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A First Course in Discrete Mathematics

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Drawing on many years'experience of teaching discrete mathem atics to students of all levels, Anderson introduces such as pects as enumeration, graph theory and configurations or arr angements. Starting with an introduction to counting and rel ated problems, he moves on to the basic ideas of graph theor y with particular emphasis on trees and planar graphs. He de scribes the inclusion-exclusion principle followed by partit ions of sets which in turn leads to a study of Stirling and Bell numbers. Then follows a treatment of Hamiltonian cycles, Eulerian circuits in graphs, and Latin squares as well as proof of Hall's theorem. He concludes with the constructions of schedules and a brief introduction to block designs. Each chapter is backed by a number of examples, with straightforw ard applications of ideas and more challenging problems.

Author(s): Ian Anderson
Series: Springer Undergraduate Mathematics Series
Edition: 2000
Publisher: Springer
Year: 2000

Language: English
Pages: 208
City: London
Tags: Combinatorial Mathematics; Discrete Mathematics; Enumeration; Graph; Graph theory; Hall's Theorem; Hamiltonian Cycle; Latin Squares; Partition

Front Matter
Pages i-viii

Counting and Binomial Coefficients
Ian Anderson
Pages 1-18

Recurrence
Ian Anderson
Pages 19-42

Introduction to Graphs
Ian Anderson
Pages 43-67

Travelling Round a Graph
Ian Anderson
Pages 69-87

Partitions and Colourings
Ian Anderson
Pages 89-105

The Inclusion-Exclusion Principle
Ian Anderson
Pages 107-119

Latin Squares and Hall’s Theorem
Ian Anderson
Pages 121-136

Schedules and 1-Factorisations
Ian Anderson
Pages 137-148

Introduction to Designs
Ian Anderson
Pages 149-177

Back Matter
Pages 179-200