Number Theory And Combinatorics
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An Introduction To Number Theoretic Combinatorics
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Author : Richard M. Beekman
language : en
Publisher: Lulu.com
Release Date : 2016-12-31
An Introduction To Number Theoretic Combinatorics written by Richard M. Beekman and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-31 with Science categories.
Introductory textbook on number-theoretic combinatorics. Combinatorial problems of distribution and occupancy are studied using a number-theoretic viewpoint. This book is best suited for advanced undergraduates or beginning graduate students in mathematics.
Combinatorial And Additive Number Theory
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Author : Melvyn B. Nathanson
language : en
Publisher: Springer
Release Date : 2014-10-18
Combinatorial And Additive Number Theory written by Melvyn B. Nathanson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-18 with Mathematics categories.
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.
Combinatorial Number Theory And Additive Group Theory
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Author : Alfred Geroldinger
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-15
Combinatorial Number Theory And Additive Group Theory written by Alfred Geroldinger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-15 with Mathematics categories.
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.
Number Theory Analysis And Combinatorics
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Author : János Pintz
language : en
Publisher: Walter de Gruyter
Release Date : 2013-12-12
Number Theory Analysis And Combinatorics written by János Pintz 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 2013-12-12 with Mathematics categories.
Paul Turán, one of the greatest Hungarian mathematicians, was born 100 years ago, on August 18, 1910. To celebrate this occasion the Hungarian Academy of Sciences, the Alfréd Rényi Institute of Mathematics, the János Bolyai Mathematical Society and the Mathematical Institute of Eötvös Loránd University organized an international conference devoted to Paul Turán's main areas of interest: number theory, selected branches of analysis, and selected branches of combinatorics. The conference was held in Budapest, August 22-26, 2011. Some of the invited lectures reviewed different aspects of Paul Turán's work and influence. Most of the lectures allowed participants to report about their own work in the above mentioned areas of mathematics.
Q Series With Applications To Combinatorics Number Theory And Physics
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Author : Bruce C. Berndt
language : en
Publisher: American Mathematical Soc.
Release Date : 2001-01-01
Q Series With Applications To Combinatorics Number Theory And Physics written by Bruce C. Berndt 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 2001-01-01 with Mathematics categories.
The subject of $q$-series can be said to begin with Euler and his pentagonal number theorem. In fact, $q$-series are sometimes called Eulerian series. Contributions were made by Gauss, Jacobi, and Cauchy, but the first attempt at a systematic development, especially from the point of view of studying series with the products in the summands, was made by E. Heine in 1847. In the latter part of the nineteenth and in the early part of the twentieth centuries, two Englishmathematicians, L. J. Rogers and F. H. Jackson, made fundamental contributions. In 1940, G. H. Hardy described what we now call Ramanujan's famous $ 1\psi 1$ summation theorem as ''a remarkable formula with many parameters.'' This is now one of the fundamental theorems of the subject. Despite humble beginnings,the subject of $q$-series has flourished in the past three decades, particularly with its applications to combinatorics, number theory, and physics. During the year 2000, the University of Illinois embraced The Millennial Year in Number Theory. One of the events that year was the conference $q$-Series with Applications to Combinatorics, Number Theory, and Physics. This event gathered mathematicians from the world over to lecture and discuss their research. This volume presents nineteen of thepapers presented at the conference. The excellent lectures that are included chart pathways into the future and survey the numerous applications of $q$-series to combinatorics, number theory, and physics.
Combinatorial Number Theory
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Author : Bruce Landman
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-22
Combinatorial Number Theory written by Bruce Landman 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 2011-12-22 with Mathematics categories.
This carefully edited volume contains selected refereed papers based on lectures presented by many distinguished speakers at the "Integers Conference 2005", an international conference in combinatorial number theory. The conference was held in celebration of the 70th birthday of Ronald Graham, a leader in several fields of mathematics.
Combinatorial Number Theory
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Author : Bruce M. Landman
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-11-04
Combinatorial Number Theory written by Bruce M. 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 2024-11-04 with Mathematics categories.
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.
Introduction To Number Theory
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Author : Anthony Vazzana
language : en
Publisher: CRC Press
Release Date : 2007-10-30
Introduction To Number Theory written by Anthony Vazzana and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-30 with Mathematics categories.
One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topics. This classroom-tested, student-friendly text covers a wide range of subjects, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments that include cryptography, the theory of elliptic curves, and the negative solution of Hilbert’s tenth problem. The authors illustrate the connections between number theory and other areas of mathematics, including algebra, analysis, and combinatorics. They also describe applications of number theory to real-world problems, such as congruences in the ISBN system, modular arithmetic and Euler’s theorem in RSA encryption, and quadratic residues in the construction of tournaments. The book interweaves the theoretical development of the material with Mathematica® and MapleTM calculations while giving brief tutorials on the software in the appendices. Highlighting both fundamental and advanced topics, this introduction provides all of the tools to achieve a solid foundation in number theory.
Combinatorial And Additive Number Theory Iv
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Author : Melvyn B. Nathanson
language : en
Publisher: Springer Nature
Release Date : 2021-08-12
Combinatorial And Additive Number Theory Iv 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 2021-08-12 with Mathematics categories.
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.
Analytic And Combinatorial Number Theory The Legacy Of Ramanujan Contributions In Honor Of Bruce C Berndt
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Author : George E Andrews
language : en
Publisher: World Scientific
Release Date : 2024-08-19
Analytic And Combinatorial Number Theory The Legacy Of Ramanujan Contributions In Honor Of Bruce C Berndt written by George E Andrews and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-19 with Mathematics categories.
This volume reflects the contributions stemming from the conference Analytic and Combinatorial Number Theory: The Legacy of Ramanujan which took place at the University of Illinois at Urbana-Champaign on June 6-9, 2019. The conference included 26 plenary talks, 71 contributed talks, and 170 participants. As was the case for the conference, this book is in honor of Bruce C Berndt and in celebration of his mathematics and his 80th birthday.Along with a number of papers previously appearing in Special Issues of the International Journal of Number Theory, the book collects together a few more papers, a biography of Bruce by Atul Dixit and Ae Ja Yee, a preface by George Andrews, a gallery of photos from the conference, a number of speeches from the conference banquet, the conference poster, a list of Bruce's publications at the time this volume was created, and a list of the talks from the conference.