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Sequences Groups And Number Theory
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Book Synopsis Sequences, Groups, and Number Theory by : Valérie Berthé
Download or read book Sequences, Groups, and Number Theory written by Valérie Berthé and published by Birkhäuser. This book was released on 2018-04-09 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.
Book Synopsis Uniform Distribution of Sequences by : L. Kuipers
Download or read book Uniform Distribution of Sequences written by L. Kuipers and published by Courier Corporation. This book was released on 2012-05-24 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of uniform distribution began with Hermann Weyl's celebrated paper of 1916. In later decades, the theory moved beyond its roots in diophantine approximations to provide common ground for topics as diverse as number theory, probability theory, functional analysis, and topological algebra. This book summarizes the theory's development from its beginnings to the mid-1970s, with comprehensive coverage of both methods and their underlying principles. A practical introduction for students of number theory and analysis as well as a reference for researchers in the field, this book covers uniform distribution in compact spaces and in topological groups, in addition to examinations of sequences of integers and polynomials. Notes at the end of each section contain pertinent bibliographical references and a brief survey of additional results. Exercises range from simple applications of theorems to proofs of propositions that expand upon results stated in the text.
Book Synopsis Algebraic Groups and Number Theory by : Vladimir Platonov
Download or read book Algebraic Groups and Number Theory written by Vladimir Platonov and published by Academic Press. This book was released on 1993-12-07 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: This milestone work on the arithmetic theory of linear algebraic groups is now available in English for the first time. Algebraic Groups and Number Theory provides the first systematic exposition in mathematical literature of the junction of group theory, algebraic geometry, and number theory. The exposition of the topic is built on a synthesis of methods from algebraic geometry, number theory, analysis, and topology, and the result is a systematic overview ofalmost all of the major results of the arithmetic theory of algebraic groups obtained to date.
Book Synopsis Numbers, Sequences and Series by : Keith Hirst
Download or read book Numbers, Sequences and Series written by Keith Hirst and published by Butterworth-Heinemann. This book was released on 1994-12-08 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concerned with the logical foundations of number systems from integers to complex numbers.
Download or read book Group Theory written by Kai N. Cheng and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-11-21 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Book Synopsis Recurrence Sequences by : Graham Everest
Download or read book Recurrence Sequences written by Graham Everest and published by American Mathematical Soc.. This book was released on 2015-09-03 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.
Book Synopsis Combinatorial Number Theory and Additive Group Theory by : Alfred Geroldinger
Download or read book Combinatorial Number Theory and Additive Group Theory written by Alfred Geroldinger and published by Springer Science & Business Media. This book was released on 2009-06-04 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Interactions between Group Theory, Symmetry and Cryptology by : María Isabel González Vasco
Download or read book Interactions between Group Theory, Symmetry and Cryptology written by María Isabel González Vasco and published by MDPI. This book was released on 2020-04-22 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cryptography lies at the heart of most technologies deployed today for secure communications. At the same time, mathematics lies at the heart of cryptography, as cryptographic constructions are based on algebraic scenarios ruled by group or number theoretical laws. Understanding the involved algebraic structures is, thus, essential to design robust cryptographic schemes. This Special Issue is concerned with the interplay between group theory, symmetry and cryptography. The book highlights four exciting areas of research in which these fields intertwine: post-quantum cryptography, coding theory, computational group theory and symmetric cryptography. The articles presented demonstrate the relevance of rigorously analyzing the computational hardness of the mathematical problems used as a base for cryptographic constructions. For instance, decoding problems related to algebraic codes and rewriting problems in non-abelian groups are explored with cryptographic applications in mind. New results on the algebraic properties or symmetric cryptographic tools are also presented, moving ahead in the understanding of their security properties. In addition, post-quantum constructions for digital signatures and key exchange are explored in this Special Issue, exemplifying how (and how not) group theory may be used for developing robust cryptographic tools to withstand quantum attacks.
