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Author: Wladyslaw Narkiewicz Publisher: Springer ISBN: 3540492666 Category : Mathematics Languages : en Pages : 144
Book Description
The book deals with certain algebraic and arithmetical questions concerning polynomial mappings in one or several variables. Algebraic properties of the ring Int(R) of polynomials mapping a given ring R into itself are presented in the first part, starting with classical results of Polya, Ostrowski and Skolem. The second part deals with fully invariant sets of polynomial mappings F in one or several variables, i.e. sets X satisfying F(X)=X . This includes in particular a study of cyclic points of such mappings in the case of rings of algebrai integers. The text contains several exercises and a list of open problems.
Author: Wladyslaw Narkiewicz Publisher: Springer ISBN: 3540492666 Category : Mathematics Languages : en Pages : 144
Book Description
The book deals with certain algebraic and arithmetical questions concerning polynomial mappings in one or several variables. Algebraic properties of the ring Int(R) of polynomials mapping a given ring R into itself are presented in the first part, starting with classical results of Polya, Ostrowski and Skolem. The second part deals with fully invariant sets of polynomial mappings F in one or several variables, i.e. sets X satisfying F(X)=X . This includes in particular a study of cyclic points of such mappings in the case of rings of algebrai integers. The text contains several exercises and a list of open problems.
Author: Władysław Narkiewicz Publisher: Springer Verlag ISBN: 9780387594354 Category : Mathematics Languages : en Pages : 130
Book Description
The book deals with certain algebraic and arithmetical questions concerning polynomial mappings in one or several variables. Algebraic properties of the ring Int(R) of polynomials mapping a given ring R into itself are presented in the first part, starting with classical results of Polya, Ostrowski and Skolem. The second part deals with fully invariant sets of polynomial mappings F in one or several variables, i.e. sets X satisfying F(X)=X . This includes in particular a study of cyclic points of such mappings in the case of rings of algebrai integers. The text contains several exercises and a list of open problems.
Author: Gabriel Katz Publisher: World Scientific Publishing Company ISBN: 9813107944 Category : Mathematics Languages : en Pages : 632
Book Description
The Shape of Algebra in the Mirrors of Mathematics is a unique text aiming to explain some elements of modern mathematics and to show its flavor and unity. It is neither a standard textbook nor a tour of algebra for a casual reader. Rather, it is an attempt to share authors' mathematical experiences and philosophy with readers who have more than a passing interest in mathematics, but only a traditional exposure to High School Algebra and some elements of Calculus. The book gives the readers a sense of visual nature of significant part of mathematics.The reader becomes an owner of and a researcher in VisuMatica, a virtual math laboratory. It is an original and comprehensive PC software package (a brainchild of the second author) that will enable the reader to experience mathematics both as a human intellectual endeavor and as an experimental science. Although it is possible to read and appreciate the book without ever visiting the VisuMatica lab, those who engage with the interactive demos found in the lab will greatly advance their understanding of the text. The book seeks to encourage an interactive, investigative style of learning that can promote the habits of mind characteristic of modern mathematical thinking.An outline of the topics that are discussed may read like a list of graduate courses: Abstract Algebra, Topology, Singularity Theory, Complex Analysis, and Number Theory. However, they are presented from an intuitive perspective that uses primarily visual models and concepts. Although the main subject is polynomials and polynomial equations, the true story line is the interplay between basic ideas from algebra, geometry, analysis and topology.The Shape of Algebra might serve as a text for an “appreciation” course in modern mathematics designed for non-mathematics majors or for students who are considering majoring in mathematics or related disciplines. The authors' goal is to present the reader with a fresh viewpoint on the sense and flavor of mathematics. The subject is often presented in a fashion that students find stale and uncompelling. The book's emphasis, in contrast, is on how a modern practitioner thinks about and works within the discipline.The book aims to attract students of all ages, particularly including professional mathematicians interested in pedagogy. In part, The Shape of Algebra is directed at secondary and college teachers and students who want to expand their horizons in the field and to find both a fresh presentation of familiar concepts and, perhaps, some unexpected results. Many of the topics and demos are self-contained and can be used individually to enhance traditional courses. Several of the ideas and materials developed in the book have been tested in high school and college classrooms. The book will enable readers to approach its content on three levels: the first level requires only some fluency with routine algebraic manipulations; the second also presumes familiarity with the notions of derivatives, and the third uses some basic concepts of multivariable calculus and linear algebra. All three levels are clearly marked in the text, and allow for a smooth reading enhanced by virtual experiments.
