Fundamentals of Ramsey Theory

2021-06-17 Mathematics

Author : Aaron Robertson
Release : 2021-06-17
Genre : Mathematics
Kind : eBook
Book Rating : 911/5 ( reviews)

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Book Synopsis Fundamentals of Ramsey Theory by : Aaron Robertson

Download or read book Fundamentals of Ramsey Theory written by Aaron Robertson. This book was released on 2021-06-17. Available in PDF, EPUB and Kindle. Book excerpt: 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-Čech 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.

Basics of Ramsey Theory

2023-06-09 Mathematics

Author : Veselin Jungić
Release : 2023-06-09
Genre : Mathematics
Kind : eBook
Book Rating : 643/5 ( reviews)

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Book Synopsis Basics of Ramsey Theory by : Veselin Jungić

Download or read book Basics of Ramsey Theory written by Veselin Jungić. This book was released on 2023-06-09. Available in PDF, EPUB and Kindle. Book excerpt: Basics of Ramsey Theory serves as a gentle introduction to Ramsey theory for students interested in becoming familiar with a dynamic segment of contemporary mathematics that combines ideas from number theory and combinatorics. The core of the of the book consists of discussions and proofs of the results now universally known as Ramsey’s theorem, van der Waerden’s theorem, Schur’s theorem, Rado’s theorem, the Hales–Jewett theorem, and the Happy End Problem of Erdős and Szekeres. The aim is to present these in a manner that will be challenging but enjoyable, and broadly accessible to anyone with a genuine interest in mathematics. Features Suitable for any undergraduate student who has successfully completed the standard calculus sequence of courses and a standard first (or second) year linear algebra course Filled with visual proofs of fundamental theorems Contains numerous exercises (with their solutions) accessible to undergraduate students Serves as both a textbook or as a supplementary text in an elective course in combinatorics and aimed at a diverse group of students interested in mathematics

Rudiments of Ramsey Theory

2015-10-01 Mathematics

Author : Ron Graham
Release : 2015-10-01
Genre : Mathematics
Kind : eBook
Book Rating : 564/5 ( reviews)

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Book Synopsis Rudiments of Ramsey Theory by : Ron Graham

Download or read book Rudiments of Ramsey Theory written by Ron Graham. This book was released on 2015-10-01. Available in PDF, EPUB and Kindle. Book excerpt: In every sufficiently large structure which has been partitioned there will always be some well-behaved structure in one of the parts. This takes many forms. For example, colorings of the integers by finitely many colors must have long monochromatic arithmetic progressions (van der Waerden's theorem); and colorings of the edges of large graphs must have monochromatic subgraphs of a specified type (Ramsey's theorem). This book explores many of the basic results and variations of this theory. Since the first edition of this book there have been many advances in this field. In the second edition the authors update the exposition to reflect the current state of the art. They also include many pointers to modern results. A co-publication of the AMS and CBMS.

Rudiments of Ramsey Theory

1981-12-31 Mathematics

Author : Ronald L. Graham
Release : 1981-12-31
Genre : Mathematics
Kind : eBook
Book Rating : 969/5 ( reviews)

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Book Synopsis Rudiments of Ramsey Theory by : Ronald L. Graham

Download or read book Rudiments of Ramsey Theory written by Ronald L. Graham. This book was released on 1981-12-31. Available in PDF, EPUB and Kindle. Book excerpt: It is no exaggeration to say that over the past several decades there has been a veritable explosion of activity in the general field of combinatorics. Ramsey theory, in particular, has shown remarkable growth. This book gives a picture of the state of the art of Ramsey theory at the time of Graham's CBMS lectures. In keeping with the style of the lectures, the exposition is informal. However, complete proofs are given for most of the basic results presented. In addition, many useful results may be found in the exercises and problems. Loosely speaking, Ramsey theory is the branch of combinatorics that deals with structures that are preserved under partitions. Typically, one looks at the following kind of question: If a particular structure (e.g., algebraic, combinatorial or geometric) is arbitrarily partitioned into finitely many classes, what kinds of substructures must always remain intact in at least one of the classes? At the time of these lectures, a number of spectacular advances had been made in the field of Ramsey theory. These include: the work of Szemeredi and Furstenberg settling the venerable conjecture of Erdos and Turan, the Nesetril-Rodl theorems on induced Ramsey properties, the results of Paris and Harrington on ``large'' Ramsey numbers and undecidability in first-order Peano arithmetic, Deuber's solution to the old partition regularity conjecture of Rado, Hindman's surprising generalization of Schur's theorem, and the resolution of Rota's conjecture on Ramsey's theorem for vector spaces by Graham, Leeb and Rothschild. It has also become apparent that the ideas and techniques of Ramsey theory span a rather broad range of mathematical areas, interacting in essential ways with parts of set theory, graph theory, combinatorial number theory, probability theory, analysis and even theoretical computer science. These lecture notes lay out the foundation on which much of this work is based. Relatively little specialized mathematical background is required for this book. It should be accessible to upper division students.

Ramsey Theory

1980 Mathematics

Author : Ronald L. Graham
Release : 1980
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Ramsey Theory by : Ronald L. Graham

Download or read book Ramsey Theory written by Ronald L. Graham. This book was released on 1980. Available in PDF, EPUB and Kindle. Book excerpt:

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