A First Course in Discrete Mathematics

✍ Scribed by Ian Anderson

• Publisher: Springer
• Year: 2002
• Tongue: English
• Leaves: 201
• Series: Springer Undergraduate Mathematics Series
• Category: Library

✦ Synopsis

Discrete mathematics has now established its place in most undergraduate mathematics courses. This textbook provides a concise, readable and accessible introduction to a number of topics in this area, such as enumeration, graph theory, Latin squares and designs. It is aimed at second-year undergraduate mathematics students, and provides them with many of the basic techniques, ideas and results. It contains many worked examples, and each chapter ends with a large number of exercises, with hints or solutions provided for most of them. As well as including standard topics such as binomial coefficients, recurrence, the inclusion-exclusion principle, trees, Hamiltonian and Eulerian graphs, Latin squares and finite projective planes, the text also includes material on the ménage problem, magic squares, Catalan and Stirling numbers, and tournament schedules.

✦ Table of Contents

Front Matter....Pages i-viii
Counting and Binomial Coefficients....Pages 1-18
Recurrence....Pages 19-42
Introduction to Graphs....Pages 43-67
Travelling Round a Graph....Pages 69-87
Partitions and Colourings....Pages 89-105
The Inclusion-Exclusion Principle....Pages 107-119
Latin Squares and Hall’s Theorem....Pages 121-136
Schedules and 1-Factorisations....Pages 137-148
Introduction to Designs....Pages 149-177
Back Matter....Pages 179-200

✦ Subjects

Combinatorics; Discrete Mathematics in Computer Science