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Problem-Solving Methods in Combinatorics

An Approach to Olympiad Problems

  • Textbook
  • © 2013

Overview

Authors:
  1. Pablo Soberón

    1. Department of Mathematics, University College London, London, United Kingdom

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  • Explains the tools necessary tools to solve olympiad combinatorics type problems, using clear examples from recent contests

  • Includes over 120 problems with hints and full, sometimes multiple, solutions

  • May be used by olympiad students and coaches but is also useful for university courses on combinatorics

  • Almost completely self-contained, requiring very little technical knowledge

  • Includes supplementary material: sn.pub/extras

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-IX
    Download chapter PDF

  2. First Concepts

    • Pablo Soberón
    Pages 1-16

  3. The Pigeonhole Principle

    • Pablo Soberón
    Pages 17-26

  4. Invariants

    • Pablo Soberón
    Pages 27-41

  5. Graph Theory

    • Pablo Soberón
    Pages 43-57

  6. Functions

    • Pablo Soberón
    Pages 59-76

  7. Generating Functions

    • Pablo Soberón
    Pages 77-92

  8. Partitions

    • Pablo Soberón
    Pages 93-99

  9. Hints for the Problems

    • Pablo Soberón
    Pages 101-112

  10. Solutions to the Problems

    • Pablo Soberón
    Pages 113-167

  11. Back Matter

    Pages 169-174
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Keywords

About this book

Every year there is at least one combinatorics problem in each of the major international mathematical olympiads. These problems can only be solved with a very high level of wit and creativity. This book explains all the problem-solving techniques necessary to tackle these problems, with clear examples from recent contests.  It also includes a large problem section for each topic, including hints and full solutions so that the reader can practice the material covered in the book.​ The material will be useful not only to participants in the olympiads and their coaches but also in university courses on combinatorics.

Reviews

From the reviews:

 “Soberón (Univ. College London, UK) presents tools, techniques, and some tricks to tackle problems of varying difficulty in combinatorial mathematics in this well-written book. … Salient features include the wealth of examples, exercises, and problems and two additional chapters with hints and solutions to the problems. Valuable for all readers interested in combinatorics and useful as a course resource on the subject. Summing Up: Highly recommended. Upper-division undergraduate through professional mathematics collections.” (D. V. Chopra, Choice, Vol. 51 (4), December, 2013)

Authors and Affiliations

  • Department of Mathematics, University College London, London, United Kingdom

    Pablo Soberón

About the author

Pablo Soberón (born 1988) is the first Mexican to obtain a gold medal in the International Mathematical Olympiad. After participating in mathematical olympiads, he has also trained Mexican teams for various international mathematical contests. He currently does research in discrete geometry at University College London and enjoys olympiad problem-solving in his free time.

Bibliographic Information

  • Book Title: Problem-Solving Methods in Combinatorics

  • Book Subtitle: An Approach to Olympiad Problems

  • Authors: Pablo Soberón

  • DOI: https://doi.org/10.1007/978-3-0348-0597-1

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Basel 2013

  • Softcover ISBN: 978-3-0348-0596-4Published: 05 April 2013

  • eBook ISBN: 978-3-0348-0597-1Published: 20 March 2013

  • Edition Number: 1

  • Number of Pages: IX, 174

  • Number of Illustrations: 55 b/w illustrations, 10 illustrations in colour

  • Topics: Combinatorics

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