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By
Amanda Chetwynd, University of Lancaster, UK
Peter Diggle, University of Lancaster, UK
Description
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.
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.
| Bibliographic details |
Paperback, 224 pages, publication date: SEP-1995
ISBN-13: 978-0-340-61047-3
ISBN-10: 0-340-61047-6
Imprint: BUTTERWORTH HEINEMANN
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| Price and Ordering |
Price:
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USD 33.95
GBP 22
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Last update: 4 Sep 2009
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