Book Synopsis Handbook of Computational Group Theory by : Derek F. Holt
Download or read book Handbook of Computational Group Theory written by Derek F. Holt and published by CRC Press. This book was released on 2005-01-13 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: The origins of computation group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics. The Handbook of Computational Group Theory offers the first complete treatment of all the fundame
Book Synopsis Contributions to Group Theory by : Kenneth I. Appel
Download or read book Contributions to Group Theory written by Kenneth I. Appel and published by American Mathematical Soc.. This book was released on 1984 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains five short articles about Roger Lyndon and his contributions to mathematics, as well as twenty-seven invited research papers in combinatorial group theory and closely related areas. Several of the articles featured in this work fall into subfields of combinatorial group theory, areas in which much of the initial work was done by Lyndon.
Book Synopsis Group Theory of Chemical Elements by : Abram I. Fet
Download or read book Group Theory of Chemical Elements written by Abram I. Fet and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-09-12 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, group-theoretical approaches are used to build a system of hadrons and qualitatively describe the properties of chemical compounds. This serves as a complement to numerically and approximately solve the many-electron Schrödinger equation, in order to understand the behavior of chemical elements. Besides general theory, specific results are compared with experimentally measured chemical properties. Content: Symmetries of a quantum system Observables of a quantum system Lie groups and Lie algebras The principles of particle classification The symmetry group of chemical elements Classification and chemical properties of elements Appendix A. Fock’s energy spectrum of the hydrogen atom Appendix B. Representations of some groups
Book Synopsis Modular Functions and Dirichlet Series in Number Theory by : Tom M. Apostol
Download or read book Modular Functions and Dirichlet Series in Number Theory written by Tom M. Apostol and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series.
Book Synopsis The Logical Approach to Automatic Sequences by : Jeffrey Shallit
Download or read book The Logical Approach to Automatic Sequences written by Jeffrey Shallit and published by Cambridge University Press. This book was released on 2022-09-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automatic sequences are sequences over a finite alphabet generated by a finite-state machine. This book presents a novel viewpoint on automatic sequences, and more generally on combinatorics on words, by introducing a decision method through which many new results in combinatorics and number theory can be automatically proved or disproved with little or no human intervention. This approach to proving theorems is extremely powerful, allowing long and error-prone case-based arguments to be replaced by simple computations. Readers will learn how to phrase their desired results in first-order logic, using free software to automate the computation process. Results that normally require multipage proofs can emerge in milliseconds, allowing users to engage with mathematical questions that would otherwise be difficult to solve. With more than 150 exercises included, this text is an ideal resource for researchers, graduate students, and advanced undergraduates studying combinatorics, sequences, and number theory.
Book Synopsis Combinatorial and Additive Number Theory IV by : Melvyn B. Nathanson
Download or read book Combinatorial and Additive Number Theory IV written by Melvyn B. Nathanson and published by Springer Nature. This book was released on 2021-08-12 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Sequences, Discrepancies and Applications by : Michael Drmota
Download or read book Sequences, Discrepancies and Applications written by Michael Drmota and published by Springer. This book was released on 2006-11-14 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to give an overview of the developments during the last 20 years in the theory of uniformly distributed sequences. The authors focus on various aspects such as special sequences, metric theory, geometric concepts of discrepancy, irregularities of distribution, continuous uniform distribution and uniform distribution in discrete spaces. Specific applications are presented in detail: numerical integration, spherical designs, random number generation and mathematical finance. Furthermore over 1000 references are collected and discussed. While written in the style of a research monograph, the book is readable with basic knowledge in analysis, number theory and measure theory.
Download or read book Local Fields written by Jean-Pierre Serre and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray.
Book Synopsis Combinatorial Group Theory, Discrete Groups, and Number Theory by : Benjamin Fine
Download or read book Combinatorial Group Theory, Discrete Groups, and Number Theory written by Benjamin Fine and published by American Mathematical Soc.. This book was released on 2006 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of contributions by participants and speakers at two conferences. The first was entitled Combinatorial Group Theory, Discrete Groups and Number Theory and was held at Fairfield University, December 8-9, 2004. It was in honor of Professor Gerhard Rosenberger's sixtieth birthday. The second was the AMS Special Session on Infinite Group Theory held at Bard College, October 8-9, 2005. The papers in this volume provide a very interesting mix of combinatorial group theory, discrete group theory and ring theory as well as contributions to noncommutative algebraic cryptography.
