Author: Melvyn B. Nathanson
Publisher: Springer Nature
ISBN: 3031107969
Category : Mathematics
Languages : en
Pages : 290
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Book Description
This proceedings volume, the fifth in a series from the Combinatorial and Additive Number Theory (CANT) conferences, is based on talks from the 19th annual workshop, held online due to the COVID-19 pandemic. Organized every year since 2003 by the New York Number Theory Seminar at the CUNY Graduate Center, the workshops survey state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. The CANT 2021 meeting featured over a hundred speakers from North and South America, Europe, Asia, Australia, and New Zealand, and was the largest CANT conference in terms of the number of both lectures and participants. These proceedings contain peer-reviewed and edited papers on current topics in number theory. Topics featured in this volume include sumsets, minimal bases, Sidon sets, analytic and prime number theory, combinatorial and discrete geometry, numerical semigroups, and a survey of expansion, divisibility, and parity. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.
Author: Melvyn B. Nathanson
Publisher: Springer Nature
ISBN: 3030311066
Category : Mathematics
Languages : en
Pages : 237
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Book Description
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: Melvyn B. Nathanson
Publisher: Springer
ISBN: 1493916017
Category : Mathematics
Languages : en
Pages : 309
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Book Description
This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems and future challenges in number theory.
Author: Melvyn B. Nathanson
Publisher: Springer Nature
ISBN: 3030679969
Category : Mathematics
Languages : en
Pages : 445
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Book Description
This is the fourth in a series of proceedings of the Combinatorial and Additive Number Theory (CANT) conferences, based on talks from the 2019 and 2020 workshops at the City University of New York. The latter was held online due to the COVID-19 pandemic, and featured speakers from North and South America, Europe, and Asia. The 2020 Zoom conference was the largest CANT conference in terms of the number of both lectures and participants. These proceedings contain 25 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003 at the CUNY Graduate Center, the workshop 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, zero-sum sequences, minimal complements, analytic and prime number theory, Hausdorff dimension, combinatorial and discrete geometry, and Ramsey theory. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.
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: Bruce M. Landman
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111395626
Category : Mathematics
Languages : en
Pages : 364
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Book Description
This volume consists of twenty articles stemming from presentations given at the 2023 Integers Conference. They represent a variety of active areas of research in combinatorial number theory, including additive number theory, multiplicative number theory, elementary number theory, the theory of partitions, Ramsey theory, sequences, algebraic combinatorics, enumerative combinatorics, and Diophantine equations.
Author: Terence Tao
Publisher: Cambridge University Press
ISBN: 1139458345
Category : Mathematics
Languages : en
Pages : 18
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Book Description
Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemerédi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.
Author: Philippe Flajolet
Publisher: Cambridge University Press
ISBN: 1139477161
Category : Mathematics
Languages : en
Pages : 825
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Book Description
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Author: R.L. Graham
Publisher: Elsevier
ISBN: 044488002X
Category : Business & Economics
Languages : en
Pages : 1283
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Book Description
