Sequences Groups And Number Theory

Author : Valérie Berthé
Publisher : Birkhäuser
ISBN 13 : 331969152X
Total Pages : 578 pages
Book Rating : 4.27/5 ( download)

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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 578 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.

Author : Istvan Mezo
Publisher : CRC Press
ISBN 13 : 1351346385
Total Pages : 480 pages
Book Rating : 4.82/5 ( download)

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Download or read book Combinatorics and Number Theory of Counting Sequences written by Istvan Mezo and published by CRC Press. This book was released on 2019-08-19 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Alfred Geroldinger
Publisher : Springer Science & Business Media
ISBN 13 : 3764389613
Total Pages : 324 pages
Book Rating : 4.11/5 ( download)

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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 2009-04-15 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.

Author : L. Kuipers
Publisher : Courier Corporation
ISBN 13 : 0486149994
Total Pages : 416 pages
Book Rating : 4.98/5 ( download)

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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.

Author : Keith Hirst
Publisher : Butterworth-Heinemann
ISBN 13 : 0340610433
Total Pages : 213 pages
Book Rating : 4.35/5 ( download)

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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.

Author : Vladimir Platonov
Publisher : Academic Press
ISBN 13 : 9780080874593
Total Pages : 614 pages
Book Rating : 4.92/5 ( download)

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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 614 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.

Author : Vladimir Platonov
Publisher : Cambridge University Press
ISBN 13 : 052111361X
Total Pages : 379 pages
Book Rating : 4.18/5 ( download)

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Download or read book Algebraic Groups and Number Theory written by Vladimir Platonov and published by Cambridge University Press. This book was released on 2023-08-31 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first volume of a two-volume book offering a comprehensive account of the arithmetic theory of algebraic groups.

Author : Keith Hirst
Publisher : Elsevier
ISBN 13 : 0080928587
Total Pages : 213 pages
Book Rating : 4.86/5 ( download)

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Download or read book Numbers, Sequences and Series written by Keith Hirst and published by Elsevier. This book was released on 1994-12-08 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Vladimir Platonov
Publisher : Cambridge University Press
ISBN 13 : 1009380656
Total Pages : 380 pages
Book Rating : 4.52/5 ( download)

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Download or read book Algebraic Groups and Number Theory: Volume 1 written by Vladimir Platonov and published by Cambridge University Press. This book was released on 2023-08-31 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Benjamin Fine
Publisher : American Mathematical Soc.
ISBN 13 : 0821839853
Total Pages : 282 pages
Book Rating : 4.50/5 ( download)

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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.