Universitext

A Course in Topological Combinatorics

Authors: de Longueville, Mark

  • First textbook in the field of topological combinatorics
  • Covers topics such as fair division, graph coloring problems, evasiveness of graph properties, and embedding problems from discrete geometry
  • Contains many figures that aid in the understanding of concepts and proofs
  • Includes an extensive appendix that helps make the book completely self-contained
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  • ISBN 978-1-4419-7910-0
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Hardcover $69.95
price for USA
  • ISBN 978-1-4419-7909-4
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  • Usually dispatched within 3 to 5 business days.
Softcover $69.95
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  • ISBN 978-1-4899-8826-3
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  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
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About this Textbook

A Course in Topological Combinatorics is the first undergraduate textbook on the field of topological combinatorics, a subject that has become an active and innovative research area in mathematics over the last thirty years with growing applications in math, computer science, and other applied areas. Topological combinatorics is concerned with solutions to combinatorial problems by applying topological tools. In most cases these solutions are very elegant and the connection between combinatorics and topology often arises as an unexpected surprise.

The textbook covers topics such as fair division, graph coloring problems, evasiveness of graph properties, and embedding problems from discrete geometry. The text contains a large number of figures that support the understanding of concepts and proofs. In many cases several alternative proofs for the same result are given, and each chapter ends with a series of exercises. The extensive appendix makes the book completely self-contained.

The textbook is well suited for advanced undergraduate or beginning graduate mathematics students. Previous knowledge in topology or graph theory is helpful but not necessary. The text may be used as a basis for a one- or two-semester course as well as a supplementary text for a topology or combinatorics class.

About the authors

Mark de Longueville is professor of Mathematics at Hochschule für Technik und Wirtschaft Berlin and faculty member of the Berlin branch of New York University.

Reviews

“This book is an excellent introduction into the subject. … The book contains a lot of figures and each chapter ends with a group of exercises which help the reader in understanding the hard constructions and proofs. The book may serve for a one- or two-semester undergraduate course depending on the preliminary knowledges of the students.” (János Kincses, Acta Scientiarum Mathematicarum, Vol. 81 (3-4), 2015)

“The present book … presents a sequence of combinatorial themes which have shown an affinity for topological methods … . This book is filled with extremely attractive mathematics … and bringing topology into the play of combinatorics and graph theory is a wonderfully elegant manoeuvre. Here it is carried out coherently, and on a pretty grand scale, and we are thus afforded the opportunity to encounter (algebraic) topology in a very seductive uniform context. What a marvelous thing!” (Michael Berg, MAA Reviews, July, 2013)

“In the book’s four main chapters, Longueville (Univ. of Applied Sciences, Germany) addresses fair-division problems; graph coloring; graph property evasiveness; and embeddings and mappings. … Basic results of algebraic topology already have powerful consequences for analysis, but the subject’s arcana can look like art for art’s sake. The author’s charting of a novel application domain for a core subject makes this book an essential acquisition. Summing Up: Essential. Upper-division undergraduates and above.” (D. V. Feldman, Choice, Vol. 50 (8), April, 2013)

“Topological combinatorics is concerned with the applications of the many powerful techniques of algebraic topology to problems in combinatorics. … The present book aims to give a clear and vivid presentation of some of the most beautiful and accessible results from the area. The text, based upon some courses by the author at Freie Universität Berlin, is designed for an advanced undergraduate student.” (Hirokazu Nishimura, zbMATH, Vol. 1273, 2013)


Table of contents (9 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-1-4419-7910-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.95
price for USA
  • ISBN 978-1-4419-7909-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $69.95
price for USA
  • ISBN 978-1-4899-8826-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
A Course in Topological Combinatorics
Authors
Series Title
Universitext
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4419-7910-0
DOI
10.1007/978-1-4419-7910-0
Hardcover ISBN
978-1-4419-7909-4
Softcover ISBN
978-1-4899-8826-3
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XII, 240
Topics