Author: Nikolay Nikolaev Publisher: Springer Science & Business Media ISBN: 0387312404 Category : Computers Languages : en Pages : 329
Book Description
This book delivers theoretical and practical knowledge for developing algorithms that infer linear and non-linear multivariate models, providing a methodology for inductive learning of polynomial neural network models (PNN) from data. The text emphasizes an organized model identification process by which to discover models that generalize and predict well. The book further facilitates the discovery of polynomial models for time-series prediction.
Author: Ken’ichi Ohshika Publisher: Springer Nature ISBN: 3030559289 Category : Mathematics Languages : en Pages : 724
Book Description
This book consists of 16 surveys on Thurston's work and its later development. The authors are mathematicians who were strongly influenced by Thurston's publications and ideas. The subjects discussed include, among others, knot theory, the topology of 3-manifolds, circle packings, complex projective structures, hyperbolic geometry, Kleinian groups, foliations, mapping class groups, Teichmüller theory, anti-de Sitter geometry, and co-Minkowski geometry. The book is addressed to researchers and students who want to learn about Thurston’s wide-ranging mathematical ideas and their impact. At the same time, it is a tribute to Thurston, one of the greatest geometers of all time, whose work extended over many fields in mathematics and who had a unique way of perceiving forms and patterns, and of communicating and writing mathematics.
Author: Antonio Giambruno Publisher: CRC Press ISBN: 9780203911549 Category : Mathematics Languages : en Pages : 442
Book Description
Polynomial Identities and Combinatorial Methods presents a wide range of perspectives on topics ranging from ring theory and combinatorics to invariant theory and associative algebras. It covers recent breakthroughs and strategies impacting research on polynomial identities and identifies new concepts in algebraic combinatorics, invariant and representation theory, and Lie algebras and superalgebras for novel studies in the field. It presents intensive discussions on various methods and techniques relating the theory of polynomial identities to other branches of algebraic study and includes discussions on Hopf algebras and quantum polynomials, free algebras and Scheier varieties.
Author: V. Bykov Publisher: Springer Science & Business Media ISBN: 9401153027 Category : Mathematics Languages : en Pages : 254
Book Description
The subject of this book is connected with a new direction in mathematics, which has been actively developed over the last few years, namely the field of polynomial computer algebra, which lies at the intersection point of algebra, mathematical analysis and programming. There were several incentives to write the book. First of all, there has lately been a considerable interest in applied nonlinear problems characterized by multiple sta tionary states. Practical needs have then in their turn led to the appearance of new theoretical results in the analysis of systems of nonlinear algebraic equations. And finally, the introduction of various computer packages for analytic manipulations has made it possible to use complicated elimination-theoretical algorithms in prac tical research. The structure of the book is accordingly represented by three main parts: Mathematical results driven to constructive algorithms, computer algebra realizations of these algorithms, and applications. Nonlinear systems of algebraic equations arise in diverse fields of science. In particular, for processes described by systems of differential equations with a poly nomial right hand side one is faced with the problem of determining the number (and location) of the stationary states in certain sets.
Author: Wladyslaw Narkiewicz
Author: Wladyslaw Narkiewicz
Author: Władysław Narkiewicz
Author: Michael Ernest Zieve
Author: John D. Randall
Author: Gabriel Katz
Author: Nikolay Nikolaev
Author: Ken’ichi Ohshika
Author: Antonio Giambruno
Author: V. Bykov
Author: Yutze Chow