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| Author | : Alfred Geroldinger |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 324 |
| Release | : 2009-04-15 |
| Genre | : Mathematics |
| ISBN | : 3764389613 |
Download Combinatorial Number Theory and Additive Group Theory Book in PDF, ePub and Kindle
Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the sum of k-th powers or the Goldbach conjecture are genuine examples of the original questions addressed in the area. One of the features of contemporary additive combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This book gathers the contributions of many of the leading researchers in the area and is divided into three parts. The two first parts correspond to the material of the main courses delivered, Additive combinatorics and non-unique factorizations, by Alfred Geroldinger, and Sumsets and structure, by Imre Z. Ruzsa. The third part collects the notes of most of the seminars which accompanied the main courses, and which cover a reasonably large part of the methods, techniques and problems of contemporary additive combinatorics.
| Author | : Mauro Di Nasso |
| Publisher | : Springer |
| Total Pages | : 206 |
| Release | : 2019-05-23 |
| Genre | : Mathematics |
| ISBN | : 3030179567 |
Download Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory Book in PDF, ePub and Kindle
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.
| Author | : Wilhelm Magnus |
| Publisher | : Courier Corporation |
| Total Pages | : 466 |
| Release | : 2004-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486438309 |
Download Combinatorial Group Theory Book in PDF, ePub and Kindle
This seminal, much-cited account begins with a fairly elementary exposition of basic concepts and a discussion of factor groups and subgroups. The topics of Nielsen transformations, free and amalgamated products, and commutator calculus receive detailed treatment. The concluding chapter surveys word, conjugacy, and related problems; adjunction and embedding problems; and more. Second, revised 1976 edition.
| Author | : Harry Furstenberg |
| Publisher | : Princeton University Press |
| Total Pages | : 216 |
| Release | : 2014-07-14 |
| Genre | : Mathematics |
| ISBN | : 1400855160 |
Download Recurrence in Ergodic Theory and Combinatorial Number Theory Book in PDF, ePub and Kindle
Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
| Author | : Lorenz J. Halbeisen |
| Publisher | : Springer |
| Total Pages | : 586 |
| Release | : 2017-12-20 |
| Genre | : Mathematics |
| ISBN | : 3319602314 |
Download Combinatorial Set Theory Book in PDF, ePub and Kindle
This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study.
| Author | : R.L. Graham |
| Publisher | : Elsevier |
| Total Pages | : 1283 |
| Release | : 1995-12-11 |
| Genre | : Business & Economics |
| ISBN | : 044488002X |
Download Handbook of Combinatorics Book in PDF, ePub and Kindle
| Author | : Roger C. Lyndon |
| Publisher | : Springer |
| Total Pages | : 354 |
| Release | : 2015-03-12 |
| Genre | : Mathematics |
| ISBN | : 3642618960 |
Download Combinatorial Group Theory Book in PDF, ePub and Kindle
From the reviews: "This book [...] defines the boundaries of the subject now called combinatorial group theory. [...] it is a considerable achievement to have concentrated a survey of the subject into 339 pages. [...] a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews
| Author | : Leo Moser |
| Publisher | : The Trillia Group |
| Total Pages | : 95 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 1931705011 |
Download An Introduction to the Theory of Numbers Book in PDF, ePub and Kindle
"This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercises as well as unsolved problems) complete the text."--Publisher's description
| Author | : Melvyn B. Nathanson |
| Publisher | : Springer Nature |
| Total Pages | : 237 |
| Release | : 2019-12-10 |
| Genre | : Mathematics |
| ISBN | : 3030311066 |
Download Combinatorial and Additive Number Theory III Book in PDF, ePub and Kindle
Based on talks from the 2017 and 2018 Combinatorial and Additive Number Theory (CANT) workshops at the City University of New York, these proceedings offer 17 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003, the workshop series surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Topics featured in this volume include sumsets, partitions, convex polytopes and discrete geometry, Ramsey theory, commutative algebra and discrete geometry, and applications of logic and nonstandard analysis to number theory. Each contribution is dedicated to a specific topic that reflects the latest results by experts in the field. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.
| Author | : Gilbert Baumslag |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 180 |
| Release | : 1993-09-01 |
| Genre | : Mathematics |
| ISBN | : 9783764329211 |
Download Topics in Combinatorial Group Theory Book in PDF, ePub and Kindle
Combinatorial group theory is a loosely defined subject, with close connections to topology and logic. With surprising frequency, problems in a wide variety of disciplines, including differential equations, automorphic functions and geometry, have been distilled into explicit questions about groups, typically of the following kind: Are the groups in a given class finite (e.g., the Burnside problem)? Finitely generated? Finitely presented? What are the conjugates of a given element in a given group? What are the subgroups of that group? Is there an algorithm for deciding for every pair of groups in a given class whether they are isomorphic or not? The objective of combinatorial group theory is the systematic development of algebraic techniques to settle such questions. In view of the scope of the subject and the extraordinary variety of groups involved, it is not surprising that no really general theory exists. These notes, bridging the very beginning of the theory to new results and developments, are devoted to a number of topics in combinatorial group theory and serve as an introduction to the subject on the graduate level.
