A Course in Topological Combinatorics

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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.

Zusammenfassung

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

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2014
Fachbereich:	Allgemeines
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Universitext
Inhalt:	xii 240 S.
ISBN-13:	9781489988263
ISBN-10:	1489988262
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	De Longueville, Mark
Hersteller:	Springer New York Springer US, New York, N.Y. Universitext
Maße:	235 x 155 x 14 mm
Von/Mit:	Mark De Longueville
Erscheinungsdatum:	15.10.2014
Gewicht:	0,388 kg

Artikel-ID: 105057963