Integers Polynomials And Rings

Author : Ronald S. Irving
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 51,8 Mb
Release : 2004-01-08
Category : Mathematics
ISBN : 9780387403977

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Integers, Polynomials, and Rings by Ronald S. Irving Pdf

This book began life as a set of notes that I developed for a course at the University of Washington entitled Introduction to Modern Algebra for Tea- ers. Originally conceived as a text for future secondary-school mathematics teachers, it has developed into a book that could serve well as a text in an - dergraduatecourseinabstractalgebraoracoursedesignedasanintroduction to higher mathematics. This book di?ers from many undergraduate algebra texts in fundamental ways; the reasons lie in the book’s origin and the goals I set for the course. The course is a two-quarter sequence required of students intending to f- ?ll the requirements of the teacher preparation option for our B.A. degree in mathematics, or of the teacher preparation minor. It is required as well of those intending to matriculate in our university’s Master’s in Teaching p- gram for secondary mathematics teachers. This is the principal course they take involving abstraction and proof, and they come to it with perhaps as little background as a year of calculus and a quarter of linear algebra. The mathematical ability of the students varies widely, as does their level of ma- ematical interest.

Author : Ronald S. Irving
Publisher : Unknown
Page : 304 pages
File Size : 47,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1475780435

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Integers, Polynomials, and Rings by Ronald S. Irving Pdf

Author : Paul-Jean Cahen,Jean-Luc Chabert
Publisher : American Mathematical Soc.
Page : 345 pages
File Size : 48,6 Mb
Release : 1997
Category : Ideals (Algebra).
ISBN : 9780821803882

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Integer-valued Polynomials by Paul-Jean Cahen,Jean-Luc Chabert Pdf

Integer-valued polynomials on the ring of integers have been known for a long time and have been used in calculus. Polya and Ostrowski generalized this notion to rings of integers of number fields. More generally still, one may consider a domain $D$ and the polynomials (with coefficients in its quotient field) mapping $D$ into itself. They form a $D$-algebra - that is, a $D$-module with a ring structure. Appearing in a very natural fashion, this ring possesses quite a rich structure, and the very numerous questions it raises allow a thorough exploration of commutative algebra. Here is the first book devoted entirely to this topic. This book features: thorough reviews of many published works; self-contained text with complete proofs; and numerous exercises.

Author : Minking Eie,Shou-Te Chang
Publisher : World Scientific
Page : 372 pages
File Size : 43,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814271905

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A Course on Abstract Algebra by Minking Eie,Shou-Te Chang Pdf

This textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the author's lecture notes at the Department of Mathematics, National Chung Cheng University of Taiwan, it begins with a description of the algebraic structures of the ring and field of rational numbers. Abstract groups are then introduced. Technical results such as Lagrange's Theorem and Sylow's Theorems follow as applications of group theory. Ring theory forms the second part of abstract algebra, with the ring of polynomials and the matrix ring as basic examples. The general theory of ideals as well as maximal ideals in the rings of polynomials over the rational numbers are also discussed. The final part of the book focuses on field theory, field extensions and then Galois theory to illustrate the correspondence between the Galois groups and field extensions. This textbook is more accessible and less ambitious than most existing books covering the same subject. Readers will also find the pedagogical material very useful in enhancing the teaching and learning of abstract algebra.

Author : Donald Yau
Publisher : World Scientific Publishing Company
Page : 204 pages
File Size : 55,9 Mb
Release : 2010-03-02
Category : Mathematics
ISBN : 9789813107847

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Lambda-Rings by Donald Yau Pdf

This book gives a self-contained introduction to the theory of lambda-rings and closely related topics, including Witt vectors, integer-valued polynomials, and binomial rings. Many of the purely algebraic results about lambda-rings presented in this book have never appeared in book form before. This book concludes with a chapter on open problems related to lambda-rings.

Author : Daniel G. Coronell
Publisher : CRC Press
Page : 693 pages
File Size : 44,8 Mb
Release : 2015-10-15
Category : Science
ISBN : 9781584885153

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Introduction to MATLAB with Applications for Chemical and Mechanical Engineers by Daniel G. Coronell Pdf

Introduction to MATLAB with Applications for Chemical and Mechanical Engineers provides applications from chemical engineering and biotechnology, such as thermodynamics, heat transfer, fluid mechanics, and mass transfer. The book features a section on input, output, and storage of data as well as a section on data analysis and parameter estimation that contains statistical analysis, curve fitting optimization, and error analysis. Many applied case studies are included from the engineering disciplines. It also offers instruction on the use of the MATLAB® optimization toolbox. With a CD-ROM of MATLAB programs, this text is essential for chemical engineers, mechanical engineers, applied mathematicians, and students.

