Invitation to Discrete Mathematics - Softcover

Matousek, Jiri

Softcover

ISBN 10: 0198502079 ISBN 13: 9780198502074

Publisher: Clarendon Press, 1998

Synopsis

This book is a clear and self-contained introduction to discrete mathematics, and in particular to combinatorics and graph theory. Aimed at undergraduate and early graduate students in mathematics and computer science, it is written with the goal of stimulating interest in mathematics and provides 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 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, invariably useful for attacking new problem. More than 400 exercises, 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 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 the presentation 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, basic graph theory and graph algorithms, finite projective planes, elementary probability and the probabilistic method, generating functions, and combinatorial applications of linear algebra. General mathematical notions beyond high-school level are thouroughly explained in the introductory chapter. An appendix summarizes the undergraduate algebra needed in some of the more advanced sections of the book.

About this title

Review

"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 "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 manyparticular 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 "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 toomuch 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 "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 itsmany 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

About 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)

Edition details

• Publisher: Clarendon Press
• Publication date: 1998
• Language: English
• ISBN 10: 0198502079
• ISBN 13: 9780198502074
• Binding: Paperback
• Number of pages: 426