Sequences Groups And Number Theory

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Sequences, Groups, and Number Theory

Valérie Berthé,Michel Rigo
Sequences Groups and Number Theory Book PDF

Author : Valérie Berthé,Michel Rigo
Publisher : Birkhäuser
Page : 578 pages
File Size : 43,8 Mb
Release : 2018-04-09
Category : Mathematics
ISBN : 9783319691527

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Sequences, Groups, and Number Theory by Valérie Berthé,Michel Rigo Pdf

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.

Combinatorics and Number Theory of Counting Sequences

Istvan Mezo
Combinatorics and Number Theory of Counting Sequences Book PDF

Author : Istvan Mezo
Publisher : CRC Press
Page : 480 pages
File Size : 52,5 Mb
Release : 2019-08-19
Category : Computers
ISBN : 9781351346382

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Combinatorics and Number Theory of Counting Sequences by Istvan Mezo Pdf

Combinatorics and Number Theory of Counting Sequences is an introduction to the theory of finite set partitions and to the enumeration of cycle decompositions of permutations. The presentation prioritizes elementary enumerative proofs. Therefore, parts of the book are designed so that even those high school students and teachers who are interested in combinatorics can have the benefit of them. Still, the book collects vast, up-to-date information for many counting sequences (especially, related to set partitions and permutations), so it is a must-have piece for those mathematicians who do research on enumerative combinatorics. In addition, the book contains number theoretical results on counting sequences of set partitions and permutations, so number theorists who would like to see nice applications of their area of interest in combinatorics will enjoy the book, too. Features The Outlook sections at the end of each chapter guide the reader towards topics not covered in the book, and many of the Outlook items point towards new research problems. An extensive bibliography and tables at the end make the book usable as a standard reference. Citations to results which were scattered in the literature now become easy, because huge parts of the book (especially in parts II and III) appear in book form for the first time.

Combinatorial Number Theory and Additive Group Theory

Alfred Geroldinger,Imre Ruzsa
Combinatorial Number Theory and Additive Group Theory Book PDF

Author : Alfred Geroldinger,Imre Ruzsa
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 46,5 Mb
Release : 2009-04-15
Category : Mathematics
ISBN : 9783764389611

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Combinatorial Number Theory and Additive Group Theory by Alfred Geroldinger,Imre Ruzsa Pdf

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.

Algebraic Groups and Number Theory

Vladimir Platonov,Andrei Rapinchuk,Rachel Rowen
Algebraic Groups and Number Theory Book PDF

Author : Vladimir Platonov,Andrei Rapinchuk,Rachel Rowen
Publisher : Academic Press
Page : 614 pages
File Size : 53,8 Mb
Release : 1993-12-07
Category : Mathematics
ISBN : 0080874592

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Algebraic Groups and Number Theory by Vladimir Platonov,Andrei Rapinchuk,Rachel Rowen Pdf

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.

Algebraic Groups and Number Theory

Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk
Algebraic Groups and Number Theory Book PDF

Author : Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk
Publisher : Cambridge University Press
Page : 379 pages
File Size : 54,5 Mb
Release : 2023-08-31
Category : Mathematics
ISBN : 9780521113618

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Algebraic Groups and Number Theory by Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk Pdf

The first volume of a two-volume book offering a comprehensive account of the arithmetic theory of algebraic groups.

Algebraic Groups and Number Theory: Volume 1

Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk
Algebraic Groups and Number Theory Volume 1 Book PDF

Author : Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk
Publisher : Cambridge University Press
Page : 380 pages
File Size : 54,6 Mb
Release : 2023-08-31
Category : Mathematics
ISBN : 9781009380652

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Algebraic Groups and Number Theory: Volume 1 by Vladimir Platonov,Andrei Rapinchuk,Igor Rapinchuk Pdf

The first edition of this book provided the first systematic exposition of the arithmetic theory of algebraic groups. This revised second edition, now published in two volumes, retains the same goals, while incorporating corrections and improvements, as well as new material covering more recent developments. Volume I begins with chapters covering background material on number theory, algebraic groups, and cohomology (both abelian and non-abelian), and then turns to algebraic groups over locally compact fields. The remaining two chapters provide a detailed treatment of arithmetic subgroups and reduction theory in both the real and adelic settings. Volume I includes new material on groups with bounded generation and abstract arithmetic groups. With minimal prerequisites and complete proofs given whenever possible, this book is suitable for self-study for graduate students wishing to learn the subject as well as a reference for researchers in number theory, algebraic geometry, and related areas.

