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Full Product Details

Author:   Hans Jürgen Prömel
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   Softcover reprint of the original 1st ed. 2013
Dimensions:   Width: 15.50cm , Height: 1.30cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9783319344867

ISBN 10:   3319344862
Pages:   232
Publication Date:   23 August 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

Foreword by Angelika Steger.- Preface.- Conventions.- Part I Roots of Ramsey Theory: 1.1 Ramsey’s theorem.- 1.2 From Hilbert’s cube lemma to Rado’s thesis.- Part II A Starting Point of Ramsey Theory: Parameter Sets: 2.1 Definitions and basic examples.- 2.2 Hales-Jewett’s theorem.- 2.3 Graham-Rothschild’s theorem.- 2.4 Canonical partitions.- Part III Back to the Roots: Sets: 3.1 Ramsey numbers.- 3.2 Rapidly growing Ramsey functions.- 3.3 Product theorems.- 3.4 A quasi Ramsey theorem.- 3.5 Partition relations for cardinal numbers.- Part IV Graphs and Hypergraphs: 4.1 Finite graphs.- 4.2 Infinite graphs.- 4.3 Hypergraphs on parameter sets.- 4.4. Ramsey statements for random graphs.- 4.5 Sparse Ramsey Theorems.- Part V Density Ramsey Theorems: 5.1 Szemerédi’s Theorem.- 5.2 Density Hales-Jewett Theorem.- 5.3 Proof of the density Hales-Jewett theorem.- References.- Index.

Reviews

From the book reviews: The results and proofs covered in the book are clearly explained and the material covered is extensive. I therefore think this book provides a strong introductory reference for students. ... Further, the monograph will be a great addition to the bookshelves of researchers in the field of Ramsey theory and related areas, as a reference on both classical results and some of the more recent breakthroughs in the subject. (Andrew Clark Treglown, Mathematical Reviews, October, 2014) Proemel (Technical Univ. Darmstadt, Germany) includes three gems of this episodic subject, each sufficient to sell the book: a self-contained treatment of the Paris-Harrington theorem showing that a certain Ramsey-type theorem witnesses the incompleteness of Peano arithmetic; a detailed treatment of the Graham-Rothschild theorem long ago made famous for its fast-growing functions by M. Gardner's Scientific American column; and a very short proof (now) of Szemeredi's theorem ... . Summing Up: Highly recommended. Upper-division undergraduates and above. (D. V. Feldman, Choice, Vol. 51 (11), August, 2014)

From the book reviews: The results and proofs covered in the book are clearly explained and the material covered is extensive. I therefore think this book provides a strong introductory reference for students. ... Further, the monograph will be a great addition to the bookshelves of researchers in the field of Ramsey theory and related areas, as a reference on both classical results and some of the more recent breakthroughs in the subject. (Andrew Clark Treglown, Mathematical Reviews, October, 2014) Promel (Technical Univ. Darmstadt, Germany) includes three gems of this episodic subject, each sufficient to sell the book: a self-contained treatment of the Paris-Harrington theorem showing that a certain Ramsey-type theorem witnesses the incompleteness of Peano arithmetic; a detailed treatment of the Graham-Rothschild theorem long ago made famous for its fast-growing functions by M. Gardner's Scientific American column; and a very short proof (now) of Szemeredi's theorem ... . Summing Up: Highly recommended. Upper-division undergraduates and above. (D. V. Feldman, Choice, Vol. 51 (11), August, 2014)

Author Information

The author was one of the driving forces of the field in the eighties and nineties of the last century. Many of the, by now standard, proofs of the field were discovered by him.

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