The Finite Field Distance Problem
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The Finite Field Distance Problem
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Author : David J. Covert
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-21
The Finite Field Distance Problem written by David J. Covert and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-21 with Education categories.
Erdős asked how many distinct distances must there be in a set of n n points in the plane. Falconer asked a continuous analogue, essentially asking what is the minimal Hausdorff dimension required of a compact set in order to guarantee that the set of distinct distances has positive Lebesgue measure in R R. The finite field distance problem poses the analogous question in a vector space over a finite field. The problem is relatively new but remains tantalizingly out of reach. This book provides an accessible, exciting summary of known results. The tools used range over combinatorics, number theory, analysis, and algebra. The intended audience is graduate students and advanced undergraduates interested in investigating the unknown dimensions of the problem. Results available until now only in the research literature are clearly explained and beautifully motivated. A concluding chapter opens up connections to related topics in combinatorics and number theory: incidence theory, sum-product phenomena, Waring's problem, and the Kakeya conjecture.
Combinatorial And Additive Number Theory Vi
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Author : Melvyn B. Nathanson
language : en
Publisher: Springer Nature
Release Date : 2025-02-21
Combinatorial And Additive Number Theory Vi written by Melvyn B. Nathanson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-21 with Mathematics categories.
This proceedings volume, the sixth in a series from the Combinatorial and Additive Number Theory (CANT) conferences, is based on talks from the 20th and 21st annual workshops, held in New York in 2022 (virtual) and 2023 (hybrid) respectively. 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. In this volume, the reader will find peer-reviewed and edited papers on current topics in number theory. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.
Finite Fields And Their Applications
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Author : Pascale Charpin
language : en
Publisher: Walter de Gruyter
Release Date : 2013-05-28
Finite Fields And Their Applications written by Pascale Charpin and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-28 with Mathematics categories.
This book is based on the invited talks of the "RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials" held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2-7, 2012. Finite fields play important roles in many application areas such as coding theory, cryptography, Monte Carlo and quasi-Monte Carlo methods, pseudorandom number generation, quantum computing, and wireless communication. In this book we will focus on sequences, character sums, and polynomials over finite fields in view of the above mentioned application areas: Chapters 1 and 2 deal with sequences mainly constructed via characters and analyzed using bounds on character sums. Chapters 3, 5, and 6 deal with polynomials over finite fields. Chapters 4 and 9 consider problems related to coding theory studied via finite geometry and additive combinatorics, respectively. Chapter 7 deals with quasirandom points in view of applications to numerical integration using quasi-Monte Carlo methods and simulation. Chapter 8 studies aspects of iterations of rational functions from which pseudorandom numbers for Monte Carlo methods can be derived. The goal of this book is giving an overview of several recent research directions as well as stimulating research in sequences and polynomials under the unified framework of character theory.
Issues In General And Specialized Mathematics Research 2013 Edition
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Author :
language : en
Publisher: ScholarlyEditions
Release Date : 2013-05-01
Issues In General And Specialized Mathematics Research 2013 Edition written by and has been published by ScholarlyEditions this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-01 with Mathematics categories.
Issues in General and Specialized Mathematics Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about General Mathematics. The editors have built Issues in General and Specialized Mathematics Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General Mathematics in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Integers
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Author : Bruce Landman
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-08-22
Integers written by Bruce Landman and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-22 with Mathematics categories.
"Integers" is a refereed online journal devoted to research in the area of combinatorial number theory. It publishes original research articles in combinatorics and number theory. Topics covered by the journal include additive number theory, multiplicative number theory, sequences and sets, extremal combinatorics, Ramsey theory, elementary number theory, classical combinatorial problems, hypergraphs, and probabilistic number theory. Integers also houses a combinatorial games section. This work presents all papers of the 2013 volume in book form.
Graph Theory And Additive Combinatorics
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Author : Yufei Zhao
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-31
Graph Theory And Additive Combinatorics written by Yufei Zhao and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-31 with Mathematics categories.
An introductory text covering classical and modern developments in graph theory and additive combinatorics, based on Zhao's MIT course.
Parallel Computing Advances And Current Issues Proceedings Of The International Conference Parco2001
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Author : Gerhard R Joubert
language : en
Publisher: World Scientific
Release Date : 2002-07-30
Parallel Computing Advances And Current Issues Proceedings Of The International Conference Parco2001 written by Gerhard R Joubert and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-30 with Computers categories.
The near future will see the increased use of parallel computing technologies at all levels of mainstream computing. Computer hardware increasingly employs parallel techniques to improve computing power for the solution of large scale and computer intensive applications. Cluster and grid technologies make possible high speed computing facilities at vastly reduced costs.These developments can be expected to result in the extended use of all types of parallel computers in virtually all areas of human endeavour. Computer intensive problems in emerging areas such as financial modelling, data mining and multimedia systems, in addition to traditional application areas of parallel computing such as scientific computing and simulation, will lead to further progress. Parallel computing as a field of scientific research and development has already become one of the fundamental computing technologies.This book gives an overview of new developments in parallel computing at the start of the 21st century, as well as a perspective on future developments.
Finite Fields And Their Applications
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Author : James A. Davis
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-10-26
Finite Fields And Their Applications written by James A. Davis and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-26 with Mathematics categories.
The volume covers wide-ranging topics from Theory: structure of finite fields, normal bases, polynomials, function fields, APN functions. Computation: algorithms and complexity, polynomial factorization, decomposition and irreducibility testing, sequences and functions. Applications: algebraic coding theory, cryptography, algebraic geometry over finite fields, finite incidence geometry, designs, combinatorics, quantum information science.
Theory And Applications Of Models Of Computation
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Author : Manindra Agrawal
language : en
Publisher: Springer
Release Date : 2012-05-04
Theory And Applications Of Models Of Computation written by Manindra Agrawal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-04 with Computers categories.
This book constitutes the refereed proceedings of the 9th International Conference on Theory and Applications of Models of Computation, TAMC 2012, held in Beijing, China, in May 2012. The conference was combined with the Turing Lectures 2012, dedicated to celebrating Alan Turing’s unique impact on mathematics, computing, computer science, informatics, morphogenesis, philosophy, and the wider scientific world. Eight Turing Lectures were given at the TAMC 2012. The 40 revised full papers presented together with invited talks were carefully reviewed and selected from 86 submissions. The papers address 4 special sessions at TAMC 2012 which were algorithms and information in networks, complexity and cryptography, models of computing and networking, programming and verification.
Topics In Mathematical Analysis
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Author : Paolo Ciatti
language : en
Publisher: World Scientific
Release Date : 2008
Topics In Mathematical Analysis written by Paolo Ciatti and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This volume consists of a series of lecture notes on mathematical analysis. The contributors have been selected on the basis of both their outstanding scientific level and their clarity of exposition. Thus, the present collection is particularly suited to young researchers and graduate students. Through this volume, the editors intend to provide the reader with material otherwise difficult to find and written in a manner which is also accessible to nonexperts.