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.
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