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Author: David J. Grynkiewicz
Publisher: Springer Science & Business Media
ISBN: 3319004166
Category : Mathematics
Languages : en
Pages : 426
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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 : 426
Get Book
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 Grynkiewicz
Publisher: Springer
ISBN: 9783319004174
Category : Mathematics
Languages : en
Pages : 426
Get Book
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
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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: 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: Bela Bajnok
Publisher: CRC Press
ISBN: 1351137611
Category : Mathematics
Languages : en
Pages : 390
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Book Description
Additive Combinatorics: A Menu of Research Problems is the first book of its kind to provide readers with an opportunity to actively explore the relatively new field of additive combinatorics. The author has written the book specifically for students of any background and proficiency level, from beginners to advanced researchers. It features an extensive menu of research projects that are challenging and engaging at many different levels. The questions are new and unsolved, incrementally attainable, and designed to be approachable with various methods. The book is divided into five parts which are compared to a meal. The first part is called Ingredients and includes relevant background information about number theory, combinatorics, and group theory. The second part, Appetizers, introduces readers to the book’s main subject through samples. The third part, Sides, covers auxiliary functions that appear throughout different chapters. The book’s main course, so to speak, is Entrees: it thoroughly investigates a large variety of questions in additive combinatorics by discussing what is already known about them and what remains unsolved. These include maximum and minimum sumset size, spanning sets, critical numbers, and so on. The final part is Pudding and features numerous proofs and results, many of which have never been published. Features: The first book of its kind to explore the subject Students of any level can use the book as the basis for research projects The text moves gradually through five distinct parts, which is suitable both for beginners without prerequisites and for more advanced students Includes extensive proofs of propositions and theorems Each of the introductory chapters contains numerous exercises to help readers
Author: Jane Qiu
Publisher: Routledge
ISBN: 1317387732
Category : Business & Economics
Languages : en
Pages : 246
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Book Description
While research in organisational studies has become increasingly rich and complex, organisation researchers are constantly challenged by the growing quest for theoretical advancement and innovation. To conduct theoretically rigorous and innovative research, contemporary researchers and students must develop in-depth understanding of the theoretical traditions and future prospects of their discipline. This book provides a collection of cutting-edge research topics in the field of organisation and management and offers advanced research findings that explore the frontiers of the field. Advancing Organisational Theory in a Complex World aims to provide deep insights into many influential organisational theories, including, contingency theory, institutional theory, stewardship theory, population ecology theory, ambidexterity, and complexity theory. All these theories have been developed to explain the external and internal factors that influence organisational survival and evolvement. We focus on these theories because they represent some of the most important ways into the modern literature, counter-points to the modern literature, and a breath of fresh air to some theories which should be better known. This book shows the fruitfulness and the continuous vitality of the theoretical field of organisational studies in a critical and innovative way. Finally, this book is dedicated to Professor Lex Donaldson who is a thought leader in the field. The field owed this to Lex, for his lifelong dedication to organisational studies and for his creation and advancement of theories that have inspired several generations of researchers.
Author: Patrick E. Shrout
Publisher: Psychology Press
ISBN: 1317781678
Category : Psychology
Languages : en
Pages : 386
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Book Description
Donald W. Fiske's professional life and collaborations are themselves a textbook in the development of the field of personality. From the field's early origins in personnel selection, rating accuracy, and psychotherapy outcomes, to its current status of theoretical and methodological maturity -- complete with mid-life crises -- the field has been fundamentally changed by Fiske's work, and the changes have influenced generations of scholars. This festschrift is a celebration of Fiske's impact, but not merely of his impact on the history of personality research. Instead, the volume focuses on ongoing debates and issues that have been framed or influenced by Fiske's work. The festschrift's three sections are organized around three themes in Fiske's writings -- themes that also correspond to three periods in his career. This volume examines current thinking about what can be known about personality, how constructs relevant to personality psychology are best measured, and how to approach specific research problems in personality and related fields. The contributors create an eminent cross-section of the development and current status of personality methods. In addition to Fiske's eminent contemporaries, the contributors to this volume include Fiske's former students, collaborators, and his two children, both of whom are behavioral scientists. The accomplishments of his students, colleagues, and children testifies to the range of psychologists who have benefited from his scholarly and practical wisdom. This collection is a valuable textbook for an advanced graduate course as well as appealing as a scholarly resource. Many of the contributors are renown psychological leaders who have made available their latest original thoughts. The book concludes with an essay by Fiske offering his perspective on the central themes: behavioral and social science metatheory, methods, and strategies.
Author: Lex Donaldson
Publisher: SAGE
ISBN: 9780761915744
Category : Business & Economics
Languages : en
Pages : 348
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Book Description
This volume presents a comprehensive, in-depth analysis of the theories, evidence and methodological issues of contingency theory - one of the major theoretical lenses used to view organizations.
Author: George A. Marcoulides
Publisher: Psychology Press
ISBN: 1317843797
Category : Psychology
Languages : en
Pages : 368
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Book Description
By focusing primarily on the application of structural equation modeling (SEM) techniques in example cases and situations, this book provides an understanding and working knowledge of advanced SEM techniques with a minimum of mathematical derivations. The book was written for a broad audience crossing many disciplines, assumes an understanding of graduate level multivariate statistics, including an introduction to SEM.
Author: Alfred Geroldinger
Publisher: Springer Science & Business Media
ISBN: 3764389613
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.
