Difference Sets: Connecting Algebra, Combinatorics, and Geometry (Student Mathematical Library) by Emily H. Moore (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review 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 MATHIt is a welcome addition to all undergraduate libraries. –ChoiceThis 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

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Was inspired – principally by

⭐Tom Johnson’s book, Other Harmony

⭐- to find out more about block designs (in my case for musical composition, not testing drugs on mice or variously coloured lighting hues on crops) and -so far – this has been by far the most successful at explaining to me how these things actually work.

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