An Introduction To Ramsey Theory
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An Introduction To Ramsey Theory
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Author : Matthew Katz
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-03
An Introduction To Ramsey Theory written by Matthew Katz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
This book takes the reader on a journey through Ramsey theory, from graph theory and combinatorics to set theory to logic and metamathematics. Written in an informal style with few requisites, it develops two basic principles of Ramsey theory: many combinatorial properties persist under partitions, but to witness this persistence, one has to start with very large objects. The interplay between those two principles not only produces beautiful theorems but also touches the very foundations of mathematics. In the course of this book, the reader will learn about both aspects. Among the topics explored are Ramsey's theorem for graphs and hypergraphs, van der Waerden's theorem on arithmetic progressions, infinite ordinals and cardinals, fast growing functions, logic and provability, Gödel incompleteness, and the Paris-Harrington theorem. Quoting from the book, “There seems to be a murky abyss lurking at the bottom of mathematics. While in many ways we cannot hope to reach solid ground, mathematicians have built impressive ladders that let us explore the depths of this abyss and marvel at the limits and at the power of mathematical reasoning at the same time. Ramsey theory is one of those ladders.”
An Introduction To Ramsey Theory
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Author : Joseph E. Jones
language : en
Publisher:
Release Date : 2006
An Introduction To Ramsey Theory written by Joseph E. Jones and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Ramsey theory categories.
Fundamentals Of Ramsey Theory
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Author : Aaron Robertson
language : en
Publisher: CRC Press
Release Date : 2021-06-17
Fundamentals Of Ramsey Theory written by Aaron Robertson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-17 with Mathematics categories.
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.
Ramsey Theory
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Author : Ronald L. Graham
language : en
Publisher: John Wiley & Sons
Release Date : 1991-01-16
Ramsey Theory written by Ronald L. Graham and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-16 with Mathematics categories.
Praise for the First Edition "Anyone interested in getting an introduction to Ramsey theorywill find this illuminating..." --MAA Reviews Covering all the major concepts, proofs, and theorems, theSecond Edition of Ramsey Theory is the ultimate guideto understanding every aspect of Shelah's proof, as well asthe original proof of van der Waerden. The book offers a historicalperspective of Ramsey's fundamental paper from 1930 andErdos' and Szekeres' article from 1935, while placingthe various theorems in the context of T. S. Motzkin'sthought on the subject of "Complete Disorder isImpossible." Ramsey Theory, Second Edition includes new and excitingcoverage of Graph Ramsey Theory and Euclidean Ramsey Theory andalso relates Ramsey Theory to other areas in discrete mathematics.In addition, the book features the unprovability results of Parisand Harrington and the methods from topological dynamics pioneeredby Furstenburg. Featuring worked proofs and outside applications, RamseyTheory, Second Edition addresses: * Ramsey and density theorems on both broad and meticulousscales * Extentions and implications of van der Waerden's Theorem,the Hales-Jewett Theorem, Roth's Theorem, Rado'sTheorem, Szemeredi's Theorem, and the Shelah Proof * Regular homogeneous and nonhomogeneous systems andequations * Special cases and broader interdisciplinary applications ofRamsey Theory principles An invaluable reference for professional mathematicians workingin discrete mathematics, combinatorics, and algorithms, RamseyTheory, Second Edition is the definitive work on thesubject.
Introductory Graph Theory
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Author : Gary Chartrand
language : en
Publisher: Courier Corporation
Release Date : 2012-04-30
Introductory Graph Theory written by Gary Chartrand and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-30 with Science categories.
Clear, lively style covers all basics of theory and application, including mathematical models, elementary graph theory, transportation problems, connection problems, party problems, diagraphs and mathematical models, games and puzzles, more.
Mathematics Of Ramsey Theory
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Author : Jaroslav Nesetril
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematics Of Ramsey Theory written by Jaroslav Nesetril and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
One of the important areas of contemporary combinatorics is Ramsey theory. Ramsey theory is basically the study of structure preserved under partitions. The general philosophy is reflected by its interdisciplinary character. The ideas of Ramsey theory are shared by logicians, set theorists and combinatorists, and have been successfully applied in other branches of mathematics. The whole subject is quickly developing and has some new and unexpected applications in areas as remote as functional analysis and theoretical computer science. This book is a homogeneous collection of research and survey articles by leading specialists. It surveys recent activity in this diverse subject and brings the reader up to the boundary of present knowledge. It covers virtually all main approaches to the subject and suggests various problems for individual research.
Walk Through Combinatorics A An Introduction To Enumeration Graph Theory And Selected Other Topics Fifth Edition
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Author : Miklos Bona
language : en
Publisher: World Scientific
Release Date : 2023-08-08
Walk Through Combinatorics A An Introduction To Enumeration Graph Theory And Selected Other Topics Fifth Edition written by Miklos Bona and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-08 with Mathematics categories.
The first half of the book walks the reader through methods of counting, both direct elementary methods and the more advanced method of generating functions. Then, in the second half of the book, the reader learns how to apply these methods to fascinating objects, such as graphs, designs, random variables, partially ordered sets, and algorithms. In short, the first half emphasizes depth by discussing counting methods at length; the second half aims for breadth, by showing how numerous the applications of our methods are.New to this fifth edition of A Walk Through Combinatorics is the addition of Instant Check exercises — more than a hundred in total — which are located at the end of most subsections. As was the case for all previous editions, the exercises sometimes contain new material that was not discussed in the text, allowing instructors to spend more time on a given topic if they wish to do so. With a thorough introduction into enumeration and graph theory, as well as a chapter on permutation patterns (not often covered in other textbooks), this book is well suited for any undergraduate introductory combinatorics class.
Basics Of Ramsey Theory
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Author : Veselin Jungić
language : en
Publisher: CRC Press
Release Date : 2023-06-09
Basics Of Ramsey Theory written by Veselin Jungić and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-09 with Mathematics categories.
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
Galois Theory For Beginners A Historical Perspective Second Edition
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Author : Jörg Bewersdorff
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-15
Galois Theory For Beginners A Historical Perspective Second Edition written by Jörg Bewersdorff and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-15 with Education categories.
Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. In this book, Bewersdorff follows the historical development of the theory, emphasizing concrete examples along the way. As a result, many mathematical abstractions are now seen as the natural consequence of particular investigations. Few prerequisites are needed beyond general college mathematics, since the necessary ideas and properties of groups and fields are provided as needed. Results in Galois theory are formulated first in a concrete, elementary way, then in the modern form. Each chapter begins with a simple question that gives the reader an idea of the nature and difficulty of what lies ahead. The applications of the theory to geometric constructions, including the ancient problems of squaring the circle, duplicating the cube, and trisecting the angle, and the construction of regular n n-gons are also presented. This new edition contains an additional chapter as well as twenty facsimiles of milestones of classical algebra. It is suitable for undergraduates and graduate students, as well as teachers and mathematicians seeking a historical and stimulating perspective on the field.
Ramsey Theory
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Author : Alexander Soifer
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-29
Ramsey Theory written by Alexander Soifer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-29 with Mathematics categories.
This book explores the theory’s history, recent developments, and some promising future directions through invited surveys written by prominent researchers in the field. The first three surveys provide historical background on the subject; the last three address Euclidean Ramsey theory and related coloring problems. In addition, open problems posed throughout the volume and in the concluding open problem chapter will appeal to graduate students and mathematicians alike.