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Difference Sets: Connecting Algebra, Combinatorics, and Geometry
 
Emily H. Moore Grinnell College, Grinnell, IA
Harriet S. Pollatsek Mount Holyoke College, South Hadley, MA
Difference Sets
Softcover ISBN:  978-0-8218-9176-6
Product Code:  STML/67
List Price: $59.00
Individual Price: $47.20
eBook ISBN:  978-1-4704-0973-9
Product Code:  STML/67.E
List Price: $49.00
Individual Price: $39.20
Softcover ISBN:  978-0-8218-9176-6
eBook: ISBN:  978-1-4704-0973-9
Product Code:  STML/67.B
List Price: $108.00 $83.50
Difference Sets
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Difference Sets: Connecting Algebra, Combinatorics, and Geometry
Emily H. Moore Grinnell College, Grinnell, IA
Harriet S. Pollatsek Mount Holyoke College, South Hadley, MA
Softcover ISBN:  978-0-8218-9176-6
Product Code:  STML/67
List Price: $59.00
Individual Price: $47.20
eBook ISBN:  978-1-4704-0973-9
Product Code:  STML/67.E
List Price: $49.00
Individual Price: $39.20
Softcover ISBN:  978-0-8218-9176-6
eBook ISBN:  978-1-4704-0973-9
Product Code:  STML/67.B
List Price: $108.00 $83.50
  • Book Details
     
     
    Student Mathematical Library
    Volume: 672013; 298 pp
    MSC: 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 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.

    Ancillaries:

    Readership

    Undergraduate 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. Bruck-Ryser-Chowla 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
  • 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 real-life 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 tailor-made 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 672013; 298 pp
MSC: 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 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.

Ancillaries:

Readership

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. Bruck-Ryser-Chowla 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 real-life 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 tailor-made 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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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