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Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory

  • Book
  • © 2019

Overview

Authors:
  1. Mauro Di Nasso

    1. Department of Mathematics, Universita di Pisa, Pisa, Italy

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  2. Isaac Goldbring

    1. Department of Mathematics, University of California, Irvine, Irvine, USA

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  3. Martino Lupini

    1. School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand

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  • Presents the first introduction to nonstandard methods geared towards combinatorics
  • Includes new nonstandard proofs of classical results in Ramsey theory
  • Provides a self-contained introduction to the literature of nonstandard methods in combinatorics
  • Numerous exercises help readers to familiarize themselves with the material

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2239)

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About this book

The goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent developments initially obtained in the nonstandard setting. This makes it the first combinatorics-focused account of nonstandard methods to be aimed at a general (graduate-level) mathematical audience. This book will provide a natural starting point for researchers interested in approaching the rapidly growing literature on combinatorial results obtained via nonstandard methods. The primary audience consists of graduate students and specialists in logic and combinatorics who wish to pursue research at the interface between these areas.


Keywords

Table of contents (17 chapters)

  1. Other Topics

    1. Triangle Removal and Szemerédi Regularity

      • Mauro Di Nasso, Isaac Goldbring, Martino Lupini
      Pages 173-180

    2. Approximate Groups

      • Mauro Di Nasso, Isaac Goldbring, Martino Lupini
      Pages 181-186

  2. Back Matter

    Pages 187-206
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Authors and Affiliations

  • Department of Mathematics, Universita di Pisa, Pisa, Italy

    Mauro Di Nasso

  • Department of Mathematics, University of California, Irvine, Irvine, USA

    Isaac Goldbring

  • School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand

    Martino Lupini

Bibliographic Information

  • Book Title: Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory

  • Authors: Mauro Di Nasso, Isaac Goldbring, Martino Lupini

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-17956-4

  • Publisher: Springer Cham

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

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Softcover ISBN: 978-3-030-17955-7Published: 24 May 2019

  • eBook ISBN: 978-3-030-17956-4Published: 23 May 2019

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVI, 206

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Combinatorics, Mathematical Logic and Foundations

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