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Author: David J. Grynkiewicz Publisher: Springer Science & Business Media ISBN: 3319004166 Category : Mathematics Languages : en Pages : 425
Book Description
Nestled between number theory, combinatorics, algebra and analysis lies a rapidly developing subject in mathematics variously known as additive combinatorics, additive number theory, additive group theory, and combinatorial number theory. Its main objects of study are not abelian groups themselves, but rather the additive structure of subsets and subsequences of an abelian group, i.e., sumsets and subsequence sums. This text is a hybrid of a research monograph and an introductory graduate textbook. With few exceptions, all results presented are self-contained, written in great detail, and only reliant upon material covered in an advanced undergraduate curriculum supplemented with some additional Algebra, rendering this book usable as an entry-level text. However, it will perhaps be of even more interest to researchers already in the field. The majority of material is not found in book form and includes many new results as well. Even classical results, when included, are given in greater generality or using new proof variations. The text has a particular focus on results of a more exact and precise nature, results with strong hypotheses and yet stronger conclusions, and on fundamental aspects of the theory. Also included are intricate results often neglected in other texts owing to their complexity. Highlights include an extensive treatment of Freiman Homomorphisms and the Universal Ambient Group of sumsets A+B, an entire chapter devoted to Hamidoune’s Isoperimetric Method, a novel generalization allowing infinite summands in finite sumset questions, weighted zero-sum problems treated in the general context of viewing homomorphisms as weights, and simplified proofs of the Kemperman Structure Theorem and the Partition Theorem for setpartitions.
Author: David J. Grynkiewicz Publisher: Springer Science & Business Media ISBN: 3319004166 Category : Mathematics Languages : en Pages : 425
Book Description
Nestled between number theory, combinatorics, algebra and analysis lies a rapidly developing subject in mathematics variously known as additive combinatorics, additive number theory, additive group theory, and combinatorial number theory. Its main objects of study are not abelian groups themselves, but rather the additive structure of subsets and subsequences of an abelian group, i.e., sumsets and subsequence sums. This text is a hybrid of a research monograph and an introductory graduate textbook. With few exceptions, all results presented are self-contained, written in great detail, and only reliant upon material covered in an advanced undergraduate curriculum supplemented with some additional Algebra, rendering this book usable as an entry-level text. However, it will perhaps be of even more interest to researchers already in the field. The majority of material is not found in book form and includes many new results as well. Even classical results, when included, are given in greater generality or using new proof variations. The text has a particular focus on results of a more exact and precise nature, results with strong hypotheses and yet stronger conclusions, and on fundamental aspects of the theory. Also included are intricate results often neglected in other texts owing to their complexity. Highlights include an extensive treatment of Freiman Homomorphisms and the Universal Ambient Group of sumsets A+B, an entire chapter devoted to Hamidoune’s Isoperimetric Method, a novel generalization allowing infinite summands in finite sumset questions, weighted zero-sum problems treated in the general context of viewing homomorphisms as weights, and simplified proofs of the Kemperman Structure Theorem and the Partition Theorem for setpartitions.
Author: Terence Tao Publisher: Cambridge University Press ISBN: 1139458345 Category : Mathematics Languages : en Pages : 18
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: Alfred Geroldinger Publisher: Springer Science & Business Media ISBN: 3764389613 Category : Mathematics Languages : en Pages : 324
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: David Grynkiewicz Publisher: Springer ISBN: 9783319004174 Category : Mathematics Languages : en Pages : 426
Book Description
Nestled between number theory, combinatorics, algebra and analysis lies a rapidly developing subject in mathematics variously known as additive combinatorics, additive number theory, additive group theory, and combinatorial number theory. Its main objects of study are not abelian groups themselves, but rather the additive structure of subsets and subsequences of an abelian group, i.e., sumsets and subsequence sums. This text is a hybrid of a research monograph and an introductory graduate textbook. With few exceptions, all results presented are self-contained, written in great detail, and only reliant upon material covered in an advanced undergraduate curriculum supplemented with some additional Algebra, rendering this book usable as an entry-level text. However, it will perhaps be of even more interest to researchers already in the field. The majority of material is not found in book form and includes many new results as well. Even classical results, when included, are given in greater generality or using new proof variations. The text has a particular focus on results of a more exact and precise nature, results with strong hypotheses and yet stronger conclusions, and on fundamental aspects of the theory. Also included are intricate results often neglected in other texts owing to their complexity. Highlights include an extensive treatment of Freiman Homomorphisms and the Universal Ambient Group of sumsets A+B, an entire chapter devoted to Hamidoune’s Isoperimetric Method, a novel generalization allowing infinite summands in finite sumset questions, weighted zero-sum problems treated in the general context of viewing homomorphisms as weights, and simplified proofs of the Kemperman Structure Theorem and the Partition Theorem for setpartitions.
Author: Melvyn B. Nathanson Publisher: Springer Nature ISBN: 3030679969 Category : Mathematics Languages : en Pages : 445
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: N. Hirschberg Publisher: Psychology Press ISBN: 1317769724 Category : Psychology Languages : en Pages : 280
Book Description
First published in 1982. Textbooks in multivariate methods proliferate, but there are few books concerned with their application. Experimental psychology and its associated method of statistical data analysis, analysis of variance, has tended to dominate psychological thinking even in such areas as social and clinical psychology, two areas that are particularly ill-suited to simple analysis-of-variance statistical models. The recent emphasis of clinical and social psychology on applied research relevant to social problems requires that more attention be paid to multivariate methods and appropriate research designs. this book illustrates and examines the multivariate approach alone, this does not imply that a multivariate approach combined with an experimental approach would not in the long run provide the best overall research design. The present collection of multivariate applications introduces some of the kinds of research problem that can be tackled by means of multivariate statistical analysis.
Author: William Estes Publisher: Psychology Press ISBN: 1317672011 Category : Psychology Languages : en Pages : 350
Book Description
Originally published in 1978 Volume 5 of this Handbook reflects a single theoretical orientation, that characterized by the term human information processing in the literature at the time, but which ranges over a very broad spectrum of cognitive activities. The first two chapters give some overall picture of the background, goals, method, and limitations of the information-processing approach. The remaining chapters treat in detail some principal areas of application – visual processing, mental chronometry, representation of spatial information in memory, problem solving, and the theory of instruction. The first three volumes of the Handbook presented an overview of the field, followed by treatments of conditioning, behavior theory, and human learning and retention. With the fourth volume, the focus of attention shifted from the domain of learning theory to that of cognitive psychology.
Author: David J. Grynkiewicz
Author: David J. Grynkiewicz
Author: Terence Tao
Author: Alfred Geroldinger
Author: David Grynkiewicz
Author: Melvyn B. Nathanson
Author: John L. Provis
Author: N. Hirschberg
Author: Norman Robert Campbell
Author: Norman Robert Campbell
Author: William Estes