Combinatorial Number Theory
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Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory
Author | : Mauro Di Nasso,Isaac Goldbring,Martino Lupini |
Publsiher | : Springer |
Total Pages | : 206 |
Release | : 2019-05-23 |
Genre | : Mathematics |
ISBN | : 9783030179564 |
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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.
Combinatorial Number Theory and Additive Group Theory
Author | : Alfred Geroldinger,Imre Ruzsa |
Publsiher | : Springer Science & Business Media |
Total Pages | : 324 |
Release | : 2009-04-15 |
Genre | : Mathematics |
ISBN | : 9783764389611 |
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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.
Combinatorial Set Theory
Author | : Lorenz J. Halbeisen |
Publsiher | : Springer |
Total Pages | : 594 |
Release | : 2017-12-20 |
Genre | : Mathematics |
ISBN | : 9783319602318 |
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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.
An Introduction to the Theory of Numbers
Author | : Leo Moser |
Publsiher | : The Trillia Group |
Total Pages | : 95 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 9781931705011 |
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"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
Combinatorial Group Theory
Author | : Roger C. Lyndon,Paul E. Schupp |
Publsiher | : Springer |
Total Pages | : 354 |
Release | : 2015-03-12 |
Genre | : Mathematics |
ISBN | : 9783642618963 |
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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
Handbook of Combinatorics
Author | : R.L. Graham,Martin Grötschel,László Lovász |
Publsiher | : Elsevier |
Total Pages | : 1283 |
Release | : 1995-12-11 |
Genre | : Business & Economics |
ISBN | : 9780444880024 |
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Old and New Problems and Results in Combinatorial Number Theory
Author | : Paul Erdős,Ronald L. Graham |
Publsiher | : Unknown |
Total Pages | : 134 |
Release | : 1980 |
Genre | : Combinatorial analysis |
ISBN | : STANFORD:36105032602836 |
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Combinatorial Group Theory
Author | : Wilhelm Magnus,Abraham Karrass,Donald Solitar |
Publsiher | : Courier Corporation |
Total Pages | : 466 |
Release | : 2004-01-01 |
Genre | : Mathematics |
ISBN | : 9780486438306 |
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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.