Numbers, Sequences and Series

Keith Hirst
Numbers Sequences and Series Book PDF

Author : Keith Hirst
Publisher : Elsevier
Page : 213 pages
File Size : 40,9 Mb
Release : 1994-12-08
Category : Mathematics
ISBN : 9780080928586

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Numbers, Sequences and Series by Keith Hirst Pdf

Number and geometry are the foundations upon which mathematics has been built over some 3000 years. This book is concerned with the logical foundations of number systems from integers to complex numbers. The author has chosen to develop the ideas by illustrating the techniques used throughout mathematics rather than using a self-contained logical treatise. The idea of proof has been emphasised, as has the illustration of concepts from a graphical, numerical and algebraic point of view. Having laid the foundations of the number system, the author has then turned to the analysis of infinite processes involving sequences and series of numbers, including power series. The book also has worked examples throughout and includes some suggestions for self-study projects. In addition there are tutorial problems aimed at stimulating group work and discussion.

Combinatorial Group Theory, Discrete Groups, and Number Theory

Benjamin Fine,Anthony M. Gaglione,Dennis Spellman
Combinatorial Group Theory Discrete Groups and Number Theory Book PDF

Author : Benjamin Fine,Anthony M. Gaglione,Dennis Spellman
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 41,5 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821839850

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Combinatorial Group Theory, Discrete Groups, and Number Theory by Benjamin Fine,Anthony M. Gaglione,Dennis Spellman Pdf

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.

Algebraic Topology

Allen Hatcher
Algebraic Topology Book PDF

Author : Allen Hatcher
Publisher : Cambridge University Press
Page : 572 pages
File Size : 41,9 Mb
Release : 2002
Category : Mathematics
ISBN : 0521795400

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Algebraic Topology by Allen Hatcher Pdf

An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.

Handbook of Computational Group Theory

Derek F. Holt,Bettina Eick,Eamonn A. O'Brien
Handbook of Computational Group Theory Book PDF

Author : Derek F. Holt,Bettina Eick,Eamonn A. O'Brien
Publisher : CRC Press
Page : 532 pages
File Size : 51,6 Mb
Release : 2005-01-13
Category : Mathematics
ISBN : 9781420035216

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Handbook of Computational Group Theory by Derek F. Holt,Bettina Eick,Eamonn A. O'Brien Pdf

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

Stream Ciphers and Number Theory

T.W. Cusick,C. Ding,Ari R. Renvall
Stream Ciphers and Number Theory Book PDF

Author : T.W. Cusick,C. Ding,Ari R. Renvall
Publisher : Elsevier
Page : 446 pages
File Size : 51,5 Mb
Release : 1998-04-20
Category : Computers
ISBN : 9780080541846

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Stream Ciphers and Number Theory by T.W. Cusick,C. Ding,Ari R. Renvall Pdf

This book is almost entirely concerned with stream ciphers, concentrating on a particular mathematical model for such ciphers which are called additive natural stream ciphers. These ciphers use a natural sequence generator to produce a periodic keystream. Full definitions of these concepts are given in Chapter 2. This book focuses on keystream sequences which can be analysed using number theory. It turns out that a great deal of information can be deducted about the cryptographic properties of many classes of sequences by applying the terminology and theorems of number theory. These connections can be explicitly made by describing three kinds of bridges between stream ciphering problems and number theory problems. A detailed summary of these ideas is given in the introductory Chapter 1. Many results in the book are new, and over seventy percent of these results described in this book are based on recent research results.

Uniform Distribution of Sequences

L. Kuipers,H. Niederreiter
Uniform Distribution of Sequences Book PDF

Author : L. Kuipers,H. Niederreiter
Publisher : Courier Corporation
Page : 416 pages
File Size : 53,6 Mb
Release : 2012-05-24
Category : Mathematics
ISBN : 9780486149998

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Uniform Distribution of Sequences by L. Kuipers,H. Niederreiter Pdf

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.

The Logical Approach to Automatic Sequences

Jeffrey Shallit
The Logical Approach to Automatic Sequences Book PDF

Author : Jeffrey Shallit
Publisher : Cambridge University Press
Page : 376 pages
File Size : 47,9 Mb
Release : 2022-09-30
Category : Computers
ISBN : 9781108786973

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The Logical Approach to Automatic Sequences by Jeffrey Shallit Pdf

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.

Combinatorial and Additive Number Theory IV

Melvyn B. Nathanson
Combinatorial and Additive Number Theory IV Book PDF

Author : Melvyn B. Nathanson
Publisher : Springer Nature
Page : 445 pages
File Size : 40,5 Mb
Release : 2021-08-12
Category : Mathematics
ISBN : 9783030679965

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Combinatorial and Additive Number Theory IV by Melvyn B. Nathanson Pdf

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.

Number Theory

Canadian Number Theory Association. Conference,Karl Dilcher
Number Theory Book PDF

Author : Canadian Number Theory Association. Conference,Karl Dilcher
Publisher : American Mathematical Soc.
Page : 460 pages
File Size : 49,5 Mb
Release : 1995
Category : Mathematics
ISBN : 0821803123

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Number Theory by Canadian Number Theory Association. Conference,Karl Dilcher Pdf

This book contains proceedings presented at the fourth Canadian Number Theory Association conference held at Dalhousie University in July 1994. The invited speakers focused on analytic, algebraic, and computational number theory. The contributed talks represented a wide variety of areas in number theory.