Author : Siegfried Bosch
Publisher : Springer
Page : 352 pages
File Size : 53,9 Mb
Release : 2018-11-02
Category : Mathematics
ISBN : 9783319951775

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Algebra by Siegfried Bosch Pdf

The material presented here can be divided into two parts. The first, sometimes referred to as abstract algebra, is concerned with the general theory of algebraic objects such as groups, rings, and fields, hence, with topics that are also basic for a number of other domains in mathematics. The second centers around Galois theory and its applications. Historically, this theory originated from the problem of studying algebraic equations, a problem that, after various unsuccessful attempts to determine solution formulas in higher degrees, found its complete clarification through the brilliant ideas of E. Galois. The study of algebraic equations has served as a motivating terrain for a large part of abstract algebra, and according to this, algebraic equations are visible as a guiding thread throughout the book. To underline this point, an introduction to the history of algebraic equations is included. The entire book is self-contained, up to a few prerequisites from linear algebra. It covers most topics of current algebra courses and is enriched by several optional sections that complement the standard program or, in some cases, provide a first view on nearby areas that are more advanced. Every chapter begins with an introductory section on "Background and Overview," motivating the material that follows and discussing its highlights on an informal level. Furthermore, each section ends with a list of specially adapted exercises, some of them with solution proposals in the appendix. The present English edition is a translation and critical revision of the eighth German edition of the Algebra book by the author. The book appeared for the first time in 1993 and, in later years, was complemented by adding a variety of related topics. At the same time it was modified and polished to keep its contents up to date.

Author : Martin Davis,Hilary Putnam
Publisher : Unknown
Page : 34 pages
File Size : 40,5 Mb
Release : 1961
Category : Algebra
ISBN : UOM:39015095248723

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Diophantine Sets Over Polynomial Rings by Martin Davis,Hilary Putnam Pdf

IT IS PROVED THAT EVERY R CURSIVELY ENUMERABLE SET IS Diophantine over a given polynomial ring. (Author).

Author : Jeffrey Humpherys,Tyler J. Jarvis,Emily J. Evans
Publisher : SIAM
Page : 710 pages
File Size : 51,5 Mb
Release : 2017-07-07
Category : Mathematics
ISBN : 9781611974898

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Foundations of Applied Mathematics, Volume I by Jeffrey Humpherys,Tyler J. Jarvis,Emily J. Evans Pdf

This book provides the essential foundations of both linear and nonlinear analysis necessary for understanding and working in twenty-first century applied and computational mathematics. In addition to the standard topics, this text includes several key concepts of modern applied mathematical analysis that should be, but are not typically, included in advanced undergraduate and beginning graduate mathematics curricula. This material is the introductory foundation upon which algorithm analysis, optimization, probability, statistics, differential equations, machine learning, and control theory are built. When used in concert with the free supplemental lab materials, this text teaches students both the theory and the computational practice of modern mathematical analysis. Foundations of Applied Mathematics, Volume 1: Mathematical Analysis includes several key topics not usually treated in courses at this level, such as uniform contraction mappings, the continuous linear extension theorem, Daniell?Lebesgue integration, resolvents, spectral resolution theory, and pseudospectra. Ideas are developed in a mathematically rigorous way and students are provided with powerful tools and beautiful ideas that yield a number of nice proofs, all of which contribute to a deep understanding of advanced analysis and linear algebra. Carefully thought out exercises and examples are built on each other to reinforce and retain concepts and ideas and to achieve greater depth. Associated lab materials are available that expose students to applications and numerical computation and reinforce the theoretical ideas taught in the text. The text and labs combine to make students technically proficient and to answer the age-old question, "When am I going to use this?

Author : J. Strother Moore
Publisher : Academic Press
Page : 291 pages
File Size : 53,9 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9780080924885

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Introduction to Abstract Algebra by J. Strother Moore Pdf

Introduction to Abstract Algebra provides insight into the methods of abstract algebra. This book provides information pertinent to the fundamental concepts of abstract algebra. Organized into five chapters, this book begins with an overview of the study of natural numbers that are used historically for the purpose of counting the objects in different assemblages. This text then examines the concepts of set and elements of a set. Other chapters contain an intuitive survey of the different kinds of real numbers, with the inclusion of many very important results on integers. This book presents as well a brief survey of algebraic systems from the trivial sets to the more highly structures groups, with emphasis on the elementary properties of groups. The final chapter deals with the simple development of complex numbers. This book is intended to be suitable for students in abstract algebra.

