Discrete Mathematics provides a concise overview of some fundamental concepts in modern mathematics: logic, sets, relations and functions, developing these ideas in the context of three particular topics: combinatorics, probability and graph theory. It takes the reader through an introductory course in easy steps, including illustrative worked examples and problems set with increasing difficulty to allow the student to develop at their own pace, while equipping them with all the tools required for the more advanced mathematics to come. Presented in an easy to read, informal style it will be invaluable to all those new to the subject. Modular Mathematics is a new series of introductory texts for undergraduates. Building on both the skills and knowledge acquired at A level, each book provides a lively and accessible account of the subject. Examples and exercises are used as teaching aids throughout and ideas for investigative and project work help to place the subject in context.
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Axiom bipartite graph called cards choose chromatic index codomain coefficient coin colour components compound proposition connected corresponds countable define denote dice equal equivalence relation Eulerian trail event exactly once Example 18 EXERCISES F F F F T F flips four function give graph G graph theory graphs shown Hamiltonian cycle Hence inductive step integers keys least logical mathematical induction mathematician natural numbers negation number of edges number of elements number of vertices objects one-one outcomes pair partition Pascal's triangle Petersen graph pigeonhole principle planar graph player positive integer possible prime number probability problem proof prove rational numbers real numbers reflexive result rule of sum sample space shown in Fig SOLUTION Let spanning tree statement subsets Suppose symmetric Theorem True or false truth table truth value unordered selection Venn diagram vertex of G write