Fundamentals of Ramsey Theory
1st Edition
Published on 26. August 2024
Book
Paperback/Softback
241 pages
978-1-032-01802-7 (ISBN)
Description
Ramsey theory is a fascinating topic. The author shares his view of the topic in this contemporary overview of Ramsey theory. He presents from several points of view, adding intuition and detailed proofs, in an accessible manner unique among most books on the topic. This book covers all of the main results in Ramsey theory along with results that have not appeared in a book before.
The presentation is comprehensive and reader friendly. The book covers integer, graph, and Euclidean Ramsey theory with many proofs being combinatorial in nature. The author motivates topics and discussion, rather than just a list of theorems and proofs. In order to engage the reader, each chapter has a section of exercises.
This up-to-date book introduces the field of Ramsey theory from several different viewpoints so that the reader can decide which flavor of Ramsey theory best suits them.
Additionally, the book offers:
A chapter providing different approaches to Ramsey theory, e.g., using topological dynamics, ergodic systems, and algebra in the Stone-Cech compactification of the integers.
A chapter on the probabilistic method since it is quite central to Ramsey-type numbers.
A unique chapter presenting some applications of Ramsey theory.
Exercises in every chapter
The intended audience consists of students and mathematicians desiring to learn about Ramsey theory. An undergraduate degree in mathematics (or its equivalent for advanced undergraduates) and a combinatorics course is assumed.
TABLE OF CONENTS
Preface
List of Figures
List of Tables
Symbols
1. Introduction
2. Integer Ramsey Theory
3. Graph Ramsey Theory
4. Euclidean Ramsey Theory
5. Other Approaches to Ramsey Theory
6. The Probabilistic Method
7. Applications
Bibliography
Index
Biography
Aaron Robertson received his Ph.D. in mathematics from Temple University under the guidance of his advisor Doron Zeilberger. Upon finishing his Ph.D. he started at Colgate University in upstate New York where he is currently Professor of Mathematics. He also serves as Associate Managing editor of the journal Integers. After a brief detour into the world of permutation patterns, he has focused most of his research on Ramsey theory.
The presentation is comprehensive and reader friendly. The book covers integer, graph, and Euclidean Ramsey theory with many proofs being combinatorial in nature. The author motivates topics and discussion, rather than just a list of theorems and proofs. In order to engage the reader, each chapter has a section of exercises.
This up-to-date book introduces the field of Ramsey theory from several different viewpoints so that the reader can decide which flavor of Ramsey theory best suits them.
Additionally, the book offers:
A chapter providing different approaches to Ramsey theory, e.g., using topological dynamics, ergodic systems, and algebra in the Stone-Cech compactification of the integers.
A chapter on the probabilistic method since it is quite central to Ramsey-type numbers.
A unique chapter presenting some applications of Ramsey theory.
Exercises in every chapter
The intended audience consists of students and mathematicians desiring to learn about Ramsey theory. An undergraduate degree in mathematics (or its equivalent for advanced undergraduates) and a combinatorics course is assumed.
TABLE OF CONENTS
Preface
List of Figures
List of Tables
Symbols
1. Introduction
2. Integer Ramsey Theory
3. Graph Ramsey Theory
4. Euclidean Ramsey Theory
5. Other Approaches to Ramsey Theory
6. The Probabilistic Method
7. Applications
Bibliography
Index
Biography
Aaron Robertson received his Ph.D. in mathematics from Temple University under the guidance of his advisor Doron Zeilberger. Upon finishing his Ph.D. he started at Colgate University in upstate New York where he is currently Professor of Mathematics. He also serves as Associate Managing editor of the journal Integers. After a brief detour into the world of permutation patterns, he has focused most of his research on Ramsey theory.
More details
Series
Language
English
Place of publication
Boca Raton
United Kingdom
Publishing group
Taylor & Francis Ltd
Illustrations
29 s/w Abbildungen, 29 s/w Zeichnungen, 4 s/w Tabellen
4 Tables, black and white; 29 Line drawings, black and white; 29 Illustrations, black and white
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 14 mm
Weight
395 gr
ISBN-13
978-1-032-01802-7 (9781032018027)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Aaron Robertson
Fundamentals of Ramsey Theory
Book
06/2021
1st Edition
CRC Press
€132.50
Shipment within 10-20 days
Aaron Robertson
Fundamentals of Ramsey Theory
E-Book
06/2021
1st Edition
Chapman & Hall/CRC
€78.99
Available for download
Aaron Robertson
Fundamentals of Ramsey Theory
E-Book
06/2021
1st Edition
Chapman & Hall/CRC
€78.99
Available for download
Person
Aaron Robertson received his Ph.D. in mathematics from Temple University under the guidance of his advisor Doron Zeilberger. Upon finishing his Ph.D. he started at Colgate University in upstate New York where he is currently Professor of Mathematics. He also serves as Associate Managing editor of the journal Integers. After a brief detour into the world of permutation patterns, he has focused most of his research on Ramsey theory.
Content
1. Introduction. 1.1. What is Ramsey Theory? 1.2. Notations and Conventions. 1.3. Prerequisites. 1.4. Compactness Principle. 1.5. Set Theoretic Considerations. 1.6. Exercises. 2. Integer Ramsey Theory. 2.1. Van der Waerden's Theorem. 2.2. Equations. 2.3. Hales-Jewett Theorem. 2.4. Finite Sums. 2.5. Density Results. 2.6. Exercises. 3. Graph Ramsey Theory. 3.1. Complete Graphs. 3.2. Other Graphs. 3.3. Hypergraphs. 3.4. Infinite Graphs. 3.5. Comparing Ramsey and van der Waerden Results. 3.6. Exercises. 4. Euclidean Ramsey Theory. 4.1. Polygons. 4.2. Chromatic Number of the Plane. 4.3. Four Color Map Theorem. 4.4. Exercises. 5. Other Approaches to Ramsey Theory. 5.1. Topological Approaches. 5.2. Ergodic Theory. 5.3. Stone-Cech Compactification. 5.4. Additive Combinatorics Methods. 5.5. Exercises. 6. The Probabilistic Method. 6.1. Lower Bounds on Ramsey, van der Waerden, and Hales-Jewett Numbers. 6.2. Turan's Theorem. 6.3. Almost-surely van der Waerden and Ramsey Numbers. 6.4. Lovasz Local Lemma. 6.5. Exercises. 7. Applications. 7.1. Fermat's Last Theorem. 7.2. Encoding Information. 7.3. Data Mining. 7.4. Exercises. Bibliography. Index.