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A Course in Topological Combinatorics

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Synopses & Reviews

Publisher Comments:

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.

Synopsis:

This undergraduate textbook in topological combinatorics covers such topics as fair division, graph coloring problems, evasiveness of graph properties, and embedding problems from discrete geometry. Includes many figures and exercises.

About the Author

Mark de Longueville is a professor of mathematics at Technische Universität Berlin.

Table of Contents

Preface.- List of Symbols and Typical Notation.- 1 Fair-Division Problems.- 2 Graph-Coloring Problems.- 3 Evasiveness of Graph Properties.- 4 Embedding and Mapping Problems.- A Basic Concepts from Graph Theory.- B Crash Course in Topology.- C Partially Ordered Sets, Order Complexes, and Their Topology.- D Groups and Group Actions.- E Some Results and Applications from Smith Theory.- References.- Index.

Product Details

ISBN:
9781441979094
Author:
Longueville, Mark De
Publisher:
Springer
Author:
Longueville, Mark de
Subject:
Combinatorics
Subject:
Brouwer s fixed point theorem
Subject:
Kneser conjecture
Subject:
Radon theorems
Subject:
Smith theory
Subject:
evasiveness of graph properties
Subject:
homological algebra
Subject:
Partially ordered sets
Subject:
theoretic topology
Subject:
topological G-spaces
Subject:
Mathematics-Combinatorics
Subject:
applications of algebraic topology
Subject:
Discrete geometry
Subject:
fair division
Subject:
Convex and Discrete Geometry
Subject:
Graph theory
Subject:
Game Theory, Economics, Social and Behav. Sciences
Subject:
Mathematics of Algorithmic Complexity
Copyright:
Edition Description:
2012
Series:
Universitext
Publication Date:
20110227
Binding:
HARDCOVER
Language:
English
Pages:
250
Dimensions:
235 x 155 mm

Related Subjects


Science and Mathematics » Chemistry » Chemical Engineering
Science and Mathematics » Mathematics » Combinatorics
Science and Mathematics » Mathematics » Geometry » General
Science and Mathematics » Mathematics » Modeling
Science and Mathematics » Mathematics » Topology

A Course in Topological Combinatorics New Hardcover
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Product details 250 pages Springer - English 9781441979094 Reviews:
"Synopsis" by , This undergraduate textbook in topological combinatorics covers such topics as fair division, graph coloring problems, evasiveness of graph properties, and embedding problems from discrete geometry. Includes many figures and exercises.
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