Transcendence in Algebra, Combinatorics, Geometry and Number Theory
Transcendence in Algebra, Combinatorics, Geometry and Number Theory

Author: Alin Bostan

Publisher: Springer Nature

Published: 2021-11-02

Total Pages: 544

ISBN-13: 3030843041

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This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.

Transcendence in Algebra, Combinatorics, Geometry and Number Theory
Transcendence in Algebra, Combinatorics, Geometry and Number Theory

Author: Alin Bostan

Publisher:

Published: 2021

Total Pages: 0

ISBN-13: 9783030843052

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This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.

Combinatorics, Automata and Number Theory
Combinatorics, Automata and Number Theory

Author: Valérie Berthé

Publisher: Cambridge University Press

Published: 2010-08-12

Total Pages: 637

ISBN-13: 1139643185

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This collaborative volume presents trends arising from the fruitful interaction between the themes of combinatorics on words, automata and formal language theory, and number theory. Presenting several important tools and concepts, the authors also reveal some of the exciting and important relationships that exist between these different fields. Topics include numeration systems, word complexity function, morphic words, Rauzy tilings and substitutive dynamical systems, Bratelli diagrams, frequencies and ergodicity, Diophantine approximation and transcendence, asymptotic properties of digital functions, decidability issues for D0L systems, matrix products and joint spectral radius. Topics are presented in a way that links them to the three main themes, but also extends them to dynamical systems and ergodic theory, fractals, tilings and spectral properties of matrices. Graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, fractals, tilings and stringology will find much of interest in this book.

The Geometry of Schemes
The Geometry of Schemes

Author: David Eisenbud

Publisher: Springer Science & Business Media

Published: 2006-04-06

Total Pages: 265

ISBN-13: 0387226397

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Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Handbook of Algebra
Handbook of Algebra

Author:

Publisher: Elsevier

Published: 1995-12-18

Total Pages: 936

ISBN-13: 0080532950

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Handbook of Algebra defines algebra as consisting of many different ideas, concepts and results. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. Each chapter of the book combines some of the features of both a graduate-level textbook and a research-level survey. This book is divided into eight sections. Section 1A focuses on linear algebra and discusses such concepts as matrix functions and equations and random matrices. Section 1B cover linear dependence and discusses matroids. Section 1D focuses on fields, Galois Theory, and algebraic number theory. Section 1F tackles generalizations of fields and related objects. Section 2A focuses on category theory, including the topos theory and categorical structures. Section 2B discusses homological algebra, cohomology, and cohomological methods in algebra. Section 3A focuses on commutative rings and algebras. Finally, Section 3B focuses on associative rings and algebras. This book will be of interest to mathematicians, logicians, and computer scientists.

Computational and Algorithmic Problems in Finite Fields
Computational and Algorithmic Problems in Finite Fields

Author: Igor Shparlinski

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 253

ISBN-13: 940111806X

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This volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types, and new applications of finite fields to other araes of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc.) The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presuppose only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.

Substitutions in Dynamics, Arithmetics and Combinatorics
Substitutions in Dynamics, Arithmetics and Combinatorics

Author: N. Pytheas Fogg

Publisher: Springer

Published: 2003-10-24

Total Pages: 411

ISBN-13: 3540457143

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A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure. The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems.

Symmetries in Algebra and Number Theory (SANT)
Symmetries in Algebra and Number Theory (SANT)

Author: Ina Kersten

Publisher: Universitätsverlag Göttingen

Published: 2009

Total Pages: 213

ISBN-13: 3940344966

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4e de couverture : "These proceedings contain most of the contributions to the Göttingen-Jerusalem Conference 2008 on "Symmetries in Algebra and Number Theory" including three addresses given at the conference opening, and two contributions to the Satellite Conference "On the Legacy of Hermann Weyl". The contributions are survey articles or report on recent work by the authors, for exemple new results on the famous Leopoldt conjecture."

Advanced Number Theory with Applications
Advanced Number Theory with Applications

Author: Richard A. Mollin

Publisher: CRC Press

Published: 2009-08-26

Total Pages: 440

ISBN-13: 1420083295

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Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page reference for every citing in the bibliography and mo

All the Math You Missed
All the Math You Missed

Author: Thomas A. Garrity

Publisher: Cambridge University Press

Published: 2021-07

Total Pages: 417

ISBN-13: 1009009192

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Fill in any gaps in your knowledge with this overview of key topics in undergraduate mathematics, now with four new chapters.