Polynomials With Special Regard To Reducibility

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Polynomials with Special Regard to Reducibility

A. Schinzel
Polynomials with Special Regard to Reducibility Book PDF

Author : A. Schinzel
Publisher : Cambridge University Press
Page : 590 pages
File Size : 41,6 Mb
Release : 2000-04-27
Category : Mathematics
ISBN : 1139426710

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Polynomials with Special Regard to Reducibility by A. Schinzel Pdf

This book covers most of the known results on reducibility of polynomials over arbitrary fields, algebraically closed fields and finitely generated fields. Results valid only over finite fields, local fields or the rational field are not covered here, but several theorems on reducibility of polynomials over number fields that are either totally real or complex multiplication fields are included. Some of these results are based on recent work of E. Bombieri and U. Zannier (presented here by Zannier in an appendix). The book also treats other subjects like Ritt's theory of composition of polynomials, and properties of the Mahler measure, and it concludes with a bibliography of over 300 items. This unique work will be a necessary resource for all number theorists and researchers in related fields.

Polynomials with Special Regard to Reducibility

A. Schinzel
Polynomials with Special Regard to Reducibility Book PDF

Author : A. Schinzel
Publisher : Cambridge University Press
Page : 570 pages
File Size : 53,5 Mb
Release : 2000-04-27
Category : Mathematics
ISBN : 0521662257

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Polynomials with Special Regard to Reducibility by A. Schinzel Pdf

This treatise covers most of the known results on reducibility of polynomials over arbitrary fields, algebraically closed fields, and finitely generated fields. The author includes several theorems on reducibility of polynomials over number fields that are either totally real or complex multiplication fields. Some of these results are based on the recent work of E. Bombieri and U. Zannier, presented here by Zannier in an appendix. The book also treats other subjects such as Ritt's theory of composition of polynomials, and properties of the Mahler measure and concludes with a bibliography of over 300 items.

Number Theory

Kalman Gyoery,Attila Pethoe,Vera T. Sos
Number Theory Book PDF

Author : Kalman Gyoery,Attila Pethoe,Vera T. Sos
Publisher : Walter de Gruyter
Page : 617 pages
File Size : 43,9 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110809794

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Number Theory by Kalman Gyoery,Attila Pethoe,Vera T. Sos Pdf

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Computer Algebra and Polynomials

Jaime Gutierrez,Josef Schicho,Martin Weimann
Computer Algebra and Polynomials Book PDF

Author : Jaime Gutierrez,Josef Schicho,Martin Weimann
Publisher : Springer
Page : 222 pages
File Size : 48,7 Mb
Release : 2015-01-20
Category : Computers
ISBN : 9783319150819

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Computer Algebra and Polynomials by Jaime Gutierrez,Josef Schicho,Martin Weimann Pdf

Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life. This book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ring. The operations on polynomials in the focus are factorization, composition and decomposition, basis computation for modules, etc. Algorithms for such operations on polynomials have always been a central interest in computer algebra, as it combines formal (the variables) and algebraic or numeric (the coefficients) aspects. The papers presented were selected from the Workshop on Computer Algebra and Polynomials, which was held in Linz at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) during November 25-29, 2013, at the occasion of the Special Semester on Applications of Algebra and Number Theory.

Number Theory and Polynomials

James Fraser McKee,Chris Smyth
Number Theory and Polynomials Book PDF

Author : James Fraser McKee,Chris Smyth
Publisher : Cambridge University Press
Page : 350 pages
File Size : 47,9 Mb
Release : 2008-05-08
Category : Mathematics
ISBN : 9780521714679

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Number Theory and Polynomials by James Fraser McKee,Chris Smyth Pdf

Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.

The Arithmetic of Polynomial Dynamical Pairs

Charles Favre,Thomas Gauthier
The Arithmetic of Polynomial Dynamical Pairs Book PDF

Author : Charles Favre,Thomas Gauthier
Publisher : Princeton University Press
Page : 252 pages
File Size : 46,9 Mb
Release : 2022-06-14
Category : Mathematics
ISBN : 9780691235486

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The Arithmetic of Polynomial Dynamical Pairs by Charles Favre,Thomas Gauthier Pdf

New mathematical research in arithmetic dynamics In The Arithmetic of Polynomial Dynamical Pairs, Charles Favre and Thomas Gauthier present new mathematical research in the field of arithmetic dynamics. Specifically, the authors study one-dimensional algebraic families of pairs given by a polynomial with a marked point. Combining tools from arithmetic geometry and holomorphic dynamics, they prove an “unlikely intersection” statement for such pairs, thereby demonstrating strong rigidity features for them. They further describe one-dimensional families in the moduli space of polynomials containing infinitely many postcritically finite parameters, proving the dynamical André-Oort conjecture for curves in this context, originally stated by Baker and DeMarco. This is a reader-friendly invitation to a new and exciting research area that brings together sophisticated tools from many branches of mathematics.

