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Basic Algebra Groups Rings And Fields

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Basic Algebra

Basic Algebra [Pdf/ePub] eBook Author: P.M. Cohn
Editor: Springer Science & Business Media
ISBN-10: 0857294288
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Basic Algebra by P.M. Cohn Book Summary:

This is the first volume of a revised edition of P.M. Cohn's classic three-volume text Algebra, widely regarded as one of the most outstanding introductory algebra textbooks. This volume covers the important results of algebra. Readers should have some knowledge of linear algebra, groups and fields, although all the essential facts and definitions are recalled.

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Algebra 1

Algebra 1 [Pdf/ePub] eBook Author: Ramji Lal
Editor: Springer
ISBN-10: 9811042535
Size: 545 kb
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Algebra 1 by Ramji Lal Book Summary:

This is the first in a series of three volumes dealing with important topics in algebra. It offers an introduction to the foundations of mathematics together with the fundamental algebraic structures, namely groups, rings, fields, and arithmetic. Intended as a text for undergraduate and graduate students of mathematics, it discusses all major topics in algebra with numerous motivating illustrations and exercises to enable readers to acquire a good understanding of the basic algebraic structures, which they can then use to find the exact or the most realistic solutions to their problems.

Download or read Algebra 1 book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). This is the first in a series of three volumes dealing with important topics in algebra. It offers an introduction to the foundations of mathematics together with the fundamental algebraic structures, namely groups, rings, fields, and arithmetic. Intended as a text for undergraduate and graduate students of mathematics, it discusses all major topics in algebra with numerous motivating illustrations and exercises to enable readers to acquire a good understanding of the basic algebraic structures, which they can then use to find the exact or the most realistic solutions to their problems.


Groups, Rings and Fields

Groups, Rings and Fields [Pdf/ePub] eBook Author: David A.R. Wallace
Editor: Springer Science & Business Media
ISBN-10: 1447104250
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Groups, Rings and Fields by David A.R. Wallace Book Summary:

This is a basic introduction to modern algebra, providing a solid understanding of the axiomatic treatment of groups and then rings, aiming to promote a feeling for the evolutionary and historical development of the subject. It includes problems and fully worked solutions, enabling readers to master the subject rather than simply observing it.

Download or read Groups, Rings and Fields book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). This is a basic introduction to modern algebra, providing a solid understanding of the axiomatic treatment of groups and then rings, aiming to promote a feeling for the evolutionary and historical development of the subject. It includes problems and fully worked solutions, enabling readers to master the subject rather than simply observing it.


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.


Further Algebra and Applications

Further Algebra and Applications [Pdf/ePub] eBook Author: Paul M. Cohn
Editor: Springer Science & Business Media
ISBN-10: 1447100395
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Further Algebra and Applications by Paul M. Cohn Book Summary:

Here is the second volume of a revised edition of P.M. Cohn's classic three-volume text Algebra, widely regarded as one of the most outstanding introductory algebra textbooks. Volume Two focuses on applications. The text is supported by worked examples, with full proofs, there are numerous exercises with occasional hints, and some historical remarks.

Download or read Further Algebra and Applications book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). Here is the second volume of a revised edition of P.M. Cohn's classic three-volume text Algebra, widely regarded as one of the most outstanding introductory algebra textbooks. Volume Two focuses on applications. The text is supported by worked examples, with full proofs, there are numerous exercises with occasional hints, and some historical remarks.


Basic Algebra

Basic Algebra [Pdf/ePub] eBook Author: Anthony W. Knapp
Editor: Springer Science & Business Media
ISBN-10: 0817645292
Size: 602 kb
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Basic Algebra by Anthony W. Knapp Book Summary:

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.

Download or read Basic Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.


