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Discrete Mathematics

Elementary and Beyond

Part of the book series: Undergraduate Texts in Mathematics (UTM)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-ix
  2. Let’s Count!

    • L. Lovász, J. Pelikán, K. Vesztergombi
    Pages 1-24
  3. Combinatorial Tools

    • L. Lovász, J. Pelikán, K. Vesztergombi
    Pages 25-42
  4. Binomial Coefficients and Pascal’s Triangle

    • L. Lovász, J. Pelikán, K. Vesztergombi
    Pages 43-64
  5. Fibonacci Numbers

    • L. Lovász, J. Pelikán, K. Vesztergombi
    Pages 65-75
  6. Combinatorial Probability

    • L. Lovász, J. Pelikán, K. Vesztergombi
    Pages 77-85
  7. Integers, Divisors, and Primes

    • L. Lovász, J. Pelikán, K. Vesztergombi
    Pages 87-123
  8. Graphs

    • L. Lovász, J. Pelikán, K. Vesztergombi
    Pages 125-140
  9. Trees

    • L. Lovász, J. Pelikán, K. Vesztergombi
    Pages 141-156
  10. Finding the Optimum

    • L. Lovász, J. Pelikán, K. Vesztergombi
    Pages 157-164
  11. Matchings in Graphs

    • L. Lovász, J. Pelikán, K. Vesztergombi
    Pages 165-178
  12. Combinatorics in Geometry

    • L. Lovász, J. Pelikán, K. Vesztergombi
    Pages 179-187
  13. Euler’s Formula

    • L. Lovász, J. Pelikán, K. Vesztergombi
    Pages 189-196
  14. Coloring Maps and Graphs

    • L. Lovász, J. Pelikán, K. Vesztergombi
    Pages 197-210
  15. Finite Geometries, Codes, Latin Squares, and Other Pretty Creatures

    • L. Lovász, J. Pelikán, K. Vesztergombi
    Pages 211-238
  16. A Glimpse of Complexity and Cryptography

    • L. Lovász, J. Pelikán, K. Vesztergombi
    Pages 239-250
  17. Answers to Exercises

    • L. Lovász, J. Pelikán, K. Vesztergombi
    Pages 251-286
  18. Back Matter

    Pages 287-292

About this book

 Discrete mathematics is quickly becoming one of the most important areas of mathematical research, with applications to cryptography, linear programming, coding theory and the theory of computing. This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of discrete mathematics, mostly from the areas of combinatorics and graph theory, with a little number theory, probability, and combinatorial geometry. Wherever possible, the authors use proofs and problem solving to help students understand the solutions to problems. In addition, there are numerous examples, figures and exercises spread throughout the book.

László Lovász is a Senior Researcher in the Theory Group at Microsoft Corporation. He is a recipient of the 1999 Wolf Prize and the Gödel Prize for the top paper in Computer Science. József Pelikán is Professor of Mathematics in the Department of Algebra and Number Theory at Eötvös Loránd University, Hungary. In 2002, he was elected Chairman of the Advisory Board of the International Mathematical Olympiad. Katalin Vesztergombi is Senior Lecturer in the Department of Mathematics at the University of Washington.

Keywords

  • Combinatorics
  • Matching
  • Prime
  • coding theory
  • combinatorial geometry
  • cryptography
  • graph theory
  • linear optimization
  • number theory

Reviews

From the reviews:

"The goal of this book is to use the introduction to discrete mathematics … . Consequently, the authors … take a lot of time to explain proof techniques and to motivate definitions and style. The language is very informal and easy to read. The level is always introductory which makes it possible to give a taste of a wide range of topics … . There are a lot of exercises … which makes it perfectly suitable for self-study." (T. Eisenkölbl, Monatshefte für Mathematik, Vol. 144 (2), 2005)

"The book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of discrete mathematics … . Wherever possible, the authors use proofs and problem solving to help students understand the solutions to problems. In addition, there are numerous examples, figures, and exercises spread throughout the book." (Zentralblatt für Didaktik der Mathematik, January, 2004)

"The title of this book is quite apposite … . The text is, in fact, based on introductory courses in discrete mathematics … . the emphasis throughout the book is on finding efficient and imaginative ways to tackle problems and to develop general results. … I would see it as a valuable resource of enrichment activities for students … . is eminently suited for self-study (there are plenty of exercises and solutions) and can be warmly recommended for the school library." (Gerry Leversha, The Mathematical Gazette, Vol. 88 (512), 2004)

"This book is an excellent introduction to a lot of problems of discrete mathematics. … The authors discuss a number of selected results and methods, mostly from the areas of combinatorics and graph theory … . This book is appealed to a broad range of readers, including students and post-graduate students, teachers of mathematics, mathematical amateurs. The authors use proofs and problem solving to help students understand the solutions to problems. In addition, there are numerous examples, figures and exercises spread throughout the book." (M.I Yadrenko, Zentralblatt MATH, Issue 1017, 2003)

"This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of discrete mathematics … . Wherever possible, the authors use proofs and problem solving to help students understand the solutions to problems. In addition, there are numerous examples, figures, and exercises spread throughout the book." (L’ Enseignement Mathematique, Vol. 49 (1-2), 2003)

"The aim of this book is NOT to cover discrete mathematics in depth. Rather, it discusses a number of selected results and methods … . The authors develop most topics to the extent that they can describe the discrete mathematics behind an important application of mathematics … . Another feature that is not covered in other discrete mathematics books is the use of ESTIMATES … . There are questions posed in the text and problems at the end of each chapter with solutions … ." (The Bulletin of Mathematics Books, Issue 43, February, 2003)

Authors and Affiliations

  • Microsoft Research, Microsoft Corporation, Redmond, USA

    L. Lovász

  • Department of Algebra and Number Theory, Eõtvõs Loránd University, Budapest, Hungary

    J. Pelikán

  • Department of Mathematics, University of Washington, Seattle, USA

    K. Vesztergombi

About the authors

 László Lovász is a Senior Researcher in the Theory Group at Microsoft Corporation. He is a recipient of the 1999 Wolf Prize and the Gödel Prize for the top paper in Computer Science. József Pelikán is Professor of Mathematics in the Department of Algebra and Number Theory at Eötvös Loránd University, Hungary. In 2002, he was elected Chairman of the Advisory Board of the International Mathematical Olympiad. Katalin Vesztergombi is Senior Lecturer in the Department of Mathematics at the University of Washington.

Bibliographic Information

  • Book Title: Discrete Mathematics

  • Book Subtitle: Elementary and Beyond

  • Authors: L. Lovász, J. Pelikán, K. Vesztergombi

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/b97469

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2003

  • Hardcover ISBN: 978-0-387-95584-1

  • Softcover ISBN: 978-0-387-95585-8

  • eBook ISBN: 978-0-387-21777-2

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: IX, 284

  • Topics: Discrete Mathematics, Number Theory

Buying options

eBook USD 44.99
Price excludes VAT (USA)
  • ISBN: 978-0-387-21777-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 59.99
Price excludes VAT (USA)
Hardcover Book USD 84.99
Price excludes VAT (USA)