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Invitation to discrete mathematics. (English) Zbl 0901.05001
Oxford: Clarendon Press. xv, 410 p. (1998).
This text is designed to accompany an undergraduate course in discrete mathematics for science and mathematics students. It is also intended as an introduction to mathematical proof and problem solving in general, and so assumes no knowledge of higher mathematics. The core of the book, covering the material for the course on which the book is based, is chapters 1-8. Chapter 1 presents the basic concepts of sets, relations, functions and induction proofs. Chapter 2 surveys basic counting techniques with inclusion-exclusion. Chapter 3 is an introduction to graph theory. Chapter 4 is devoted to trees and algorithms on trees. Chapter 5 introduces planar graphs. Chapter 6 studies parity arguments including a proof of Sperner’s theorem. Chapter 7 presents several methods for counting the number of labeled trees. Chapter 8 is devoted to finite projective planes. In addition there are three chapters covering the basics of the probabilistic method, generating functions, and the linear algebra approach. The book has comparatively few, though well chosen, problems since the authors have purposely omitted routine exercises. Hints for the more challenging problems can be found at the end of the book. The writing is often casual but always clear, and should appeal to the target audience. The emphasis is on mathematical ideas and techniques rather than applications, and sometimes more than one proof is given for a result, together with an explanation of the value of each approach. Although there are numerous illustrations and diagrams, some of them quite whimsical, the text is typographically conservative, resisting the current trend in undergraduate texts to look more and more like web pages.

05-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics