Introduction To Applied Algebraic Systems

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Introduction to Applied Algebraic Systems

Norman R Reilly
Introduction to Applied Algebraic Systems Book PDF

Author : Norman R Reilly
Publisher : Oxford University Press
Page : 524 pages
File Size : 53,9 Mb
Release : 2009-11-02
Category : Mathematics
ISBN : 9780199709922

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Introduction to Applied Algebraic Systems by Norman R Reilly Pdf

This upper-level undergraduate textbook provides a modern view of algebra with an eye to new applications that have arisen in recent years. A rigorous introduction to basic number theory, rings, fields, polynomial theory, groups, algebraic geometry and elliptic curves prepares students for exploring their practical applications related to storing, securing, retrieving and communicating information in the electronic world. It will serve as a textbook for an undergraduate course in algebra with a strong emphasis on applications. The book offers a brief introduction to elementary number theory as well as a fairly complete discussion of major algebraic systems (such as rings, fields, and groups) with a view of their use in bar coding, public key cryptosystems, error-correcting codes, counting techniques, and elliptic key cryptography. This is the only entry level text for algebraic systems that includes an extensive introduction to elliptic curves, a topic that has leaped to prominence due to its importance in the solution of Fermats Last Theorem and its incorporation into the rapidly expanding applications of elliptic curve cryptography in smart cards. Computer science students will appreciate the strong emphasis on the theory of polynomials, algebraic geometry and Groebner bases. The combination of a rigorous introduction to abstract algebra with a thorough coverage of its applications makes this book truly unique.

Introduction to Applied Linear Algebra

Stephen Boyd,Lieven Vandenberghe
Introduction to Applied Linear Algebra Book PDF

Author : Stephen Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 477 pages
File Size : 48,7 Mb
Release : 2018-06-07
Category : Business & Economics
ISBN : 9781316518960

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Introduction to Applied Linear Algebra by Stephen Boyd,Lieven Vandenberghe Pdf

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

An Introduction to Linear Algebra

Ravi P. Agarwal,Elena Cristina Flaut
An Introduction to Linear Algebra Book PDF

Author : Ravi P. Agarwal,Elena Cristina Flaut
Publisher : CRC Press
Page : 232 pages
File Size : 46,7 Mb
Release : 2017-08-07
Category : Mathematics
ISBN : 9781351804301

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An Introduction to Linear Algebra by Ravi P. Agarwal,Elena Cristina Flaut Pdf

The techniques of linear algebra are used extensively across the applied sciences, and in many different areas of algebra such as group theory, module theory, representation theory, ring theory, and Galois theory. Written by experienced researchers with a decades of teaching experience, Introduction to Linear Algebra is a clear and rigorous introductory text on this key topic for students of both applied sciences and pure mathematics.

Applied Linear Algebra

Peter J. Olver,Chehrzad Shakiban
Applied Linear Algebra Book PDF

Author : Peter J. Olver,Chehrzad Shakiban
Publisher : Springer
Page : 679 pages
File Size : 51,8 Mb
Release : 2018-05-30
Category : Mathematics
ISBN : 9783319910413

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Applied Linear Algebra by Peter J. Olver,Chehrzad Shakiban Pdf

This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics. Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the underlying linear algebraic techniques, thereby enabling students not only to learn how to apply the mathematical tools in routine contexts, but also to understand what is required to adapt to unusual or emerging problems. No previous knowledge of linear algebra is needed to approach this text, with single-variable calculus as the only formal prerequisite. However, the reader will need to draw upon some mathematical maturity to engage in the increasing abstraction inherent to the subject. Once equipped with the main tools and concepts from this book, students will be prepared for further study in differential equations, numerical analysis, data science and statistics, and a broad range of applications. The first author’s text, Introduction to Partial Differential Equations, is an ideal companion volume, forming a natural extension of the linear mathematical methods developed here.

Abstract Algebra

Clive Reis
Abstract Algebra Book PDF

Author : Clive Reis
Publisher : World Scientific Publishing Company
Page : 508 pages
File Size : 52,5 Mb
Release : 2011-05-05
Category : Mathematics
ISBN : 9789813100718

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Abstract Algebra by Clive Reis Pdf

This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya–Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems. Considerable emphasis is placed on the algebraic system consisting of congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced — via congruence classes — to the idea of cosets and factor groups. This enables the transition to cosets and factor objects in a more abstract setting to be relatively painless. The chapters dealing with applications help to reinforce the concepts and methods developed in the context of more down-to-earth problems. Most introductory texts in abstract algebra either avoid cosets, factor objects and homomorphisms completely or introduce them towards the end of the book. In this book, these topics are dealt with early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible, even if there are alternative methods of proof.