Codes and Automata

Jean Berstel,Dominique Perrin,Christophe Reutenauer
Codes and Automata Book PDF

Author : Jean Berstel,Dominique Perrin,Christophe Reutenauer
Publisher : Cambridge University Press
Page : 634 pages
File Size : 53,7 Mb
Release : 2010
Category : Computers
ISBN : 9780521888318

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Codes and Automata by Jean Berstel,Dominique Perrin,Christophe Reutenauer Pdf

This major revision of Berstel and Perrin's classic Theory of Codes has been rewritten with a more modern focus and a much broader coverage of the subject. The concept of unambiguous automata, which is intimately linked with that of codes, now plays a significant role throughout the book, reflecting developments of the last 20 years. This is complemented by a discussion of the connection between codes and automata, and new material from the field of symbolic dynamics. The authors have also explored links with more practical applications, including data compression and cryptography. The treatment remains self-contained: there is background material on discrete mathematics, algebra and theoretical computer science. The wealth of exercises and examples make it ideal for self-study or courses. In summary, this is a comprehensive reference on the theory of variable-length codes and their relation to automata.

Aggregation Functions

Michel Grabisch,Jean-Luc Marichal,Radko Mesiar,Endre Pap
Aggregation Functions Book PDF

Author : Michel Grabisch,Jean-Luc Marichal,Radko Mesiar,Endre Pap
Publisher : Cambridge University Press
Page : 481 pages
File Size : 46,8 Mb
Release : 2009-07-09
Category : Computers
ISBN : 9781139643221

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Aggregation Functions by Michel Grabisch,Jean-Luc Marichal,Radko Mesiar,Endre Pap Pdf

Aggregation is the process of combining several numerical values into a single representative value, and an aggregation function performs this operation. These functions arise wherever aggregating information is important: applied and pure mathematics (probability, statistics, decision theory, functional equations), operations research, computer science, and many applied fields (economics and finance, pattern recognition and image processing, data fusion, etc.). This is a comprehensive, rigorous and self-contained exposition of aggregation functions. Classes of aggregation functions covered include triangular norms and conorms, copulas, means and averages, and those based on nonadditive integrals. The properties of each method, as well as their interpretation and analysis, are studied in depth, together with construction methods and practical identification methods. Special attention is given to the nature of scales on which values to be aggregated are defined (ordinal, interval, ratio, bipolar). It is an ideal introduction for graduate students and a unique resource for researchers.

Purity, Spectra and Localisation

Mike Prest
Purity Spectra and Localisation Book PDF

Author : Mike Prest
Publisher : Cambridge University Press
Page : 798 pages
File Size : 45,8 Mb
Release : 2009-06-04
Category : Mathematics
ISBN : 9781139643894

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Purity, Spectra and Localisation by Mike Prest Pdf

It is possible to associate a topological space to the category of modules over any ring. This space, the Ziegler spectrum, is based on the indecomposable pure-injective modules. Although the Ziegler spectrum arose within the model theory of modules and plays a central role in that subject, this book concentrates specifically on its algebraic aspects and uses. The central aim is to understand modules and the categories they form through associated structures and dimensions, which reflect the complexity of these, and similar, categories. The structures and dimensions considered arise particularly through the application of model-theoretic and functor-category ideas and methods. Purity and associated notions are central, localisation is an ever-present theme and various types of spectrum play organising roles. This book presents a unified, coherent account of material which is often presented from very different viewpoints and clarifies the relationships between these various approaches.

Finite Fields: Theory and Applications

Gary McGuire
Finite Fields Theory and Applications Book PDF

Author : Gary McGuire
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 50,7 Mb
Release : 2010
Category : Computers
ISBN : 9780821847862

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Finite Fields: Theory and Applications by Gary McGuire Pdf

This volume contains the proceedings of the Ninth International Conference on Finite Fields and Applications, held in Ireland, July 13-17, 2009. It includes survey papers by all invited speakers as well as selected contributed papers. Finite fields continue to grow in mathematical importance due to applications in many diverse areas. This volume contains a variety of results advancing the theory of finite fields and connections with, as well as impact on, various directions in number theory, algebra, and algebraic geometry. Areas of application include algebraic coding theory, cryptology, and combinatorial design theory.

