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Description
This undergraduate text is designed for a single-semester introductory course in discrete mathematics. It is aimed at students of mathematics and computer science, as well as problem-solving enthusiasts or anyone with some familiarity with proofs seeking a concise introduction to the subject. The primary goal is to acquaint readers with key structures and ideas in combinatorial and discrete mathematics that will support further study in mathematics and its applications.
Requiring minimal prerequisites, the book seeks to build appreciation while offering a clear foundation for developing combinatorial reasoning. Special attention is given to the basics of enumeration and generating functions. Background concepts are presented accessibly, and examples appear early and frequently. When suitable, multiple proofs are provided for the same result, offering insight into mathematical thinking and the interconnectedness of ideas. Each chapter concludes with a selection of exercises spanning a wide range of difficulty, and a collection of hints and solutions is included at the end of the book.
1 Introduction.- 2 Elementary enumerative combinatorics.- 3 Inclusion-exclusion.- 4 Set partitions, equivalence relations and partial orders.- 5 Graphs.- 6 Generating functions.-7 Discrete probability.- Appendix A A glimpse of algebra.- Appendix B Hints-Solutions to selected exercises.
Christos A. Athanasiadis is a professor of Mathematics at the National and Kapodistrian University of Athens. He received his Ph.D from MIT in 1996. His research interests lie in algebraic and geometric combinatorics.
