Invitation to Discrete Mathematics / Edition 2

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Overview

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.
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Editorial Reviews

Booknews
Designed primarily for undergraduate and early graduate students, this book is based on the notion that mathematics should cultivate clear and logical thinking. To this end, Matousek (computer science) and Nesetril (mathematics) both of Charles University, Prague, have included over 400 exercises ranging in difficulty and many with hints or suggestions for solution. The authors have used a narrow focus to examine combinatorics and graph theory in depth, rather than the whole range of discrete mathematics. Some specific topics covered include asymptotic estimates, finite projective planes, probability, generating functions, and graph algorithms. Annotation c. Book News, Inc., Portland, OR (booknews.com)
From the Publisher

"Offers an introduction to nonlinear chemical dynamics written especially for chemists, covering oscillating reactions, chaos, and chemical pattern formation. Begins with a brief history of nonlinear chemical dynamics and a review of necessary mathematics and chemistry, then provides an overview of nonlinear dynamics, starting with the flow reactor and moving on to a detailed discussion of chemical oscillators. Later chapters cover advanced topics such as biological systems, polymers, and interactions between fields and waves. Includes a series of classroom-tested demonstrations and experiments appropriate for an undergraduate laboratory. Assumes an undergraduate knowledge of chemistry. Epstein is a professor of chemistry at Brandeis University. Pojman is a professor of chemistry and biochemistry at the University of Southern Mississippi."--SciTech Book News

"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. . . . 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."--Choice

"The primary aim of the book, as stated in the preface, is 'to lead the student to understand and appreciate mathematical notions, definitions, and proofs, to solve problems requiring more than just standard recipes, and to express mathematical thought precisely and rigorously.' The book delivers what it promises. From the opening chapter, which sets the mathematical and pedagogical tone for the book, to the last, on linear algebra applications to graph theory, Invitation to Discrete Mathematics is an honest, detailed, and mathematically rigorous text. All 451 exercises are classified according to difficulty. Most of them involve mathematical argumentation, and hints are given for many. Included in the exercise sets are frequent 'fun' problems that are only loosely related to the preceding textual material. These problems help build the student's mathematical sophistication and facility in conjecture, proof, and refutation."--Mathematics Teacher

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Product Details

  • ISBN-13: 9780198570431
  • Publisher: Oxford University Press, USA
  • Publication date: 7/15/2008
  • Edition number: 2
  • Pages: 456
  • Product dimensions: 6.40 (w) x 9.30 (h) x 1.20 (d)

Meet the Author

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 Berlin). Prize for Young Mathematicians of the 2nd European Congress of Mathematics in Budapest in 1996, speaker at the ICM 1998.
Jaroslav Nesetril received his PhD from the Charles University in Prague in 1975 and is now Professor of Mathematics at Charles University Prague. He has held several visiting positions abroad (U.S.A., Canada, Germany). Currently he is the head of the Centre for Theoretical Computer Science (ITI) at Charles University and the director of the international center for Discrete Mathematics, Theoretical Computer Science and Their Applications (DIMATIA).

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Table of Contents

1 Introduction and basic concepts 1

2 Orderings 43

3 Combinatorial counting 59

4 Graphs: an introduction 109

5 Trees 153

6 Drawing graphs in the plane 182

7 Double-counting 217

8 The number of spanning trees 239

9 Finite projective planes 261

10 Probability and probabilistic proofs 284

11 Order from disorder: Ramsey's theorem 317

12 Generating functions 325

13 Applications of linear algebra 364

App Prerequisites from algebra 395

Bibliography 402

Hints to selected exercises 407

Index 433

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