Introduction To Ramsey Spaces Am 174

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Introduction to Ramsey Spaces (AM-174)

Author : Stevo Todorcevic
Publisher : Princeton University Press
ISBN 13 : 1400835402
Total Pages : 296 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Introduction to Ramsey Spaces (AM-174) by : Stevo Todorcevic

Download or read book Introduction to Ramsey Spaces (AM-174) written by Stevo Todorcevic and published by Princeton University Press. This book was released on 2010-07-01 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ramsey theory is a fast-growing area of combinatorics with deep connections to other fields of mathematics such as topological dynamics, ergodic theory, mathematical logic, and algebra. The area of Ramsey theory dealing with Ramsey-type phenomena in higher dimensions is particularly useful. Introduction to Ramsey Spaces presents in a systematic way a method for building higher-dimensional Ramsey spaces from basic one-dimensional principles. It is the first book-length treatment of this area of Ramsey theory, and emphasizes applications for related and surrounding fields of mathematics, such as set theory, combinatorics, real and functional analysis, and topology. In order to facilitate accessibility, the book gives the method in its axiomatic form with examples that cover many important parts of Ramsey theory both finite and infinite. An exciting new direction for combinatorics, this book will interest graduate students and researchers working in mathematical subdisciplines requiring the mastery and practice of high-dimensional Ramsey theory.

Theorems of the 21st Century

Author : Bogdan Grechuk
Publisher : Springer
ISBN 13 : 303019096X
Total Pages : 446 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Theorems of the 21st Century by : Bogdan Grechuk

Download or read book Theorems of the 21st Century written by Bogdan Grechuk and published by Springer. This book was released on 2019-06-15 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of short descriptions of 106 mathematical theorems, which belong to the great achievements of 21st century mathematics but require relatively little mathematical background to understand their formulation and appreciate their importance. The selected theorems of this volume, chosen from the famous Annals of Mathematics journal, cover a broad range of topics from across mathematics. Each theorem description is essentially self-contained, can be read independently of the others, and requires as little preliminary knowledge as possible. Although the sections often start with an informal discussion and toy examples, all the necessary definitions are included and each description culminates in the precise formulation of the corresponding theorem. Filling the gap between surveys written for mathematicians and popular mathematics, this book is intended for readers with a keen interest in contemporary mathematics.

Ramsey Theory for Product Spaces

Author : Pandelis Dodos
Publisher : American Mathematical Soc.
ISBN 13 : 1470428083
Total Pages : 245 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Ramsey Theory for Product Spaces by : Pandelis Dodos

Download or read book Ramsey Theory for Product Spaces written by Pandelis Dodos and published by American Mathematical Soc.. This book was released on 2016-05-16 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ramsey theory is a dynamic area of combinatorics that has various applications in analysis, ergodic theory, logic, number theory, probability theory, theoretical computer science, and topological dynamics. This book is devoted to one of the most important areas of Ramsey theory—the Ramsey theory of product spaces. It is a culmination of a series of recent breakthroughs by the two authors and their students who were able to lift this theory to the infinite-dimensional case. The book presents many major results and methods in the area, such as Szemerédi's regularity method, the hypergraph removal lemma, and the density Hales–Jewett theorem. This book addresses researchers in combinatorics but also working mathematicians and advanced graduate students who are interested in Ramsey theory. The prerequisites for reading this book are rather minimal: it only requires familiarity, at the graduate level, with probability theory and real analysis. Some familiarity with the basics of Ramsey theory would be beneficial, though not necessary.

The Fascinating World of Graph Theory

Author : Arthur Benjamin
Publisher : Princeton University Press
ISBN 13 : 0691175632
Total Pages : 338 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis The Fascinating World of Graph Theory by : Arthur Benjamin

Download or read book The Fascinating World of Graph Theory written by Arthur Benjamin and published by Princeton University Press. This book was released on 2017-06-06 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history, formulas, and most famous puzzles of graph theory Graph theory goes back several centuries and revolves around the study of graphs—mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics—and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducing fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, and each chapter contains math exercises for readers to savor. An eye-opening journey into the world of graphs, The Fascinating World of Graph Theory offers exciting problem-solving possibilities for mathematics and beyond.

Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory

Author : Mauro Di Nasso
Publisher : Springer
ISBN 13 : 3030179567
Total Pages : 206 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory by : Mauro Di Nasso

Download or read book Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory written by Mauro Di Nasso and published by Springer. This book was released on 2019-05-23 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Essential Discrete Mathematics for Computer Science

Author : Harry Lewis
Publisher : Princeton University Press
ISBN 13 : 0691179298
Total Pages : 408 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Essential Discrete Mathematics for Computer Science by : Harry Lewis

Download or read book Essential Discrete Mathematics for Computer Science written by Harry Lewis and published by Princeton University Press. This book was released on 2019-03-19 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete mathematics is the basis of much of computer science, from algorithms and automata theory to combinatorics and graph theory. Essential Discrete Mathematics for Computer Science aims to teach mathematical reasoning as well as concepts and skills by stressing the art of proof. It is fully illustrated in color, and each chapter includes a concise summary as well as a set of exercises.

Combinatorial Set Theory

Author : Lorenz J. Halbeisen
Publisher : Springer Science & Business Media
ISBN 13 : 9781447121732
Total Pages : 456 pages
Book Rating : 4.1/5 (217 download)

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Book Synopsis Combinatorial Set Theory by : Lorenz J. Halbeisen

Download or read book Combinatorial Set Theory written by Lorenz J. Halbeisen and published by Springer Science & Business Media. This book was released on 2011-11-24 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.

Frontiers in Complex Dynamics

Author : Araceli Bonifant
Publisher : Princeton University Press
ISBN 13 : 0691159297
Total Pages : 799 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Frontiers in Complex Dynamics by : Araceli Bonifant

Download or read book Frontiers in Complex Dynamics written by Araceli Bonifant and published by Princeton University Press. This book was released on 2014-03-16 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing. This collection will be useful to students and researchers for decades to come. The contributors are Marco Abate, Marco Arizzi, Alexander Blokh, Thierry Bousch, Xavier Buff, Serge Cantat, Tao Chen, Robert Devaney, Alexandre Dezotti, Tien-Cuong Dinh, Romain Dujardin, Hugo García-Compeán, William Goldman, Rotislav Grigorchuk, John Hubbard, Yunping Jiang, Linda Keen, Jan Kiwi, Genadi Levin, Daniel Meyer, John Milnor, Carlos Moreira, Vincente Muñoz, Viet-Anh Nguyên, Lex Oversteegen, Ricardo Pérez-Marco, Ross Ptacek, Jasmin Raissy, Pascale Roesch, Roberto Santos-Silva, Dierk Schleicher, Nessim Sibony, Daniel Smania, Tan Lei, William Thurston, Vladlen Timorin, Sebastian van Strien, and Alberto Verjovsky.

The Knot Book

Author : Colin Conrad Adams
Publisher : American Mathematical Soc.
ISBN 13 : 0821836781
Total Pages : 330 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Knot Book by : Colin Conrad Adams

Download or read book The Knot Book written by Colin Conrad Adams and published by American Mathematical Soc.. This book was released on 2004 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.

Reverse Mathematics

Author : Damir D. Dzhafarov
Publisher : Springer Nature
ISBN 13 : 3031113675
Total Pages : 498 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Reverse Mathematics by : Damir D. Dzhafarov

Download or read book Reverse Mathematics written by Damir D. Dzhafarov and published by Springer Nature. This book was released on 2022-07-25 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reverse mathematics studies the complexity of proving mathematical theorems and solving mathematical problems. Typical questions include: Can we prove this result without first proving that one? Can a computer solve this problem? A highly active part of mathematical logic and computability theory, the subject offers beautiful results as well as significant foundational insights. This text provides a modern treatment of reverse mathematics that combines computability theoretic reductions and proofs in formal arithmetic to measure the complexity of theorems and problems from all areas of mathematics. It includes detailed introductions to techniques from computable mathematics, Weihrauch style analysis, and other parts of computability that have become integral to research in the field. Topics and features: Provides a complete introduction to reverse mathematics, including necessary background from computability theory, second order arithmetic, forcing, induction, and model construction Offers a comprehensive treatment of the reverse mathematics of combinatorics, including Ramsey's theorem, Hindman's theorem, and many other results Provides central results and methods from the past two decades, appearing in book form for the first time and including preservation techniques and applications of probabilistic arguments Includes a large number of exercises of varying levels of difficulty, supplementing each chapter The text will be accessible to students with a standard first year course in mathematical logic. It will also be a useful reference for researchers in reverse mathematics, computability theory, proof theory, and related areas. Damir D. Dzhafarov is an Associate Professor of Mathematics at the University of Connecticut, CT, USA. Carl Mummert is a Professor of Computer and Information Technology at Marshall University, WV, USA.

