Additive Number Theory: Inverse Problems and the Geometry of Sumsets PDF Download
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Author: Melvyn B. Nathanson
Publisher: Springer Science & Business Media
ISBN: 9780387946559
Category : Mathematics
Languages : en
Pages : 320
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Book Description
Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer H -> 2, and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. By contrast, in an inverse problem, one starts with a sumset hA, and attempts to describe the structure of the underlying set A. In recent years there has been ramrkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plünnecke, Vosper, and others. This volume includes their results, and culminates with an elegant proof by Ruzsa of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an n-dimensional arithmetic progression.
Author: Melvyn B. Nathanson
Publisher: Springer Science & Business Media
ISBN: 9780387946559
Category : Mathematics
Languages : en
Pages : 320
Get Book Here
Book Description
Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer H -> 2, and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. By contrast, in an inverse problem, one starts with a sumset hA, and attempts to describe the structure of the underlying set A. In recent years there has been ramrkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plünnecke, Vosper, and others. This volume includes their results, and culminates with an elegant proof by Ruzsa of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an n-dimensional arithmetic progression.
Author: Melvyn Bernard Nathanson
Publisher:
ISBN:
Category :
Languages : en
Pages : 293
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Book Description
Author: David Chudnovsky
Publisher: Springer Science & Business Media
ISBN: 0387683615
Category : Mathematics
Languages : en
Pages : 361
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Book Description
This impressive volume is dedicated to Mel Nathanson, a leading authoritative expert for several decades in the area of combinatorial and additive number theory. For several decades, Mel Nathanson's seminal ideas and results in combinatorial and additive number theory have influenced graduate students and researchers alike. The invited survey articles in this volume reflect the work of distinguished mathematicians in number theory, and represent a wide range of important topics in current research.
Author: Melvyn B. Nathanson
Publisher: Springer
ISBN: 3319680323
Category : Mathematics
Languages : en
Pages : 309
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Book Description
Based on talks from the 2015 and 2016 Combinatorial and Additive Number Theory (CANT) workshops at the City University of New York, these proceedings offer 19 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. Sumsets, partitions, convex polytopes and discrete geometry, Ramsey theory, primality testing, and cryptography are among the topics featured in this volume. Each contribution is dedicated to a specific topic that reflects the latest results by experts in the field. Researchers and graduate students interested in the current progress in number theory will find this selection of articles relevant and compelling.
Author: Alfred Geroldinger
Publisher: Springer Science & Business Media
ISBN: 3764389621
Category : Mathematics
Languages : en
Pages : 324
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Book Description
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: Melvyn B. Nathanson
Publisher: Springer
ISBN: 9780387709987
Category : Mathematics
Languages : en
Pages : 400
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Book Description
A central problem in additive number theory is the growth of sumsets. If A is a finite or infinite subset of the integers and the lattice points, or more generally, of any abelian group or semigroup G, then the h-fold sumset of A is the set LA consisting of all elements of G that can be represented as the sum of L not necessarily distinct elements of A. The goal is to understand the asymptotics of the sumsets LA, that is, the size and structure of LA, as L tends to infinity. If A is finite, then the size of LA is its cardinality. If A is infinite, then the size of LA is measured by various duality functions. These problems have natural analogues when A is a subset of a nonabelian group. Additive Number Theory: Density Theorems and the Growth of Sumsets presents material that deals with the above problem. Ideas and techniques from many parts of mathematics are used to prove theorems in this subject. For example, the authors use number theory, combinatorics, commutative algebra, ultrafilters and logic, and nonstandard analysis. The book is self-contained, and includes short introductions to the various techniques that are not standard in this field. Graduate students and researchers in mathematics will find this book useful. Prerequisites include undergraduate elementary number theory and algebra.
Author: Herbert J. Kaufmann
Publisher: Springer Verlag
ISBN: 9780387565415
Category : Medical
Languages : en
Pages : 124
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Book Description
Author: Alain M. Robert
Publisher: Springer Science & Business Media
ISBN: 1475732546
Category : Mathematics
Languages : en
Pages : 451
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Book Description
Discovered at the turn of the 20th century, p-adic numbers are frequently used by mathematicians and physicists. This text is a self-contained presentation of basic p-adic analysis with a focus on analytic topics. It offers many features rarely treated in introductory p-adic texts such as topological models of p-adic spaces inside Euclidian space, a special case of Hazewinkel’s functional equation lemma, and a treatment of analytic elements.
Author: John M. Lee
Publisher: Springer Science & Business Media
ISBN: 038722727X
Category : Mathematics
Languages : en
Pages : 395
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Book Description
Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.
Author: M. Scott Osborne
Publisher: Springer Science & Business Media
ISBN: 9780387989341
Category : Mathematics
Languages : en
Pages : 414
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Book Description
From the reviews: "The book is well written. We find here many examples. Each chapter is followed by exercises, and at the end of the book there are outline solutions to some of them. [...] I especially appreciated the lively style of the book; [...] one is quickly able to find necessary details." EMS Newsletter
