# Discrete Mathematics

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.

Audience
First and second year undergraduate mathematicians. Also suitable for first year undergraduates in engineering, computer science and physical science.

Paperback, 224 Pages

Published: September 1995

Imprint: Butterworth Heinemann

ISBN: 978-0-340-61047-3

## Contents

• 1. Logic - Introduction * Truth tables * Conditional propositions * Quantifiers * Types of proof * Mathematical induction * Project * Summary. 2. Sets - Introduction * Operations on sets * De Morgan's Laws * Power sets * Inclusion-exclusion * Products and partitions * Finite and infinite * Paradoxes * Projects * Summary. 3. Relations and Functions - Relations * Equivalence relations * Partial orders * Diagrams of relations * Functions * One-one and onto * Composition of functions * The inverse of a function * The pigeonhole principle * Projects * Summary. 4. Combinatorics - History * Sum and product * Premutations and combinations * Pascal's triangle * The binominal theorem * Multinominals and rearrangements * Projects * Summary 5. Probability - Introduction * Equally likely outcomes * Experiments with outcomes which are not equally likely * The sample space, outcomes and events * Conditional probability, independence and Bayes' theorem * Projects * Summary. 6. Graphs - Introduction * Definitions and examples * Representations of graphs and graph isomorphism * Paths, cycles and connectivity * Trees * Hamiltonian and Eulerian graphs * Planar graphs * Graph colouring * Projects * Summary * Glossary * Index.