Discrete Mathematics: An Introduction for Software Engineers

Mike Piff

doi:10.1017/CBO9781139172332

Computing developed as a branch of mathematics, only to drift away from this home as computer science diverged towards more general topics such as the theory of how a computer works. Recently the emphasis has become more mathematical and the new disciplines of software engineering and information technology have emerged. This book is designed to form the basis of a one year course in discrete mathematics for first year computer scientists or software engineers. The material presented covers much of undergraduate algebra with a particular bias towards the computing applications. Topics covered include mathematical logic, set theory, finite and infinite relations and mappings, graphs, graphical algorithms and axiom systems. It concludes with implementations of many of the algorithms in Modula-2 to illustrate how the mathematics may be turned into concrete calculations. Numerous examples and exercises are included with selected solutions to the problems appearing in the appendix. Discrete mathematics is the basic language which every student of computing should take pride in mastering and this book should prove an essential tool in this aim.

"A useful refresher for those who wish to refamiliarize themselves with the material." Choice

"...a very good freshman-level discrete math textbook." Mukkai S. Krishnamoorthy, Mathematical Reviews

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Discrete Mathematics

An Introduction for Software Engineers

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Preface
pp ix-xii

1 - Introduction
pp 1-3

2 - Logic
pp 4-42

3 - Set theory
pp 43-63

4 - Relations
pp 64-95

5 - Mappings
pp 96-137

6 - Graphs
pp 138-174

7 - Graph algorithms
pp 175-196

8 - Abstract algebra
pp 197-239

Appendices

A - Solutions to selected exercises
pp 240-268

B - Example programs
pp 269-306

C - Further reading
pp 307-308

Index
pp 309-318

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Discrete Mathematics

An Introduction for Software Engineers

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