Algebraic Structures

Algebraic Structures [Pdf/ePub] eBook Author: George R. Kempf
Editor: Springer Science & Business Media
ISBN-10: 3322802787
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Algebraic Structures by George R. Kempf Book Summary:

In algebra there are four basic structures: groups, rings, fields and modules. In this book the theory of these basic structures is presented and the laws of composition - the basic operations of algebra - are studied. Essentially, no previous knowledge is required, it is only assumed as background that the reader has learned some linear algebra over the real numbers.Dieses Lehrbuch, verfasst von einem anerkannten amerikanischen Mathematiker, ist eine unkonventionelle Einführung in die Algebra. Es gibt vier grundlegende Strukturen in der Algebra: Gruppen, Ringe, Körper und Moduln. Das Buch behandelt die Theorie dieser Strukturen und beschreibt die Verknüpfungsregeln, die grundlegenden Operationen der Algebra. Die Darstellung ist elementar: es werden nur Kenntnisse der Linearen Algebra vorausgesetzt, weitere Fachkenntnisse sind nicht erforderlich.

Download or read Algebraic Structures book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). In algebra there are four basic structures: groups, rings, fields and modules. In this book the theory of these basic structures is presented and the laws of composition - the basic operations of algebra - are studied. Essentially, no previous knowledge is required, it is only assumed as background that the reader has learned some linear algebra over the real numbers.Dieses Lehrbuch, verfasst von einem anerkannten amerikanischen Mathematiker, ist eine unkonventionelle Einführung in die Algebra. Es gibt vier grundlegende Strukturen in der Algebra: Gruppen, Ringe, Körper und Moduln. Das Buch behandelt die Theorie dieser Strukturen und beschreibt die Verknüpfungsregeln, die grundlegenden Operationen der Algebra. Die Darstellung ist elementar: es werden nur Kenntnisse der Linearen Algebra vorausgesetzt, weitere Fachkenntnisse sind nicht erforderlich.


A History of Abstract Algebra

A History of Abstract Algebra [Pdf/ePub] eBook Author: Israel Kleiner
Editor: Springer Science & Business Media
ISBN-10: 081764685X
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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: Stephen Lovett
Editor: CRC Press
ISBN-10: 1482248913
Size: 1074 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


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
Size: 1265 kb
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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


Basic Modern Algebra with Applications

Basic Modern Algebra with Applications [Pdf/ePub] eBook Author: Mahima Ranjan Adhikari,Avishek Adhikari
Editor: Springer Science & Business Media
ISBN-10: 8132215990
Size: 935 kb
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Basic Modern Algebra with Applications by Mahima Ranjan Adhikari,Avishek Adhikari Book Summary:

The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a way that it encourages independent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. In addition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to structure theory of rings and homological algebra. Algebraic aspects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraic topology, category theory, algebraic geometry, algebraic number theory, cryptography and theoretical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, with the help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, examples, exercises and historical notes represents a valuable and unique resource.

Download or read Basic Modern Algebra with Applications book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a way that it encourages independent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. In addition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theory to structure theory of rings and homological algebra. Algebraic aspects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraic topology, category theory, algebraic geometry, algebraic number theory, cryptography and theoretical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, with the help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, examples, exercises and historical notes represents a valuable and unique resource.


Representation Theory

Representation Theory [Pdf/ePub] eBook Author: Alexander Zimmermann
Editor: Springer
ISBN-10: 3319079689
Size: 501 kb
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Representation Theory by Alexander Zimmermann Book Summary:

Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.

Download or read Representation Theory book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.


Algebra: Chapter 0

Algebra: Chapter 0 [Pdf/ePub] eBook Author: Paolo Aluffi
Editor: American Mathematical Soc.
ISBN-10: 0821847813
Size: 483 kb
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Algebra: Chapter 0 by Paolo Aluffi Book Summary:

Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.

Download or read Algebra: Chapter 0 book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.


Introduction to Abstract Algebra

Introduction to Abstract Algebra [Pdf/ePub] eBook Author: Jonathan D. H. Smith
Editor: CRC Press
ISBN-10: 1498731627
Size: 686 kb
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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, 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.


