Description
Book SynopsisA 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.
Trade Review“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 ContentsPreface.- 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.