Introduction to Algebraic Geometry

Serge Lang
Introduction to Algebraic Geometry Book PDF

Author : Serge Lang
Publisher : Courier Dover Publications
Page : 273 pages
File Size : 42,6 Mb
Release : 2019-03-20
Category : Mathematics
ISBN : 9780486839806

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Introduction to Algebraic Geometry by Serge Lang Pdf

Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.

Methods of Algebraic Geometry in Control Theory: Part I

Peter Falb
Methods of Algebraic Geometry in Control Theory Part I Book PDF

Author : Peter Falb
Publisher : Springer
Page : 202 pages
File Size : 53,9 Mb
Release : 2018-08-25
Category : Mathematics
ISBN : 9783319980263

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Methods of Algebraic Geometry in Control Theory: Part I by Peter Falb Pdf

"An introduction to the ideas of algebraic geometry in the motivated context of system theory." Thus the author describes his textbook that has been specifically written to serve the needs of students of systems and control. Without sacrificing mathematical care, the author makes the basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis is on constructive methods and clarity rather than abstraction. The student will find here a clear presentation with an applied flavor, of the core ideas in the algebra-geometric treatment of scalar linear system theory. The author introduces the four representations of a scalar linear system and establishes the major results of a similar theory for multivariable systems appearing in a succeeding volume (Part II: Multivariable Linear Systems and Projective Algebraic Geometry). Prerequisites are the basics of linear algebra, some simple notions from topology and the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises are an integral part of the treatment and are used where relevant in the main body of the text. The present, softcover reprint is designed to make this classic textbook available to a wider audience. "This book is a concise development of affine algebraic geometry together with very explicit links to the applications...[and] should address a wide community of readers, among pure and applied mathematicians." —Monatshefte für Mathematik

Introduction to Algebraic System Theory

Sain
Introduction to Algebraic System Theory Book PDF

Author : Sain
Publisher : Academic Press
Page : 346 pages
File Size : 43,8 Mb
Release : 1981-07-23
Category : Computers
ISBN : 9780080956596

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Introduction to Algebraic System Theory by Sain Pdf

Introduction to Algebraic System Theory

Applied Discrete Structures - Part 2- Algebraic Structures

Ken Levasseur,Al Doerr
Applied Discrete Structures Part 2 Algebraic Structures Book PDF

Author : Ken Levasseur,Al Doerr
Publisher : Lulu.com
Page : 254 pages
File Size : 42,6 Mb
Release : 2017-05-15
Category : Electronic
ISBN : 9781105618987

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Applied Discrete Structures - Part 2- Algebraic Structures by Ken Levasseur,Al Doerr Pdf

Applied Discrete Structures, Part II - Algebraic Structures, is an introduction to groups, monoids, vector spaces, lattices, boolean algebras, rings and fields. It corresponds with the content of Discrete Structures II at UMass Lowell, which is a required course for students in Computer Science. It presumes background contained in Part I - Fundamentals. Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http: //www.aimath.org/textbooks/. This version was created using Mathbook XML (https: //mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at UMass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at UMass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.

Vectors, Pure and Applied

T. W. Körner
Vectors Pure and Applied Book PDF

Author : T. W. Körner
Publisher : Cambridge University Press
Page : 457 pages
File Size : 54,6 Mb
Release : 2013
Category : Mathematics
ISBN : 9781107033566

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Vectors, Pure and Applied by T. W. Körner Pdf

Explains both the how and the why of linear algebra to get students thinking like mathematicians.

Abstract Algebra

Clive Reis,Stuart A Rankin
Abstract Algebra Book PDF

Author : Clive Reis,Stuart A Rankin
Publisher : World Scientific Publishing Company
Page : 576 pages
File Size : 54,8 Mb
Release : 2016-08-30
Category : Mathematics
ISBN : 9789814730563

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Abstract Algebra by Clive Reis,Stuart A Rankin Pdf

This second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata. This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya–Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems. Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced — via congruence classes — to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless. In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.

