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The Discrete Mathematical Charms of Paul Erdős
A Simple Introduction

$29.99 (P)

  • Date Published: November 2021
  • availability: In stock
  • format: Paperback
  • isbn: 9781108927406

$ 29.99 (P)
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About the Authors
  • Paul Erdős published more papers during his lifetime than any other mathematician, especially in discrete mathematics. He had a nose for beautiful, simply-stated problems with solutions that have far-reaching consequences across mathematics. This captivating book, written for students, provides an easy-to-understand introduction to discrete mathematics by presenting questions that intrigued Erdős, along with his brilliant ways of working toward their answers. It includes young Erdős's proof of Bertrand's postulate, the Erdős-Szekeres Happy End Theorem, De Bruijn-Erdős theorem, Erdős-Rado delta-systems, Erdős-Ko-Rado theorem, Erdős-Stone theorem, the Erdős-Rényi-Sós Friendship Theorem, Erdős-Rényi random graphs, the Chvátal-Erdős theorem on Hamilton cycles, and other results of Erdős, as well as results related to his work, such as Ramsey's theorem or Deza's theorem on weak delta-systems. Its appendix covers topics normally missing from introductory courses. Filled with personal anecdotes about Erdős, this book offers a behind-the-scenes look at interactions with the legendary collaborator.

    • Introduces students to foundational results in discrete mathematics and many key theorems posited by Erdős and colleagues
    • Presents different proofs of a single theorem to show the reader a view of mathematics as an unfolding adventure rather than an ossified discipline
    • Classroom-tested expanded lecture notes accessible to university students at all levels, including contestants in mathematical olympiads
    • Includes up-to-date references to latest breakthrough results in the field
    • 64 figures, including rare archival material and never before published photographs from George Csicsery's film N Is a Number.
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    Reviews & endorsements

    'Vašek Chvátal was born to write this one-of-a-kind book. Readers cannot help but be captivated by the evident love with which every page has been written. The human side of mathematics is intertwined beautifully with first-rate exposition of first-rate results.' Donald Knuth, Stanford University

    ‘This book is a treasure trove from so many viewpoints. It is a wonderful introduction and an alluring invitation to discrete mathematics - now a central field of mathematics identified mostly with the hero of this book. With lucid, carefully planned chapters on different topics it demonstrates the unique way in which Paul Erdős, one of the most prolific and influential mathematicians of the twentieth century, invented and approached problems. Sprinkled with historical and personal anecdotes and pictures, it opens a window to the unique personality of ‘Uncle Paul’. And implicitly, it reveals the charming and candid way in which Vašek Chvátal, an authority in the field and a lifelong friend and collaborator of Erdős, likes to combine teaching and story-telling.’ Avi Wigderson, IAS, Princeton

    ‘Paul Erdős is one of the founding fathers of modern combinatorics, whose ability to pose beautiful problems greatly determined the development of this field and influenced many other areas of mathematics. This book uses some basic questions, which intrigued Paul Erdős, to give a nice introduction to many topics in discrete mathematics. It contains a collection of beautiful results, covering such diverse subjects as discrete geometry, Ramsey theory, graph colorings, extremal problems for graphs and set systems and some others. It presents many elegant proofs and exposes the reader to various powerful combinatorial techniques.’ Benjamin Sudakov, ETH Zurich

    ‘This is a brilliant book. It manages in one fell swoop to survey and develop a large part of combinatorial mathematics while at the same time chronicling the work of Paul Erdős. His contributions to different areas of mathematics are seen here to be part of a coherent whole. Chvátal’s presentation is particularly appealing and accessible. The wonderful personal recollections add to the mathematical content to provide a portrait of Erdős' mind recognizable to those who knew him.’ Bruce Rothschild, University of California, Los Angeles

    ‘Vašek Chvátal's book is a gem. Paul Erdős' favorite problems and best work are beautifully laid out. Readers unfamiliar with Erdős' work cannot fail to appreciate its power and elegance, and those who have seen bits and pieces will have the pleasure of seeing it thoughtfully and lovingly presented by a master. It's hard to imagine now, but there was a time when combinatorics was thought to be a jumble of results without depth or coherence. 'Uncle' Paul understood its heart and soul, and nowhere is this more evident than in Chvátal's wonderful compendium. This volume belongs on every math-lover's night-table!’ Peter Winkler, Dartmouth College

    ‘Beautiful mathematics is presented with great care and clarity in Vašek Chvátal's book, complemented with well-written anecdotes and personal reminiscences about Paul Erdős. This combination makes the book a very enjoyable reading and a lively tribute to the memory of one of the most prolific mathematicians of all time. Studying discrete mathematics from this book is likely to give a great experience to students and established researchers alike.’ Gábor Simonyi, Rényi Institute, Budapest

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    Product details

    • Date Published: November 2021
    • format: Paperback
    • isbn: 9781108927406
    • length: 266 pages
    • dimensions: 243 x 169 x 10 mm
    • weight: 0.54kg
    • availability: In stock
  • Table of Contents

    Foreword
    Preface
    Acknowledgments
    Introduction
    1. A glorious beginning – Bertrand's postulate
    2. Discrete geometry and spinoffs
    3. Ramsey's theorem
    4. Delta-systems
    5. Extremal set theory
    6. Van der Waerden's theorem
    7. Extremal graph theory
    8. The friendship theorem
    9. Chromatic number
    10. Thresholds of graph properties
    11. Hamilton cycles
    Appendix A. A few tricks of the trade
    Appendix B. Definitions, terminology, notation
    Appendix C. More on Erdős
    References
    Index.

  • Author

    Vašek Chvátal, Concordia University, Montréal
    Vašek Chvátal is Professor Emeritus of Concordia University, where he served as Canada Research Chair in Combinatorial Optimization (2004–2011) and Canada Research Chair in Discrete Mathematics from 2011 to his retirement in 2014. He is the author of Linear Programming (1983) and co-author of The Traveling Salesman Problem: A Computational Study (2007). In the 1970s, he wrote three joint papers with Paul Erdős. He is a recipient of the CSGSS Award for Excellence in Teaching, Rutgers University (1992, 1993, 2001) and co-recipient of the Beale-Orchard-Hays Prize (2000), Frederick W. Lanchester Prize (2007), and John von Neumann Theory Prize (2015).

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