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First Course in Discrete Mathematics
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113 b
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Drawing on many years' experience of teaching discrete mathematics to students of all levels, the author introduces the various aspects of discrete mathematics including enumeration, graph theory and configurations or arrangements. Starting off with an introduction to counting and counting problems, the text proceeds to introduce the basic ideas of graph theory with particular emphasis on trees and planar graphs. The inclusion-exclusion principle is described and followed by a chapter on partitions of sets which leads to a study of Stirling and Bell numbers. Hamiltonian cycles and Eulerian circuits in graphs are described, Latin squares are defined and Hall's theorem is proved. The book concludes with chapters on the constructions of schedules and a brief introduction to block designs. Each chapter is supported by a number of examples, with straightforward applications of ideas alongside more challenging problems.
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