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Introduction To Abstract Algebra

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Introduction to Abstract Algebra

Introduction to Abstract Algebra [Pdf/ePub] eBook Author: Jonathan D. H. Smith
Editor: CRC Press
ISBN-10: 1498731627
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Introduction to Abstract Algebra by Jonathan D. H. Smith Book Summary:

Introduction to Abstract Algebra, Second Edition presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It avoids the usual groups first/rings first dilemma by introducing semigroups and monoids, the multiplicative structures of rings, along with groups. This new edition of a widely adopted textbook covers applications from biology, science, and engineering. It offers numerous updates based on feedback from first edition adopters, as well as improved and simplified proofs of a number of important theorems. Many new exercises have been added, while new study projects examine skewfields, quaternions, and octonions. The first three chapters of the book show how functional composition, cycle notation for permutations, and matrix notation for linear functions provide techniques for practical computation. These three chapters provide a quick introduction to algebra, sufficient to exhibit irrational numbers or to gain a taste of cryptography. Chapters four through seven cover abstract groups and monoids, orthogonal groups, stochastic matrices, Lagrange’s theorem, groups of units of monoids, homomorphisms, rings, and integral domains. The first seven chapters provide basic coverage of abstract algebra, suitable for a one-semester or two-quarter course. Each chapter includes exercises of varying levels of difficulty, chapter notes that point out variations in notation and approach, and study projects that cover an array of applications and developments of the theory. The final chapters deal with slightly more advanced topics, suitable for a second-semester or third-quarter course. These chapters delve deeper into the theory of rings, fields, and groups. They discuss modules, including vector spaces and abelian groups, group theory, and quasigroups. This textbook is suitable for use in an undergraduate course on abstract algebra for mathematics, computer science, and education majors, along with students from other STEM fields.

Download or read Introduction to Abstract Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).


Introduction to Abstract Algebra

Introduction to Abstract Algebra [Pdf/ePub] eBook Author: Benjamin Fine,Anthony M. Gaglione,Gerhard Rosenberger
Editor: JHU Press
ISBN-10: 1421411776
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Introduction to Abstract Algebra by Benjamin Fine,Anthony M. Gaglione,Gerhard Rosenberger Book Summary:

This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach. Topics covered include:; Rings; Integral domains; The fundamental theorem of arithmetic; Fields; Groups; Lagrange's theorem; Isomorphism theorems for groups; Fundamental theorem of finite abelian groups; The simplicity of An for n5; Sylow theorems; The Jordan-Hölder theorem; Ring isomorphism theorems; Euclidean domains; Principal ideal domains; The fundamental theorem of algebra; Vector spaces; Algebras; Field extensions: algebraic and transcendental; The fundamental theorem of Galois theory; The insolvability of the quintic

Download or read Introduction to Abstract Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach. Topics covered include:; Rings; Integral domains; The fundamental theorem of arithmetic; Fields; Groups; Lagrange's theorem; Isomorphism theorems for groups; Fundamental theorem of finite abelian groups; The simplicity of An for n5; Sylow theorems; The Jordan-Hölder theorem; Ring isomorphism theorems; Euclidean domains; Principal ideal domains; The fundamental theorem of algebra; Vector spaces; Algebras; Field extensions: algebraic and transcendental; The fundamental theorem of Galois theory; The insolvability of the quintic


Introduction to Abstract Algebra

Introduction to Abstract Algebra [Pdf/ePub] eBook Author: J. Strother Moore
Editor: Academic Press
ISBN-10: 0080924883
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Introduction to Abstract Algebra by J. Strother Moore Book Summary:

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.

Download or read Introduction to Abstract Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). 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.


Introduction to Abstract Algebra

Introduction to Abstract Algebra [Pdf/ePub] eBook Author: W. Keith Nicholson
Editor: John Wiley & Sons
ISBN-10: 1118311736
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Introduction to Abstract Algebra by W. Keith Nicholson Book Summary:

Praise for the Third Edition ". . . an expository masterpiece of the highest didacticvalue that has gained additional attractivity through the variousimprovements . . ."—Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebracontinues to provide an accessible approach to the basic structuresof abstract algebra: groups, rings, and fields. The book's uniquepresentation helps readers advance to abstract theory by presentingconcrete examples of induction, number theory, integers modulo n,and permutations before the abstract structures are defined.Readers can immediately begin to perform computations usingabstract concepts that are developed in greater detail later in thetext. The Fourth Edition features important concepts as well asspecialized topics, including: The treatment of nilpotent groups, including the Frattini andFitting subgroups Symmetric polynomials The proof of the fundamental theorem of algebra using symmetricpolynomials The proof of Wedderburn's theorem on finite division rings The proof of the Wedderburn-Artin theorem Throughout the book, worked examples and real-world problemsillustrate concepts and their applications, facilitating a completeunderstanding for readers regardless of their background inmathematics. A wealth of computational and theoretical exercises,ranging from basic to complex, allows readers to test theircomprehension of the material. In addition, detailed historicalnotes and biographies of mathematicians provide context for andilluminate the discussion of key topics. A solutions manual is alsoavailable for readers who would like access to partial solutions tothe book's exercises. Introduction to Abstract Algebra, Fourth Edition is anexcellent book for courses on the topic at the upper-undergraduateand beginning-graduate levels. The book also serves as a valuablereference and self-study tool for practitioners in the fields ofengineering, computer science, and applied mathematics.

Download or read Introduction to Abstract Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). Praise for the Third Edition ". . . an expository masterpiece of the highest didacticvalue that has gained additional attractivity through the variousimprovements . . ."—Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebracontinues to provide an accessible approach to the basic structuresof abstract algebra: groups, rings, and fields. The book's uniquepresentation helps readers advance to abstract theory by presentingconcrete examples of induction, number theory, integers modulo n,and permutations before the abstract structures are defined.Readers can immediately begin to perform computations usingabstract concepts that are developed in greater detail later in thetext. The Fourth Edition features important concepts as well asspecialized topics, including: The treatment of nilpotent groups, including the Frattini andFitting subgroups Symmetric polynomials The proof of the fundamental theorem of algebra using symmetricpolynomials The proof of Wedderburn's theorem on finite division rings The proof of the Wedderburn-Artin theorem Throughout the book, worked examples and real-world problemsillustrate concepts and their applications, facilitating a completeunderstanding for readers regardless of their background inmathematics. A wealth of computational and theoretical exercises,ranging from basic to complex, allows readers to test theircomprehension of the material. In addition, detailed historicalnotes and biographies of mathematicians provide context for andilluminate the discussion of key topics. A solutions manual is alsoavailable for readers who would like access to partial solutions tothe book's exercises. Introduction to Abstract Algebra, Fourth Edition is anexcellent book for courses on the topic at the upper-undergraduateand beginning-graduate levels. The book also serves as a valuablereference and self-study tool for practitioners in the fields ofengineering, computer science, and applied mathematics.


Introduction to Abstract Algebra

Introduction to Abstract Algebra [Pdf/ePub] eBook Author: Jonathan D. H. Smith
Editor: CRC Press
ISBN-10: 9781420063721
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Introduction to Abstract Algebra by Jonathan D. H. Smith Book Summary:

Taking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps students fully understand groups, rings, semigroups, and monoids by rigorously building concepts from first principles. A Quick Introduction to Algebra The first three chapters of the book show how functional composition, cycle notation for permutations, and matrix notation for linear functions provide techniques for practical computation. The author also uses equivalence relations to introduce rational numbers and modular arithmetic as well as to present the first isomorphism theorem at the set level. The Basics of Abstract Algebra for a First-Semester Course Subsequent chapters cover orthogonal groups, stochastic matrices, Lagrange’s theorem, and groups of units of monoids. The text also deals with homomorphisms, which lead to Cayley’s theorem of reducing abstract groups to concrete groups of permutations. It then explores rings, integral domains, and fields. Advanced Topics for a Second-Semester Course The final, mostly self-contained chapters delve deeper into the theory of rings, fields, and groups. They discuss modules (such as vector spaces and abelian groups), group theory, and quasigroups.

Download or read Introduction to Abstract Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). Taking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps students fully understand groups, rings, semigroups, and monoids by rigorously building concepts from first principles. A Quick Introduction to Algebra The first three chapters of the book show how functional composition, cycle notation for permutations, and matrix notation for linear functions provide techniques for practical computation. The author also uses equivalence relations to introduce rational numbers and modular arithmetic as well as to present the first isomorphism theorem at the set level. The Basics of Abstract Algebra for a First-Semester Course Subsequent chapters cover orthogonal groups, stochastic matrices, Lagrange’s theorem, and groups of units of monoids. The text also deals with homomorphisms, which lead to Cayley’s theorem of reducing abstract groups to concrete groups of permutations. It then explores rings, integral domains, and fields. Advanced Topics for a Second-Semester Course The final, mostly self-contained chapters delve deeper into the theory of rings, fields, and groups. They discuss modules (such as vector spaces and abelian groups), group theory, and quasigroups.


Introduction to Abstract Algebra, Third Edition

Introduction to Abstract Algebra, Third Edition [Pdf/ePub] eBook Author: T.A. Whitelaw
Editor: Routledge
ISBN-10: 1351437305
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Introduction to Abstract Algebra, Third Edition by T.A. Whitelaw Book Summary:

The first and second editions of this successful textbook have been highly praised for their lucid and detailed coverage of abstract algebra. In this third edition, the author has carefully revised and extended his treatment, particularly the material on rings and fields, to provide an even more satisfying first course in abstract algebra.

Download or read Introduction to Abstract Algebra, Third Edition book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). The first and second editions of this successful textbook have been highly praised for their lucid and detailed coverage of abstract algebra. In this third edition, the author has carefully revised and extended his treatment, particularly the material on rings and fields, to provide an even more satisfying first course in abstract algebra.


Linear Algebra

Linear Algebra [Pdf/ePub] eBook Author: Robert J. Valenza
Editor: Springer Science & Business Media
ISBN-10: 1461209013
Size: 1957 kb
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Linear Algebra by Robert J. Valenza Book Summary:

Based on lectures given at Claremont McKenna College, this text constitutes a substantial, abstract introduction to linear algebra. The presentation emphasizes the structural elements over the computational - for example by connecting matrices to linear transformations from the outset - and prepares the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems.

Download or read Linear Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). Based on lectures given at Claremont McKenna College, this text constitutes a substantial, abstract introduction to linear algebra. The presentation emphasizes the structural elements over the computational - for example by connecting matrices to linear transformations from the outset - and prepares the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems.


An Introduction to Linear Algebra

An Introduction to Linear Algebra [Pdf/ePub] eBook Author: Ravi P. Agarwal,Elena Cristina Flaut
Editor: CRC Press
ISBN-10: 1351804308
Size: 308 kb
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An Introduction to Linear Algebra by Ravi P. Agarwal,Elena Cristina Flaut Book Summary:

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.

Download or read An Introduction to Linear Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). 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.


A Concrete Approach to Abstract Algebra

A Concrete Approach to Abstract Algebra [Pdf/ePub] eBook Author: Jeffrey Bergen
Editor: Academic Press
ISBN-10: 9780080958620
Size: 1871 kb
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A Concrete Approach to Abstract Algebra by Jeffrey Bergen Book Summary:

A Concrete Approach to Abstract Algebra presents a solid and highly accessible introduction to abstract algebra by providing details on the building blocks of abstract algebra. It begins with a concrete and thorough examination of familiar objects such as integers, rational numbers, real numbers, complex numbers, complex conjugation, and polynomials. The author then builds upon these familiar objects and uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices. The final four chapters present the more theoretical material needed for graduate study. This text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics which arise in courses in algebra, geometry, trigonometry, precalculus, and calculus. Presents a more natural 'rings first' approach to effectively leading the student into the the abstract material of the course by the use of motivating concepts from previous math courses to guide the discussion of abstract algebra Bridges the gap for students by showing how most of the concepts within an abstract algebra course are actually tools used to solve difficult, but well-known problems Builds on relatively familiar material (Integers, polynomials) and moves onto more abstract topics, while providing a historical approach of introducing groups first as automorphisms Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices

Download or read A Concrete Approach to Abstract Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). A Concrete Approach to Abstract Algebra presents a solid and highly accessible introduction to abstract algebra by providing details on the building blocks of abstract algebra. It begins with a concrete and thorough examination of familiar objects such as integers, rational numbers, real numbers, complex numbers, complex conjugation, and polynomials. The author then builds upon these familiar objects and uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices. The final four chapters present the more theoretical material needed for graduate study. This text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics which arise in courses in algebra, geometry, trigonometry, precalculus, and calculus. Presents a more natural 'rings first' approach to effectively leading the student into the the abstract material of the course by the use of motivating concepts from previous math courses to guide the discussion of abstract algebra Bridges the gap for students by showing how most of the concepts within an abstract algebra course are actually tools used to solve difficult, but well-known problems Builds on relatively familiar material (Integers, polynomials) and moves onto more abstract topics, while providing a historical approach of introducing groups first as automorphisms Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices


Abstract Algebra

Abstract Algebra [Pdf/ePub] eBook Author: Gregory T. Lee
Editor: Springer
ISBN-10: 3319776495
Size: 790 kb
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Abstract Algebra by Gregory T. Lee Book Summary:

This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the Sylow theorems and the classification of finite abelian groups. An introduction to ring theory follows, leading to a discussion of fields and polynomials that includes sections on splitting fields and the construction of finite fields. The final part contains applications to public key cryptography as well as classical straightedge and compass constructions. Explaining key topics at a gentle pace, this book is aimed at undergraduate students. It assumes no prior knowledge of the subject and contains over 500 exercises, half of which have detailed solutions provided.

Download or read Abstract Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the Sylow theorems and the classification of finite abelian groups. An introduction to ring theory follows, leading to a discussion of fields and polynomials that includes sections on splitting fields and the construction of finite fields. The final part contains applications to public key cryptography as well as classical straightedge and compass constructions. Explaining key topics at a gentle pace, this book is aimed at undergraduate students. It assumes no prior knowledge of the subject and contains over 500 exercises, half of which have detailed solutions provided.


Abstract Algebra

Abstract Algebra [Pdf/ePub] eBook Author: Clive Reis
Editor: World Scientific Publishing Company
ISBN-10: 9813100710
Size: 741 kb
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Abstract Algebra by Clive Reis Book Summary:

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.

Download or read Abstract Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). 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.


An Introduction to Linear Algebra

An Introduction to Linear Algebra [Pdf/ePub] eBook Author: L. Mirsky
Editor: Courier Corporation
ISBN-10: 0486166449
Size: 1566 kb
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An Introduction to Linear Algebra by L. Mirsky Book Summary:

Rigorous, self-contained coverage of determinants, vectors, matrices and linear equations, quadratic forms, more. Elementary, easily readable account with numerous examples and problems at the end of each chapter.

Download or read An Introduction to Linear Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). Rigorous, self-contained coverage of determinants, vectors, matrices and linear equations, quadratic forms, more. Elementary, easily readable account with numerous examples and problems at the end of each chapter.


Abstract Algebra

Abstract Algebra [Pdf/ePub] eBook Author: Stephen Lovett
Editor: CRC Press
ISBN-10: 1482248913
Size: 1258 kb
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Abstract Algebra by Stephen Lovett Book Summary:

A Discovery-Based Approach to Learning about Algebraic Structures Abstract Algebra: Structures and Applications helps students understand the abstraction of modern algebra. It emphasizes the more general concept of an algebraic structure while simultaneously covering applications. The text can be used in a variety of courses, from a one-semester introductory course to a full two-semester sequence. The book presents the core topics of structures in a consistent order: Definition of structure Motivation Examples General properties Important objects Description Subobjects Morphisms Subclasses Quotient objects Action structures Applications The text uses the general concept of an algebraic structure as a unifying principle and introduces other algebraic structures besides the three standard ones (groups, rings, and fields). Examples, exercises, investigative projects, and entire sections illustrate how abstract algebra is applied to areas of science and other branches of mathematics. "Lovett (Wheaton College) takes readers through the variegated landscape of algebra, from elementary modular arithmetic through groups, semigroups, and monoids, past rings and fields and group actions, beyond modules and algebras, to Galois theory, multivariable polynomial rings, and Gröbner bases." Choice Reviewed: Recommended

Download or read Abstract Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). A Discovery-Based Approach to Learning about Algebraic Structures Abstract Algebra: Structures and Applications helps students understand the abstraction of modern algebra. It emphasizes the more general concept of an algebraic structure while simultaneously covering applications. The text can be used in a variety of courses, from a one-semester introductory course to a full two-semester sequence. The book presents the core topics of structures in a consistent order: Definition of structure Motivation Examples General properties Important objects Description Subobjects Morphisms Subclasses Quotient objects Action structures Applications The text uses the general concept of an algebraic structure as a unifying principle and introduces other algebraic structures besides the three standard ones (groups, rings, and fields). Examples, exercises, investigative projects, and entire sections illustrate how abstract algebra is applied to areas of science and other branches of mathematics. "Lovett (Wheaton College) takes readers through the variegated landscape of algebra, from elementary modular arithmetic through groups, semigroups, and monoids, past rings and fields and group actions, beyond modules and algebras, to Galois theory, multivariable polynomial rings, and Gröbner bases." Choice Reviewed: Recommended


A History of Abstract Algebra

A History of Abstract Algebra [Pdf/ePub] eBook Author: Israel Kleiner
Editor: Springer Science & Business Media
ISBN-10: 081764685X
Size: 1783 kb
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A History of Abstract Algebra by Israel Kleiner Book Summary:

This book does nothing less than provide an account of the intellectual lineage of abstract algebra. The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared insoluble by classical means. A major theme of the book is to show how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved. Mathematics instructors, algebraists, and historians of science will find the work a valuable reference.

Download or read A History of Abstract Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). This book does nothing less than provide an account of the intellectual lineage of abstract algebra. The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared insoluble by classical means. A major theme of the book is to show how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved. Mathematics instructors, algebraists, and historians of science will find the work a valuable reference.


Abstract Algebra

Abstract Algebra [Pdf/ePub] eBook Author: Gary L. Mullen,James A. Sellers
Editor: CRC Press
ISBN-10: 1482250071
Size: 1258 kb
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Abstract Algebra by Gary L. Mullen,James A. Sellers Book Summary:

Abstract Algebra: A Gentle Introduction advantages a trend in mathematics textbook publishing towards smaller, less expensive and brief introductions to primary courses. The authors move away from the ‘everything for everyone’ approach so common in textbooks. Instead, they provide the reader with coverage of numerous algebraic topics to cover the most important areas of abstract algebra. Through a careful selection of topics, supported by interesting applications, the authors Intend the book to be used for a one-semester course in abstract algebra. It is suitable for an introductory course in for mathematics majors. The text is also very suitable for education majors who need to have an introduction to the topic. As textbooks go through various editions and authors employ the suggestions of numerous well-intentioned reviewers, these book become larger and larger and subsequently more expensive. This book is meant to counter that process. Here students are given a "gentle introduction," meant to provide enough for a course, yet also enough to encourage them toward future study of the topic. Features Groups before rings approach Interesting modern applications Appendix includes mathematical induction, the well-ordering principle, sets, functions, permutations, matrices, and complex nubers. Numerous exercises at the end of each section Chapter "Hint and Partial Solutions" offers built in solutions manual

Download or read Abstract Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). Abstract Algebra: A Gentle Introduction advantages a trend in mathematics textbook publishing towards smaller, less expensive and brief introductions to primary courses. The authors move away from the ‘everything for everyone’ approach so common in textbooks. Instead, they provide the reader with coverage of numerous algebraic topics to cover the most important areas of abstract algebra. Through a careful selection of topics, supported by interesting applications, the authors Intend the book to be used for a one-semester course in abstract algebra. It is suitable for an introductory course in for mathematics majors. The text is also very suitable for education majors who need to have an introduction to the topic. As textbooks go through various editions and authors employ the suggestions of numerous well-intentioned reviewers, these book become larger and larger and subsequently more expensive. This book is meant to counter that process. Here students are given a "gentle introduction," meant to provide enough for a course, yet also enough to encourage them toward future study of the topic. Features Groups before rings approach Interesting modern applications Appendix includes mathematical induction, the well-ordering principle, sets, functions, permutations, matrices, and complex nubers. Numerous exercises at the end of each section Chapter "Hint and Partial Solutions" offers built in solutions manual


Contemporary Abstract Algebra

Contemporary Abstract Algebra [Pdf/ePub] eBook Author: Joseph Gallian
Editor: Nelson Education
ISBN-10: 1305657969
Size: 833 kb
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Contemporary Abstract Algebra by Joseph Gallian Book Summary:

CONTEMPORARY ABSTRACT ALGEBRA, NINTH EDITION provides a solid introduction to the traditional topics in abstract algebra while conveying to students that it is a contemporary subject used daily by working mathematicians, computer scientists, physicists, and chemists. The text includes numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings giving the subject a current feel which makes the content interesting and relevant for students. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Download or read Contemporary Abstract Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). CONTEMPORARY ABSTRACT ALGEBRA, NINTH EDITION provides a solid introduction to the traditional topics in abstract algebra while conveying to students that it is a contemporary subject used daily by working mathematicians, computer scientists, physicists, and chemists. The text includes numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings giving the subject a current feel which makes the content interesting and relevant for students. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.


A Concrete Approach to Abstract Algebra

A Concrete Approach to Abstract Algebra [Pdf/ePub] eBook Author: W. W. Sawyer
Editor: Courier Dover Publications
ISBN-10: 0486833313
Size: 452 kb
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A Concrete Approach to Abstract Algebra by W. W. Sawyer Book Summary:

Brief, clear, and well written, this introductory treatment bridges the gap between traditional and modern algebra. Includes exercises with complete solutions. The only prerequisite is high school-level algebra. 1959 edition.

Download or read A Concrete Approach to Abstract Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). Brief, clear, and well written, this introductory treatment bridges the gap between traditional and modern algebra. Includes exercises with complete solutions. The only prerequisite is high school-level algebra. 1959 edition.


Solutions Manual to accompany Introduction to Abstract Algebra, 4e, Solutions Manual

Solutions Manual to accompany Introduction to Abstract Algebra, 4e, Solutions Manual [Pdf/ePub] eBook Author: W. Keith Nicholson
Editor: John Wiley & Sons
ISBN-10: 1118347897
Size: 1203 kb
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Solutions Manual to accompany Introduction to Abstract Algebra, 4e, Solutions Manual by W. Keith Nicholson Book Summary:

An indispensable companion to the book hailed an "expository masterpiece of the highest didactic value" by Zentralblatt MATH This solutions manual helps readers test and reinforce the understanding of the principles and real-world applications of abstract algebra gained from their reading of the critically acclaimed Introduction to Abstract Algebra. Ideal for students, as well as engineers, computer scientists, and applied mathematicians interested in the subject, it provides a wealth of concrete examples of induction, number theory, integers modulo n, and permutations. Worked examples and real-world problems help ensure a complete understanding of the subject, regardless of a reader's background in mathematics.

Download or read Solutions Manual to accompany Introduction to Abstract Algebra, 4e, Solutions Manual book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). An indispensable companion to the book hailed an "expository masterpiece of the highest didactic value" by Zentralblatt MATH This solutions manual helps readers test and reinforce the understanding of the principles and real-world applications of abstract algebra gained from their reading of the critically acclaimed Introduction to Abstract Algebra. Ideal for students, as well as engineers, computer scientists, and applied mathematicians interested in the subject, it provides a wealth of concrete examples of induction, number theory, integers modulo n, and permutations. Worked examples and real-world problems help ensure a complete understanding of the subject, regardless of a reader's background in mathematics.


Introduction To Non-linear Algebra

Introduction To Non-linear Algebra [Pdf/ePub] eBook Author: Morozov Alexei,Dolotin Valery
Editor: World Scientific Publishing Company
ISBN-10: 9813107006
Size: 1707 kb
Format File: Pdf
Read: 1707

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Introduction To Non-linear Algebra by Morozov Alexei,Dolotin Valery Book Summary:

This unique text presents the new domain of consistent non-linear counterparts for all basic objects and tools of linear algebra, and develops an adequate calculus for solving non-linear algebraic and differential equations. It reveals the non-linear algebraic activity as an essentially wider and diverse field with its own original methods, of which the linear one is a special restricted case.This volume contains a detailed and comprehensive description of basic objects and fundamental techniques arising from the theory of non-linear equations, which constitute the scope of what should be called non-linear algebra. The objects of non-linear algebra are presented in parallel with the corresponding linear ones, followed by an exposition of specific non-linear properties treated with the use of classical (such as the Koszul complex) and original new tools. This volume extensively uses a new diagram technique and is enriched with a variety of illustrations throughout the text. Thus, most of the material is new and is clearly exposed, starting from the elementary level. With the scope of its perspective applications spreading from general algebra to mathematical physics, it will interest a broad audience of physicists; mathematicians, as well as advanced undergraduate and graduate students.

Download or read Introduction To Non-linear Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). This unique text presents the new domain of consistent non-linear counterparts for all basic objects and tools of linear algebra, and develops an adequate calculus for solving non-linear algebraic and differential equations. It reveals the non-linear algebraic activity as an essentially wider and diverse field with its own original methods, of which the linear one is a special restricted case.This volume contains a detailed and comprehensive description of basic objects and fundamental techniques arising from the theory of non-linear equations, which constitute the scope of what should be called non-linear algebra. The objects of non-linear algebra are presented in parallel with the corresponding linear ones, followed by an exposition of specific non-linear properties treated with the use of classical (such as the Koszul complex) and original new tools. This volume extensively uses a new diagram technique and is enriched with a variety of illustrations throughout the text. Thus, most of the material is new and is clearly exposed, starting from the elementary level. With the scope of its perspective applications spreading from general algebra to mathematical physics, it will interest a broad audience of physicists; mathematicians, as well as advanced undergraduate and graduate students.