Graph Theory in America

Author : Robin Wilson
Publisher : Princeton University Press
ISBN 13 : 0691194025
Total Pages : 320 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Graph Theory in America by : Robin Wilson

Download or read book Graph Theory in America written by Robin Wilson and published by Princeton University Press. This book was released on 2023-01-17 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: How a new mathematical field grew and matured in America Graph Theory in America focuses on the development of graph theory in North America from 1876 to 1976. At the beginning of this period, James Joseph Sylvester, perhaps the finest mathematician in the English-speaking world, took up his appointment as the first professor of mathematics at the Johns Hopkins University, where his inaugural lecture outlined connections between graph theory, algebra, and chemistry—shortly after, he introduced the word graph in our modern sense. A hundred years later, in 1976, graph theory witnessed the solution of the long-standing four color problem by Kenneth Appel and Wolfgang Haken of the University of Illinois. Tracing graph theory’s trajectory across its first century, this book looks at influential figures in the field, both familiar and less known. Whereas many of the featured mathematicians spent their entire careers working on problems in graph theory, a few such as Hassler Whitney started there and then moved to work in other areas. Others, such as C. S. Peirce, Oswald Veblen, and George Birkhoff, made excursions into graph theory while continuing their focus elsewhere. Between the main chapters, the book provides short contextual interludes, describing how the American university system developed and how graph theory was progressing in Europe. Brief summaries of specific publications that influenced the subject’s development are also included. Graph Theory in America tells how a remarkable area of mathematics landed on American soil, took root, and flourished.

Partial Differential Equations

Author : Walter A. Strauss
Publisher : John Wiley & Sons
ISBN 13 : 0470054565
Total Pages : 467 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Partial Differential Equations by : Walter A. Strauss

Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Introductory Combinatorics

Author : Kenneth P. Bogart
Publisher : Harcourt Brace College Publishers
ISBN 13 :
Total Pages : 648 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Introductory Combinatorics by : Kenneth P. Bogart

Download or read book Introductory Combinatorics written by Kenneth P. Bogart and published by Harcourt Brace College Publishers. This book was released on 1990 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory, Combinatorics, Third Edition is designed for introductory courses in combinatorics, or more generally, discrete mathematics. The author, Kenneth Bogart, has chosen core material of value to students in a wide variety of disciplines: mathematics, computer science, statistics, operations research, physical sciences, and behavioral sciences. The rapid growth in the breadth and depth of the field of combinatorics in the last several decades, first in graph theory and designs and more recently in enumeration and ordered sets, has led to a recognition of combinatorics as a field with which the aspiring mathematician should become familiar. This long-overdue new edition of a popular set presents a broad comprehensive survey of modern combinatorics which is important to the various scientific fields of study.

Introduction to Random Graphs

Author : Alan Frieze
Publisher : Cambridge University Press
ISBN 13 : 1107118506
Total Pages : 483 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Introduction to Random Graphs by : Alan Frieze

Download or read book Introduction to Random Graphs written by Alan Frieze and published by Cambridge University Press. This book was released on 2016 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.

An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics

Author : Matthew Katz
Publisher : American Mathematical Soc.
ISBN 13 : 1470442906
Total Pages : 207 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics by : Matthew Katz

Download or read book An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics written by Matthew Katz and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Quantum Field Theory

Author : Michael E. Peskin
Publisher : CRC Press
ISBN 13 : 0429972105
Total Pages : 866 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis An Introduction To Quantum Field Theory by : Michael E. Peskin

Download or read book An Introduction To Quantum Field Theory written by Michael E. Peskin and published by CRC Press. This book was released on 2018-05-04 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.

Discrete Mathematics

Author : Oscar Levin
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781724572639
Total Pages : 238 pages
Book Rating : 4.5/5 (726 download)

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Book Synopsis Discrete Mathematics by : Oscar Levin

Download or read book Discrete Mathematics written by Oscar Levin and published by Createspace Independent Publishing Platform. This book was released on 2018-07-30 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.