Computer Algebra in Scientific Computing

V.G. Ganzha,E.W. Mayr,E.V. Vorozhtsov
Computer Algebra in Scientific Computing Book PDF

Author : V.G. Ganzha,E.W. Mayr,E.V. Vorozhtsov
Publisher : Springer
Page : 314 pages
File Size : 48,5 Mb
Release : 2006-11-30
Category : Computers
ISBN : 9783540451952

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Computer Algebra in Scientific Computing by V.G. Ganzha,E.W. Mayr,E.V. Vorozhtsov Pdf

This book constitutes the refereed proceedings of the 9th International Workshop on Computer Algebra in Scientific Computing, CASC 2006. The book presents 25 revised full papers together with 2 invited papers, covering various expanding applications of computer algebra to scientific computing, the computer algebra systems themselves, and the CA algorithms. Topics addressed are studies in Gröbner bases, polynomial algebra, homological algebra, quantifier elimination, celestial mechanics, and more.

Point-Counting and the Zilber–Pink Conjecture

Jonathan Pila
Point Counting and the Zilber Pink Conjecture Book PDF

Author : Jonathan Pila
Publisher : Cambridge University Press
Page : 267 pages
File Size : 41,7 Mb
Release : 2022-06-09
Category : Mathematics
ISBN : 9781009170321

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Point-Counting and the Zilber–Pink Conjecture by Jonathan Pila Pdf

Explores the recent spectacular applications of point-counting in o-minimal structures to functional transcendence and diophantine geometry.

Convex Functions

Jonathan M. Borwein,Jon D. Vanderwerff
Convex Functions Book PDF

Author : Jonathan M. Borwein,Jon D. Vanderwerff
Publisher : Cambridge University Press
Page : 533 pages
File Size : 46,5 Mb
Release : 2010-01-14
Category : Mathematics
ISBN : 9781139811095

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Convex Functions by Jonathan M. Borwein,Jon D. Vanderwerff Pdf

Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programming and game theory. This book, which is the product of a collaboration of over 15 years, is unique in that it focuses on convex functions themselves, rather than on convex analysis. The authors explore the various classes and their characteristics and applications, treating convex functions in both Euclidean and Banach spaces. The book can either be read sequentially for a graduate course, or dipped into by researchers and practitioners. Each chapter contains a variety of specific examples, and over 600 exercises are included, ranging in difficulty from early graduate to research level.

Variational Principles in Mathematical Physics, Geometry, and Economics

Alexandru Kristály,V. Rădulescu,Vicenţiu D. Rădulescu,Csaba Varga
Variational Principles in Mathematical Physics Geometry and Economics Book PDF

Author : Alexandru Kristály,V. Rădulescu,Vicenţiu D. Rădulescu,Csaba Varga
Publisher : Cambridge University Press
Page : 385 pages
File Size : 49,5 Mb
Release : 2010-08-19
Category : Mathematics
ISBN : 9780521117821

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Variational Principles in Mathematical Physics, Geometry, and Economics by Alexandru Kristály,V. Rădulescu,Vicenţiu D. Rădulescu,Csaba Varga Pdf

A comprehensive introduction to modern applied functional analysis. Assumes only basic notions of calculus, real analysis, geometry, and differential equations.

Number Theory and Related Fields

Jonathan M. Borwein,Igor Shparlinski,Wadim Zudilin
Number Theory and Related Fields Book PDF

Author : Jonathan M. Borwein,Igor Shparlinski,Wadim Zudilin
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 55,6 Mb
Release : 2013-05-16
Category : Mathematics
ISBN : 9781461466420

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Number Theory and Related Fields by Jonathan M. Borwein,Igor Shparlinski,Wadim Zudilin Pdf

“Number Theory and Related Fields” collects contributions based on the proceedings of the "International Number Theory Conference in Memory of Alf van der Poorten," hosted by CARMA and held March 12-16th 2012 at the University of Newcastle, Australia. The purpose of the conference was to promote number theory research in Australia while commemorating the legacy of Alf van der Poorten, who had written over 170 papers on the topic of number theory and collaborated with dozens of researchers. The research articles and surveys presented in this book were written by some of the most distinguished mathematicians in the field of number theory, and articles will include related topics that focus on the various research interests of Dr. van der Poorten.​