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Invitation to Discrete Mathematics
Second Edition
Jirí Matousek and Jaroslav Nesetril
464 pages
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234x156mm
978-0-19-857042-4
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Paperback
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09 October 2008
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- Informal and entertaining style, yet mathematically precise and entertaining
- Concentrates on developing mathematical thinking and skills rather than accumulating facts
- Written by internationally renowned mathematicians with extensive teaching experience
- Large collection of exercises and problems
- Over 200 drawings and diagrams
New to this edition - New chapters on partially ordered sets and Ramsey's Theorem
- New sections on Tuarán's Theorem
- Proofs of the Cauchy-Schwarz inequality, Cayley's Formula, and the determinant formula for counting spanning trees
This second edition of Invitation to Discrete Mathematics is a clear and self-contained introduction to discrete mathematics. Aimed mainly at undergraduate and early graduate students of mathematics and computer science, it is written with the goal of stimulating interest in mathematics and an active, problem-solving approach to the presented material. The reader is led to an understanding of the basic principles and methods of actually doing mathematics (and having fun at that). By focussing on a more selective range of topics than many discrete mathematics textbooks, allowing greater depth of treatment
using a number of different approaches, 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 useful for attacking new problems. More than 400 enclosed exercises with a wide range of difficulty, many of them accompanied by hints for solution, support this approach to teaching. The 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 basic mathematical education wishing to apply discrete mathematics in their field can use the book as a useful source, and even experts in combinatorics may occasionally learn from pointers
to research literature or from presentations of recent results. Invitation to Discrete Mathematics should make delightful reading both for beginners and for mathematical professionals.
The main topics include: elementary counting problems, asymptotic estimates, partially ordered sets, basic graph theory and graph algorithms, finite projective planes, elementary probability and the probabilistic method, generating functions, Ramsey's theorem, and combinatorial applications of linear algebra. General mathematical notions going beyond the high-school level are thoroughly explained in the introductory chapter. An appendix summarizes the undergraduate algebra needed in some of the more advanced sections of the
book.Readership: Undergraduates and early graduates in mathematics and computer science
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Jirí Matousek, Professor of Computer Science, Charles University, Prague, and Jaroslav Nesetril, Professor of Mathematics, Charles University, Prague
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Review(s) from previous edition
"'The book is a self-contained introduction to discrete mathematics, and in particular to combinatorics and graph theory. It is aimed at undergraduate and early graduate students and encourages an active, problem-solving approach to the material. The book treats selected topics in unusual depth and from several points of view.'
- Zentralblatt fur Didaktik der Mathematik
"'...a far-from-traditional textbook and...a joy to read. The text is lucid and sprinkled with small jokes and background stories.'
" - Times Higher Education Supplement, Friday 26th November 1999
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Preface to the second edition
Preface to the first edition
1: Introduction and basic concepts
2: Orderings
3: Combinatorial counting
4: Graphs: an introduction
5: Trees
6: Drawing graphs in the plane
7: Double-counting
8: The number of spanning trees
9: Finite projective planes
10: Probability and probabilistic proofs
11: Order from disorder: Ramsey's theorem
12: Generating functions
13: Applications of linear algebra
Appendix
Bibliography
Hints to selected exercises
Index
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