Invitation to discrete mathematics

Jiří Matoušek, Jaroslav Nešetřil

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.

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[目次]

  • 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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この本の情報

書名 Invitation to discrete mathematics
著作者等 Matoušek, Jiří
Nesetril, Jaroslav
Nesetril Jaroslav
Matousek Jiri
出版元 Oxford University Press
刊行年月 2009
版表示 2nd ed
ページ数 xvii, 443 p.
大きさ 24 cm
ISBN 9780198570424
9780198570431
NCID BA87489774
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国
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