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A Course in Topological Combinatorics

  • Mark de Longueville

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Mark de Longueville
    Pages 1-35
  3. Mark de Longueville
    Pages 37-68
  4. Mark de Longueville
    Pages 69-95
  5. Mark de Longueville
    Pages 97-143
  6. Mark de Longueville
    Pages 145-162
  7. Mark de Longueville
    Pages 163-197
  8. Mark de Longueville
    Pages 209-218
  9. Back Matter
    Pages 229-238

About this book

Introduction

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.

Keywords

applications of algebraic topology combinatorics discrete geometry fair division

Authors and affiliations

  • Mark de Longueville
    • 1
  1. 1.und Wirtschaft Berlin, University of Applied SciencesHochschule für TechnikBerlinGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-7910-0
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-7909-4
  • Online ISBN 978-1-4419-7910-0
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site