Introduction to Higher Algebra

A. Mostowski,M. Stark
Introduction to Higher Algebra Book PDF

Author : A. Mostowski,M. Stark
Publisher : Elsevier
Page : 475 pages
File Size : 49,9 Mb
Release : 2014-07-18
Category : Mathematics
ISBN : 9781483280356

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Introduction to Higher Algebra by A. Mostowski,M. Stark Pdf

Introduction to Higher Algebra is an 11-chapter text that covers some mathematical investigations concerning higher algebra. After an introduction to sets of functions, mathematical induction, and arbitrary numbers, this book goes on considering some combinatorial problems, complex numbers, determinants, vector spaces, and linear equations. These topics are followed by discussions of the determination of polynomials in ne variable, rings of real and complex polynomials, and algebraic and transcendental numbers. The final chapters deal with the polynomials in several variables, symmetric functions, the theory of elimination, and the quadratic and Hermitian forms. This book will be of value to mathematicians and students.

Numerical Linear Algebra

William Layton,Myron Mike Sussman
Numerical Linear Algebra Book PDF

Author : William Layton,Myron Mike Sussman
Publisher : World Scientific
Page : 274 pages
File Size : 54,6 Mb
Release : 2020-07-14
Category : Mathematics
ISBN : 9789811223914

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Numerical Linear Algebra by William Layton,Myron Mike Sussman Pdf

'The numerical algorithms presented are written in pseudocode and based on MATLAB, a programming and numeric computing platform widely used in STEM fields. Thus, no formal training in computer science or knowledge of any specific programming language is needed to parse the algorithms. Summing up: Recommended.'CHOICEMany students come to numerical linear algebra from science and engineering seeking modern tools and an understanding of how the tools work and their limitations. Often their backgrounds and experience are extensive in applications of numerical methods but limited in abstract mathematics and matrix theory. Often enough it is limited to multivariable calculus, basic differential equations and methods of applied mathematics. This book introduces modern tools of numerical linear algebra based on this background, heavy in applied analysis but light in matrix canonical forms and their algebraic properties. Each topic is presented as algorithmic ideas and through a foundation based on mostly applied analysis. By picking a path through the book appropriate for the level, it has been used for both senior level undergraduates and beginning graduate classes with students from diverse fields and backgrounds.

Computer Algebra in Applied Mathematics

Richard H. Rand
Computer Algebra in Applied Mathematics Book PDF

Author : Richard H. Rand
Publisher : Pitman Advanced Publishing Program
Page : 208 pages
File Size : 50,9 Mb
Release : 1984
Category : Mathematics
ISBN : UOM:39015014349701

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Computer Algebra in Applied Mathematics by Richard H. Rand Pdf

The book has the dual goal of showing how computer algebra can play an important role in applied mathematics, while introducing the reader to the computer system MACSYMA, which is designed to support such computations. In order to provide realistic applications of computer algebra, the level of the mathematical treatment must be substantially beyond a first course in calculus. Thus this book is aimed at a reader who has had at least three years of college level calculus and differential equations. Currently, computer algebra is a rarely used research tool, but the author believes it is destined for a major roll in engineering and applied mathematics. It will not be long before computer algebra is as common to an engineering student as the now obsolete slide rule once was.

Number Systems

Sergei Ovchinnikov
Number Systems Book PDF

Author : Sergei Ovchinnikov
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 54,7 Mb
Release : 2015-02-26
Category : Mathematics
ISBN : 9781470420185

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Number Systems by Sergei Ovchinnikov Pdf

This book offers a rigorous and coherent introduction to the five basic number systems of mathematics, namely natural numbers, integers, rational numbers, real numbers, and complex numbers. It is a subject that many mathematicians believe should be learned by any student of mathematics including future teachers. The book starts with the development of Peano arithmetic in the first chapter which includes mathematical induction and elements of recursion theory. It proceeds to an examination of integers that also covers rings and ordered integral domains. The presentation of rational numbers includes material on ordered fields and convergence of sequences in these fields. Cauchy and Dedekind completeness properties of the field of real numbers are established, together with some properties of real continuous functions. An elementary proof of the Fundamental Theorem of Algebra is the highest point of the chapter on complex numbers. The great merit of the book lies in its extensive list of exercises following each chapter. These exercises are designed to assist the instructor and to enhance the learning experience of the students.