Invitation to Discrete Mathematics

Paperback | October 1, 2008

byJiri Matousek, Jaroslav Nesetril

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This book 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 thepresented material. The reader is led to an understanding of the basic principles and methods of actually doing mathematics (and having fun at that). Being more narrowly focused than many discrete mathematics textbooks and treating selected topics in an unusual depth and from several points 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 useful for attacking new problems. More than 400 enclosed exercises with a widerange 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 mathematicaleducation 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. iInvitation to Discrete Mathematics/i should make a delightfulreading 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 oflinear 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.

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From the Publisher

This book 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 thepresented material. The reader is led to an underst...

Jiri Matousek received his PhD in Mathematics from the Charles University in Prague in 1990 and is now Professor of Computer Science at Charles University Prague. He has held several visiting positions at universities in the U.S., Germany, Switzerland, Japan, and other countries. Humboldt Research Fellow in 1992 (Free University Berl...

other books by Jiri Matousek

Understanding and Using Linear Programming
Understanding and Using Linear Programming

Paperback|Nov 14 2006

$89.50 online$90.95list price
Format:PaperbackDimensions:456 pages, 9.21 × 6.14 × 0.95 inPublished:October 1, 2008Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198570422

ISBN - 13:9780198570424

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Table of Contents

Preface to the second editionPreface to the first edition1. Introduction and basic concepts2. Orderings3. Combinatorial counting4. Graphs: an introduction5. Trees6. Drawing graphs in the plane7. Double-counting8. The number of spanning trees9. Finite projective planes10. Probability and probabilistic proofs11. Order from disorder: Ramsey's theorem12. Generating functions13. Applications of linear algebraAppendixBibliographyHints to selected exercisesIndex

Editorial Reviews

"...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