Difference sets : connecting algebra, combinatorics and geometry
Material type:
TextSeries: Student mathematical library ; v. 67Publication details: India : Universities Press, 2025. Description: xiii, 298 pages : illustrations ; 22 cmISBN: 9789349750715Subject(s): Difference sets | Combinatorial geometry | Combinatorics -- Designs and configurations -- Difference sets (number-theoretic, group-theoretic, etc.) | Combinatorics -- Designs and configurations -- Matrices (incidence, Hadamard, etc.) | Combinatorics -- Designs and configurations -- Finite geometries | Group theory and generalizations -- Representation theory of groups -- Ordinary representations and charactersDDC classification: 510.22 Online resources: Table of Contents | Reviews 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 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.
| Item type | Current library | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
NBHM Books
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SMS Library | 510.22 MOO-D (Browse shelf(Opens below)) | Available | N480 |
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| 510 YAH-I Iranian mathematics competitons 1973-2007 | 510.2 GOW-S Short history of greek mathematics(a) | 510.22 KAP-S Set theory and metric spaces | 510.22 MOO-D Difference sets : connecting algebra, combinatorics and geometry | 510.223 TAK-A Axiomatic set theory | 510.5 BOR-E Elementary convexity with optimization | 510.5 COR-I Introduction to algorithms |
Includes bibliographical references and indexes.
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.
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