Download or read book Polynomials with Special Regard to Reducibility written by A. Schinzel and published by Cambridge University Press. This book was released on 2000-04-27 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Polynomials with Special Regard to Reducibility written by A. Schinzel and published by Cambridge University Press. This book was released on 2000-04-27 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Number Theory written by Kalman Gyoery and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computer Algebra and Polynomials written by Jaime Gutierrez and published by Springer. This book was released on 2015-01-20 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Number Theory and Polynomials written by James Fraser McKee and published by Cambridge University Press. This book was released on 2008-05-08 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.
Download or read book The Arithmetic of Polynomial Dynamical Pairs written by Charles Favre and published by Princeton University Press. This book was released on 2022-06-14 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Codes and Automata written by Jean Berstel and published by Cambridge University Press. This book was released on 2010 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Purity Spectra and Localisation written by Mike Prest and published by Cambridge University Press. This book was released on 2009-06-04 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Aggregation Functions written by Michel Grabisch and published by Cambridge University Press. This book was released on 2009-07-09 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computer Algebra in Scientific Computing written by V.G. Ganzha and published by Springer. This book was released on 2006-11-30 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Finite Fields Theory and Applications written by Gary McGuire and published by American Mathematical Soc.. This book was released on 2010 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Point Counting and the Zilber Pink Conjecture written by Jonathan Pila and published by Cambridge University Press. This book was released on 2022-06-09 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores the recent spectacular applications of point-counting in o-minimal structures to functional transcendence and diophantine geometry.
Download or read book Stochastic Partial Differential Equations with L vy Noise written by S. Peszat and published by Cambridge University Press. This book was released on 2007-10-11 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive monograph by two leading international experts; includes applications to statistical and fluid mechanics and to finance.
Download or read book Convex Functions written by Jonathan M. Borwein and published by Cambridge University Press. This book was released on 2010-01-14 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Variational Principles in Mathematical Physics Geometry and Economics written by Alexandru Kristály and published by Cambridge University Press. This book was released on 2010-08-19 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to modern applied functional analysis. Assumes only basic notions of calculus, real analysis, geometry, and differential equations.
Download or read book Large Deviations and Metastability written by Enzo Olivieri and published by Cambridge University Press. This book was released on 2005-02-21 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description
Download or read book The Mountain Pass Theorem written by Youssef Jabri and published by Cambridge University Press. This book was released on 2003-09-15 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2003 book presents min-max methods through a study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led from the most accessible results to the forefront of the theory, and at each step in this walk between the hills, the author presents the extensions and variants of the MPT in a complete and unified way. Coverage includes standard topics, but it also covers other topics covered nowhere else in book form: the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants. Each chapter has a section with supplementary comments and bibliographical notes, and there is a rich bibliography and a detailed index to aid the reader. The book is suitable for researchers and graduate students. Nevertheless, the style and the choice of the material make it accessible to all newcomers to the field.
