Cover image for Invitation to discrete mathematics
Invitation to discrete mathematics
Matoušek, Jiří.
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Publication Information:
Oxford : Clarendon Press ; Oxford ; New York : Oxford University Press, 1998.
Physical Description:
xv, 410 pages : illustrations ; 24 cm
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QA39.2 .M3935 1998 Adult Non-Fiction Non-Fiction Area

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This book is a clear and self-contained introduction to discrete mathematics, and in particular to combinatorics and graph theory. Aimed at undergraduates and early graduate students in mathematics and computer science, it is written with the goal of stimulating interest in mathematics andencourages an active, problem-solving approach to the material. The reader is led to an understanding of the basic principles and methods of actually doing mathematics. It is more narrowly focused than many discrete mathematics textbooks and treats selected topics in unusual depth and from severalpoints of view. The book reflects the conviction of the authors, active and internationally renowned mathematicians, that the most important gain from studying mathematics is the cultivation of clear and logical thinking and habits, invariably useful for attacking new problems. More than 400exercises, ranging widely in difficulty, and many accompanied by hints for solution, support this approach to teaching. Readers will appreciate the lively and informal style of the text, accompanied by more than 200 drawings and diagrams. Specialists in various parts of science ( with a basicmathematical education) wishing to apply discrete mathematics in their field will find the book a useful source, and even experts in combinatorics may occasionally learn from pointers to research literature or from the presentation of recent results. Invitation to Discrete Mathematics should makedelightful reading both for beginners and mathematical professionals.

Author Notes

Jiri Matousek and Jaroslav Nesetril are both at Charles University, Prague.

Reviews 1

Choice Review

In current parlance, "discrete mathematics" simply means all the mathematics that a computer scientist ought to master. Since only a fuzzy border separates theoretical computer science from mathematics anyway, one may either construe discrete mathematics broadly (so that it includes topics such as logic, formal languages, automata, recursive function theory, and algorithm analysis) or narrowly (so that it concentrates only on, say, combinatorics and graph theory). Matousek and Nesetril's book reflects the narrow interpretation, but the authors still take care that the book should nevertheless serve the needs of computer science students. Thus it will provide the greatest utility (whether in the classroom or on the library shelf) at those campuses where the mathematics department teaches discrete mathematics to audiences including but not limited to computer science majors. Viewed pedagogically, combinatorics has the advantage of including concrete, elementary problems, but the disadvantage of solving them with a diverse panoply of techniques. This book has the outstanding feature of focusing on overarching problem-solving principles and methods of proof without sacrificing too much the depth of treatment of its many particular topics. Thoughtfully and carefully constructed throughout with the student reader in mind. Recommended for college libraries. Undergraduates and up. D. V. Feldman University of New Hampshire

Table of Contents

1 Introduction and basic concepts
2 Combinatorial counting
3 Graphs: an introduction
4 Trees
5 Drawing graphs in the plane
6 Double-counting
7 The number of spanning trees
8 Finite projective planes
9 Probability and probabilistic proofs
10 Generating functions
11 Applications of linear algebra
Appendix: Prerequisites from algebra
Hints to selected exercises