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Polynomials With Special Regard To Reducibility

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Polynomials With Special Regard To Reducibility

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Author : A. Schinzel
language : en
Publisher: Cambridge University Press
Release Date : 2000-04-27

Polynomials With Special Regard To Reducibility written by A. Schinzel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-27 with Mathematics categories.

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

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Author : A. Schinzel
language : en
Publisher: Cambridge University Press
Release Date : 2000-04-27

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.

Purity Spectra And Localisation

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Author : Mike Prest
language : en
Publisher: Cambridge University Press
Release Date : 2009-06-04

Purity Spectra And Localisation written by Mike Prest and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-04 with Mathematics categories.

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.

Aggregation Functions

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Author : Michel Grabisch
language : en
Publisher: Cambridge University Press
Release Date : 2009-07-09

Aggregation Functions written by Michel Grabisch and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-09 with Computers categories.

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.

Finite Fields Theory And Applications

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Author : Gary McGuire
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

Finite Fields Theory And Applications written by Gary McGuire and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.

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.

Point Counting And The Zilber Pink Conjecture

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Author : Jonathan Pila
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-09

Point Counting And The Zilber Pink Conjecture written by Jonathan Pila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-09 with Mathematics categories.

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

Computer Algebra In Scientific Computing

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Author : V.G. Ganzha
language : en
Publisher: Springer
Release Date : 2006-11-30

Computer Algebra In Scientific Computing written by V.G. Ganzha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-30 with Computers categories.

This volume contains revised versions of the papers submitted to the workshop by the participants and accepted by the program committee after a thorough reviewing process. The collection of papers included in the proceedings covers not only various expanding applications of computer algebra to scienti?c computing but also the computer algebra systems themselves and the CA algorithms. The eight earlier CASC conferences, CASC 1998, CASC 1999, CASC 2000, CASC 2001, CASC 2002, CASC 2003, CASC 2004, and CASC 2005 were held, - spectively, in St. Petersburg, Russia, in Munich, Germany, in Samarkand, Uzb- istan, in Konstanz, Germany, in Crimea, Ukraine, in Passau, Germany, in St. Petersburg, Russia, and in Kalamata, Greece, and they proved to be successful. It was E. A. Grebenikow (Computing Center of the Russian Academy of S- ences, Moscow) who drew our attention to the group of mathematicians and c- puter scientists at the Academy of Sciences of Moldova conducting research in the ?eld of computer algebra. We were impressed that this group not only is concerned with applications of CA methods to problems of scienti?c computing but also c- ries out research on the fundamental principles underlying the current computer algebra systems themselves, see also their papers in the present proceedings v- ume. It was therefore decided to organize the 9th workshop on Computer Algebra in Scienti?c Computing, CASC 2006, in Chi ̧ sin? au, the capital of Moldova.

Topics In Topological Graph Theory

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Author : Lowell W. Beineke
language : en
Publisher: Cambridge University Press
Release Date : 2009-07-09

Topics In Topological Graph Theory written by Lowell W. Beineke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-09 with Mathematics categories.

The use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature. Other books cover portions of the material here, but there are no other books with such a wide scope. This book contains fifteen expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory and the topology of surfaces. Each chapter concludes with an extensive list of references.

Variational Principles In Mathematical Physics Geometry And Economics

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Author : Alexandru Kristály
language : en
Publisher: Cambridge University Press
Release Date : 2010-08-19

Variational Principles In Mathematical Physics Geometry And Economics written by Alexandru Kristály and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-19 with Mathematics categories.

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

Convex Functions

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Author : Jonathan M. Borwein
language : en
Publisher: Cambridge University Press
Release Date : 2010-01-14

Convex Functions written by Jonathan M. Borwein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-14 with Mathematics categories.

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.

Polynomials With Special Regard To Reducibility

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