Author : Shahriar Shahriar
Publisher : American Mathematical Soc.
Page : 675 pages
File Size : 51,7 Mb
Release : 2017-08-16
Category : Algebra
ISBN : 9781470428495

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Algebra in Action: A Course in Groups, Rings, and Fields by Shahriar Shahriar Pdf

This text—based on the author's popular courses at Pomona College—provides a readable, student-friendly, and somewhat sophisticated introduction to abstract algebra. It is aimed at sophomore or junior undergraduates who are seeing the material for the first time. In addition to the usual definitions and theorems, there is ample discussion to help students build intuition and learn how to think about the abstract concepts. The book has over 1300 exercises and mini-projects of varying degrees of difficulty, and, to facilitate active learning and self-study, hints and short answers for many of the problems are provided. There are full solutions to over 100 problems in order to augment the text and to model the writing of solutions. Lattice diagrams are used throughout to visually demonstrate results and proof techniques. The book covers groups, rings, and fields. In group theory, group actions are the unifying theme and are introduced early. Ring theory is motivated by what is needed for solving Diophantine equations, and, in field theory, Galois theory and the solvability of polynomials take center stage. In each area, the text goes deep enough to demonstrate the power of abstract thinking and to convince the reader that the subject is full of unexpected results.

Author : Craig Huneke,Irena Swanson
Publisher : Cambridge University Press
Page : 446 pages
File Size : 44,5 Mb
Release : 2006-10-12
Category : Mathematics
ISBN : 9780521688604

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Integral Closure of Ideals, Rings, and Modules by Craig Huneke,Irena Swanson Pdf

Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.

Author : David William Sharpe
Publisher : CUP Archive
Page : 132 pages
File Size : 46,8 Mb
Release : 1987-08-28
Category : Mathematics
ISBN : 0521337186

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Rings and Factorization by David William Sharpe Pdf

This textbook is an introduction to the concept of factorization and its application to problems in algebra and number theory. With the minimum of prerequisites, the reader is introduced to the notion of rings, fields, prime elements and unique factorization. The author shows how concepts can be applied to a variety of examples such as factorizing polynomials, finding determinants of matrices and Fermat's 'two-squares theorem'. Based on an undergraduate course given at the University of Sheffield, Dr Sharpe has included numerous examples which demonstrate how frequently these ideas are useful in concrete, rather than abstract, settings. The book also contains many exercises of varying degrees of difficulty together with hints and solutions. Second and third year undergraduates will find this a readable and enjoyable account of a subject lying at the heart of much of mathematics.

Author : John J. Watkins
Publisher : Princeton University Press
Page : 228 pages
File Size : 50,5 Mb
Release : 2009-02-09
Category : Mathematics
ISBN : 9781400828173

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Topics in Commutative Ring Theory by John J. Watkins Pdf

Topics in Commutative Ring Theory is a textbook for advanced undergraduate students as well as graduate students and mathematicians seeking an accessible introduction to this fascinating area of abstract algebra. Commutative ring theory arose more than a century ago to address questions in geometry and number theory. A commutative ring is a set-such as the integers, complex numbers, or polynomials with real coefficients--with two operations, addition and multiplication. Starting from this simple definition, John Watkins guides readers from basic concepts to Noetherian rings-one of the most important classes of commutative rings--and beyond to the frontiers of current research in the field. Each chapter includes problems that encourage active reading--routine exercises as well as problems that build technical skills and reinforce new concepts. The final chapter is devoted to new computational techniques now available through computers. Careful to avoid intimidating theorems and proofs whenever possible, Watkins emphasizes the historical roots of the subject, like the role of commutative rings in Fermat's last theorem. He leads readers into unexpected territory with discussions on rings of continuous functions and the set-theoretic foundations of mathematics. Written by an award-winning teacher, this is the first introductory textbook to require no prior knowledge of ring theory to get started. Refreshingly informal without ever sacrificing mathematical rigor, Topics in Commutative Ring Theory is an ideal resource for anyone seeking entry into this stimulating field of study.

Author : I.B.S. Passi
Publisher : Springer
Page : 144 pages
File Size : 51,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540352976

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Group Rings and Their Augmentation Ideals by I.B.S. Passi Pdf