Sequences Groups And Number Theory PDF Download
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Author | : Valérie Berthé |
Publisher | : Birkhäuser |
Total Pages | : 578 |
Release | : 2018-04-09 |
Genre | : Mathematics |
ISBN | : 331969152X |
Download Sequences, Groups, and Number Theory Book in PDF, ePub and Kindle
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 |
Total Pages | : 480 |
Release | : 2019-08-19 |
Genre | : Computers |
ISBN | : 1351346385 |
Download Combinatorics and Number Theory of Counting Sequences Book in PDF, ePub and Kindle
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 | : L. Kuipers |
Publisher | : Courier Corporation |
Total Pages | : 416 |
Release | : 2012-05-24 |
Genre | : Mathematics |
ISBN | : 0486149994 |
Download Uniform Distribution of Sequences Book in PDF, ePub and Kindle
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 | : Alfred Geroldinger |
Publisher | : Springer Science & Business Media |
Total Pages | : 324 |
Release | : 2009-04-15 |
Genre | : Mathematics |
ISBN | : 3764389613 |
Download Combinatorial Number Theory and Additive Group Theory Book in PDF, ePub and Kindle
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 | : Keith Hirst |
Publisher | : Butterworth-Heinemann |
Total Pages | : 213 |
Release | : 1994-12-08 |
Genre | : Mathematics |
ISBN | : 0340610433 |
Download Numbers, Sequences and Series Book in PDF, ePub and Kindle
Concerned with the logical foundations of number systems from integers to complex numbers.
Author | : Vladimir Platonov |
Publisher | : Cambridge University Press |
Total Pages | : 379 |
Release | : 2023-08-31 |
Genre | : Mathematics |
ISBN | : 052111361X |
Download Algebraic Groups and Number Theory Book in PDF, ePub and Kindle
The first volume of a two-volume book offering a comprehensive account of the arithmetic theory of algebraic groups.
Author | : Vladimir Platonov |
Publisher | : Cambridge University Press |
Total Pages | : 380 |
Release | : 2023-08-31 |
Genre | : Mathematics |
ISBN | : 1009380656 |
Download Algebraic Groups and Number Theory: Volume 1 Book in PDF, ePub and Kindle
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 | : Vladimir Platonov |
Publisher | : Academic Press |
Total Pages | : 614 |
Release | : 1993-12-07 |
Genre | : Mathematics |
ISBN | : 9780080874593 |
Download Algebraic Groups and Number Theory Book in PDF, ePub and Kindle
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 | : Benjamin Fine |
Publisher | : American Mathematical Soc. |
Total Pages | : 282 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 0821839853 |
Download Combinatorial Group Theory, Discrete Groups, and Number Theory Book in PDF, ePub and Kindle
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.
Author | : Tom M. Apostol |
Publisher | : Springer Science & Business Media |
Total Pages | : 218 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461209994 |
Download Modular Functions and Dirichlet Series in Number Theory Book in PDF, ePub and Kindle
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.