As an introduction to discrete mathematics, this text provides a straightforward overview of the range of mathematical techniques available to students. Assuming very little prior knowledge, and with the minimum of technical complication, it gives an account of the foundations of modern mathematics: logic; sets; relations and functions. It then develops these ideas in the context of three particular topics: combinatorics (the mathematics of counting); probability (the mathematics of chance) and graph theory (the mathematics of connections in networks).
Worked examples and graded exercises are used throughout to develop ideas and concepts. The format of this book is such that it can be easily used as the basis for a complete modular course in discrete mathematics.
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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