Difference sets : connecting algebra, combinatorics and geometry
 Author/Creator
 Moore, Emily H., 1948
 Language
 English.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2013]
 Physical description
 xiii, 298 pages : illustrations ; 22 cm.
 Series
 Student mathematical library ; v. 67.
Access
Available online

Stacks

Unknown
QA166.25 .M66 2013

Unknown
QA166.25 .M66 2013
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Contributors
 Contributor
 Pollatsek, Harriet Suzanne Katcher.
Contents/Summary
 Bibliography
 Includes bibliographical references and indexes.
 Contents

 Table of Contents:* Introduction * Designs * Automorphisms of designs * Introducing difference sets * BruckRyserChowla theorem * Multipliers * Necessary group conditions * Difference sets from geometry * Families from Hadamard matrices * Representation theory * Group characters * Using algebraic number theory * Applications * Background * Notation * Hints and solutions to selected exercises * Bibliography * Index * Index of parameters.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 emphasising 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Difference sets.
 Combinatorial geometry.
 Combinatorics  Designs and configurations  Difference sets (numbertheoretic, grouptheoretic, etc.)
 Combinatorics  Designs and configurations  Matrices (incidence, Hadamard, etc.)
 Combinatorics  Designs and configurations  Finite geometries.
 Number theory  Algebraic number theory: global fields  Algebraic numbers; rings of algebraic integers.
 Group theory and generalizations  Representation theory of groups  Ordinary representations and characters.
 Geometry  Finite geometry and special incidence structures  Affine and projective planes.
Bibliographic information
 Publication date
 2013
 Responsibility
 Emily H. Moore, Harriet S. Pollatsek.
 Series
 Student mathematical library ; volume 67
 ISBN
 9780821891766 (alk. paper)
 0821891766 (alk. paper)