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A Course in Enumeration (Graduate Texts in Mathematics) [Englisch] [Gebundene Ausgabe]

Martin Aigner

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26. Juni 2007 3540390324 978-3540390329 2007

Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from basic notions of combinatorial enumeration to a variety of topics, ranging from algebra to statistical physics. The book is organized in three parts: Basics, Methods, and Topics. The aim is to introduce readers to a fascinating field, and to offer a sophisticated source of information for professional mathematicians desiring to learn more. There are 666 exercises, and every chapter ends with a highlight section, discussing in detail a particularly beautiful or famous result.

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From the reviews:

"The goal of the text is present enumerative combinatorics together with its many applications, including chapters not common in enumerative combinatorics texts, like the ones on hypergeometric summations, on the Tutte polynomial, and on models from statistical physics. … good number of exercises carry additional material, and a number of selected exercises are given a solution at the end. … A nice trend in recent books – closing chapters with some spectacular ‘book proofs’ – is followed and will help at keeping the attention of the students." (László A. Székely, Zentralblatt MATH, Vol. 1123 (1), 2008)

"The book is divided into three parts … . the structure and topics of this book are well-designed, and there are nearly 700 exercises sprinkled throughout – many with hints and solutions in the back – which make the book far more appealing. I think it would be a good … textbook for any graduate student wishing to learn about enumerative combinatorics." (Darren Glass, MathDL, January, 2008)

"In this graduate textbook on enumerative combinatorics, the author follows the classic structure of basics-methods-special topics. … Each chapter ends with a ‘Highlight’, which is a specific, high-level application of the material learned in that chapter. This will benefit instructors and interested students alike. … the book will broaden access to several special topics and will turn them into more mainstream knowledge. The scope of the book is large, so most readers will find several sections that will teach them many facts, methods and theories." (Miklós Bóna, Mathematical Reviews, Issue 2008 f)

"The techniques one needs to be an expert in enumeration are very involved, sometimes quite genius. … This book moves this important technique much closer to the classrooms than it used to be. … The arguments throughout the book are very clear, many exercises are presented … . This way the lecturers with talented audience will find many ideas how to hold out the beauty behind the dry techniques. We highly recommend this book for anyone related to enumeration … ." (Péter Hajnal, Acta Scientiarum Mathematicarum, Vol. 74, 2008)

“It provides mathematical analysis of combinatorial sets … . Martin Aigner has a reputation as a good expositor of mathematics … and the book does not disappoint. The explanations, while often brief, are quite good. … As the book gets more and more advanced, the explanations grow correspondingly in size. … contains the clearest explanation of graph polynomials that I have ever found. … the book contains good and readable expositions of an interesting and beautiful subject.” (Peter Boothe, SIGACT News, Vol. 41 (2), 2010)

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5.0 von 5 Sternen On Enumeration without enumerative exposition, enjoyably organized and progressive 12. März 2014
Von D. Taylor - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe|Verifizierter Kauf
Enumerative combinatorics often gets the handbook or encyclopedia treatment owing to the enormous breadth and discontinuity of the subject and the seeming infinite binomial identities that doge the subject. Such variety, much complication. On the flip side, you might find a tome based on a pet-species-framework that tries to be the one finite ring to rule them all, and haz a cheezburger at the same time. Lucky for us, we have a happy medium right here in this book. It's well-organized and cohesively laid out. The author addresses the issues of mixed-bag wikinomics vs. exposition from the start, taking his cue from John Riordan's earlier attempts at unification of identities. Concrete in focus (as enumeration should be), the author stays away from name dropping in the Grand Eponymous Taxonomy game of inter-disciplinary authorial backscratching. Nor is it heavily weighted toward "word" trends in combinatorics, or even the analytic generating function aspects (both are still discussed in limited form). You've probably have your own sources for that, and the book is thick enough already. It has a weakness to my mind, it's a lack of "open problems" and relatedness to open problems recently solved or otherwise.
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