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Author: Alin Bostan
Publisher: Springer Nature
ISBN: 3030843041
Category : Mathematics
Languages : en
Pages : 544
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Book Description
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.
Author: Alin Bostan
Publisher: Springer Nature
ISBN: 3030843041
Category : Mathematics
Languages : en
Pages : 544
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Book Description
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.
Author: Alin Bostan
Publisher:
ISBN: 9783030843052
Category :
Languages : en
Pages : 0
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Book Description
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.
Author: Valérie Berthé
Publisher: Cambridge University Press
ISBN: 1139643185
Category : Mathematics
Languages : en
Pages : 637
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Book Description
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.
Author:
Publisher: Elsevier
ISBN: 0080532950
Category : Mathematics
Languages : en
Pages : 936
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Book Description
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.
Author: Igor Shparlinski
Publisher: Springer Science & Business Media
ISBN: 940111806X
Category : Mathematics
Languages : en
Pages : 253
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Book Description
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.
Author: Ina Kersten
Publisher: Universitätsverlag Göttingen
ISBN: 3940344966
Category : Algebraic number theory
Languages : en
Pages : 213
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Book Description
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."
Author: N. Pytheas Fogg
Publisher: Springer
ISBN: 3540457143
Category : Mathematics
Languages : en
Pages : 411
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Book Description
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.
Author: Marcelo Aguiar
Publisher: American Mathematical Soc.
ISBN: 1470437112
Category : Mathematics
Languages : en
Pages : 639
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Book Description
This monograph studies the interplay between various algebraic, geometric and combinatorial aspects of real hyperplane arrangements. It provides a careful, organized and unified treatment of several recent developments in the field, and brings forth many new ideas and results. It has two parts, each divided into eight chapters, and five appendices with background material. Part I gives a detailed discussion on faces, flats, chambers, cones, gallery intervals, lunes and other geometric notions associated with arrangements. The Tits monoid plays a central role. Another important object is the category of lunes which generalizes the classical associative operad. Also discussed are the descent and lune identities, distance functions on chambers, and the combinatorics of the braid arrangement and related examples. Part II studies the structure and representation theory of the Tits algebra of an arrangement. It gives a detailed analysis of idempotents and Peirce decompositions, and connects them to the classical theory of Eulerian idempotents. It introduces the space of Lie elements of an arrangement which generalizes the classical Lie operad. This space is the last nonzero power of the radical of the Tits algebra. It is also the socle of the left ideal of chambers and of the right ideal of Zie elements. Zie elements generalize the classical Lie idempotents. They include Dynkin elements associated to generic half-spaces which generalize the classical Dynkin idempotent. Another important object is the lune-incidence algebra which marks the beginning of noncommutative Möbius theory. These ideas are also brought upon the study of the Solomon descent algebra. The monograph is written with clarity and in sufficient detail to make it accessible to graduate students. It can also serve as a useful reference to experts.
Author: Math Vault
Publisher: Math Vault Publishing
ISBN:
Category : Mathematics
Languages : en
Pages : 86
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Book Description
The Definitive Guide to Learning Higher Mathematics is a comprehensive, illustrated guide to help you optimize higher mathematical learning, thinking and problem solving through 10 foundational principles and countless actionable tips. In 10 chapters and 86 pages, it’ll take you around the different aspects of higher mathematical learning, leaving no stone unturned from material selection, big picture thinking, proximal zone, cognitive techniques to proactive learning, head-processing, scientific method and social learning. Hightlights - Extensive actionable tips to illustrate each principle involved - Extensive annotations, pro-tips, quotes and illustrations for better insight - Carefully prepared after-chapter summaries for better understanding - Printable PDF format (8.5 in. x 11 in.) with linkable table of contents and index for handy reference and reviewing Table of Contents 0. Preface 1. Choose Your Materials Judiciously 2. Always Keep the Big Picture in Mind 3. Operate within the Proximal Zone 4. Isolate Until Mastered Before Moving On 5. Be a Proactive, Independent Thinker and Learner 6. Do Most Things Inside Your Head 7. Practice the Scientific Method in a Creative Way 8. Don’t Fret Too Much About Real-life Applicability 9. Scale Up Learning by Going Social 10. Embrace the Mathematical Experience 11. Last Few Words 12. Index
Author: Steven J. Miller
Publisher: Princeton University Press
ISBN: 0691215979
Category : Mathematics
Languages : en
Pages : 526
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Book Description
In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class.
