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Author: Valérie Berthé Publisher: Birkhäuser ISBN: 331969152X Category : Mathematics Languages : en Pages : 578
Book Description
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: Valérie Berthé Publisher: Birkhäuser ISBN: 331969152X Category : Mathematics Languages : en Pages : 578
Book Description
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: 1351346385 Category : Computers Languages : en Pages : 480
Book Description
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: 3764389613 Category : Mathematics Languages : en Pages : 324
Book Description
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: 0486149994 Category : Mathematics Languages : en Pages : 416
Book Description
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: Istvan Mezo Publisher: CRC Press ISBN: 1351346377 Category : Computers Languages : en Pages : 364
Book Description
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: Vladimir Platonov Publisher: Academic Press ISBN: 9780080874593 Category : Mathematics Languages : en Pages : 614
Book Description
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: 1009380656 Category : Mathematics Languages : en Pages : 380
Book Description
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: Keith Hirst Publisher: Elsevier ISBN: 0080928587 Category : Mathematics Languages : en Pages : 208
Book Description
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: Valérie Berthé
Author: Valérie Berthé
Author: Istvan Mezo
Author: Alfred Geroldinger
Author: Keith Hirst
Author: L. Kuipers
Author: Istvan Mezo
Author: Vladimir Platonov
Author: Vladimir Platonov
Author: Vladimir Platonov
Author: Keith Hirst