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Invitation to Discrete Mathematics Jiri Matousek

Invitation to Discrete Mathematics By Jiri Matousek

Invitation to Discrete Mathematics by Jiri Matousek


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Summary

Aims to be an introduction and a comprehensive textbook for courses in combinatorics and graph theory. This book also contains introductory chapters for specialized courses such as probabilistic methods, applied linear algebra, combinatorial enumeration, and operations research. It also contains illustrations, examples and exercises.

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Invitation to Discrete Mathematics Summary

Invitation to Discrete Mathematics by Jiri Matousek

This book is a clear and self-contained introduction to discrete mathematics, and in particular to combinatories 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 combinatories 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 thoroughly explained in the introductory chapter. An appendix summarizes the undergraduate algebra needed in some of the more advanced sections of the book.

Invitation to Discrete Mathematics Reviews

"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


"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 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 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


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; Bibliography; Hints to selected exercises; Index

Additional information

CIN0198502079G
9780198502074
0198502079
Invitation to Discrete Mathematics by Jiri Matousek
Used - Good
Paperback
Oxford University Press
1998-07-23
426
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in good condition, but if you are not entirely satisfied please get in touch with us

Customer Reviews - Invitation to Discrete Mathematics