebra and combinatorics.

Chapters

Chapter 1. Introduction

Chapter 2. Designs

Chapter 3. Automorphisms of designs

Chapter 4. Introducing difference sets

Chapter 5. BruckRyserChowla theorem

Chapter 6. Multipliers

Chapter 7. Necessary group conditions

Chapter 8. Difference sets from geometry

Chapter 9. Families from Hadamard matrices

Chapter 10. Representation theory

Chapter 11. Group characters

Chapter 12. Using algebraic number theory

Chapter 13. Applications

Appendix A. Background

Appendix B. Notation

Appendix C. Hints and solutions to selected exercises

This is one among the beautiful books on the subject of difference sets that I came across in the field of mathematics and especially in combinatorics because of its lucid style and simplicity...The present book overviews these subjects if not exhaustively but impressively with required theorems sometimes with full proofs and sometimes with comprehensive explanations and required examples. By the study of this book, one gains an opportunity to further explore the subject with confidence in different angles enriching one's vision for further research with the orientation of applications in the reallife situations as the authors mention such lines as well...This book lays a good foundation for the study of difference sets together with the subjects related to it and prepares the students for further extensive research.
Ratnakaram Nava Mohan, Zentralblatt MATH 
It is a welcome addition to all undergraduate libraries.
CHOICE 
This book would seem tailormade as a text for a senior seminar or capstone course. It is clearly written, emphasizes motivation, contains lots of examples, has a good bibliography and contains a respectable number of exercises at the end of each chapter. ... Reading this book taught me some nice mathematics that I didn't know before, and it did so in an interesting, enjoyable way.
MAA Reviews