A Classical Introduction to Modern Number Theory

A Classical Introduction to Modern Number Theory [Pdf/ePub] eBook Author: K. Ireland,M. Rosen
Editor: Springer Science & Business Media
ISBN-10: 1475717792
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A Classical Introduction to Modern Number Theory by K. Ireland,M. Rosen Book Summary:

This book is a revised and greatly expanded version of our book Elements of Number Theory published in 1972. As with the first book the primary audience we envisage consists of upper level undergraduate mathematics majors and graduate students. We have assumed some familiarity with the material in a standard undergraduate course in abstract algebra. A large portion of Chapters 1-11 can be read even without such background with the aid of a small amount of supplementary reading. The later chapters assume some knowledge of Galois theory, and in Chapters 16 and 18 an acquaintance with the theory of complex variables is necessary. Number theory is an ancient subject and its content is vast. Any intro ductory book must, of necessity, make a very limited selection from the fascinat ing array of possible topics. Our focus is on topics which point in the direction of algebraic number theory and arithmetic algebraic geometry. By a careful selection of subject matter we have found it possible to exposit some rather advanced material without requiring very much in the way oftechnical background. Most of this material is classical in the sense that is was dis covered during the nineteenth century and earlier, but it is also modern because it is intimately related to important research going on at the present time.

Download or read A Classical Introduction to Modern Number Theory 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 a revised and greatly expanded version of our book Elements of Number Theory published in 1972. As with the first book the primary audience we envisage consists of upper level undergraduate mathematics majors and graduate students. We have assumed some familiarity with the material in a standard undergraduate course in abstract algebra. A large portion of Chapters 1-11 can be read even without such background with the aid of a small amount of supplementary reading. The later chapters assume some knowledge of Galois theory, and in Chapters 16 and 18 an acquaintance with the theory of complex variables is necessary. Number theory is an ancient subject and its content is vast. Any intro ductory book must, of necessity, make a very limited selection from the fascinat ing array of possible topics. Our focus is on topics which point in the direction of algebraic number theory and arithmetic algebraic geometry. By a careful selection of subject matter we have found it possible to exposit some rather advanced material without requiring very much in the way oftechnical background. Most of this material is classical in the sense that is was dis covered during the nineteenth century and earlier, but it is also modern because it is intimately related to important research going on at the present time.


Mathematical Foundations of Public Key Cryptography

Mathematical Foundations of Public Key Cryptography [Pdf/ePub] eBook Author: Xiaoyun Wang,Guangwu Xu,Mingqiang Wang,Xianmeng Meng
Editor: CRC Press
ISBN-10: 1498702244
Size: 806 kb
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Mathematical Foundations of Public Key Cryptography by Xiaoyun Wang,Guangwu Xu,Mingqiang Wang,Xianmeng Meng Book Summary:

In Mathematical Foundations of Public Key Cryptography, the authors integrate the results of more than 20 years of research and teaching experience to help students bridge the gap between math theory and crypto practice. The book provides a theoretical structure of fundamental number theory and algebra knowledge supporting public-key cryptography.R

Download or read Mathematical Foundations of Public Key Cryptography book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). In Mathematical Foundations of Public Key Cryptography, the authors integrate the results of more than 20 years of research and teaching experience to help students bridge the gap between math theory and crypto practice. The book provides a theoretical structure of fundamental number theory and algebra knowledge supporting public-key cryptography.R


Elements of Number Theory

Elements of Number Theory [Pdf/ePub] eBook Author: John Stillwell
Editor: Springer Science & Business Media
ISBN-10: 0387217355
Size: 1211 kb
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Elements of Number Theory by John Stillwell Book Summary:

Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.

Download or read Elements of Number Theory book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.


Advanced Algebra

Advanced Algebra [Pdf/ePub] eBook Author: Anthony W. Knapp
Editor: Springer Science & Business Media
ISBN-10: 0817646132
Size: 343 kb
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Advanced Algebra by Anthony W. Knapp Book Summary:

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole.

Download or read Advanced Algebra book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole.


Contemporary Abstract Algebra

Contemporary Abstract Algebra [Pdf/ePub] eBook Author: Joseph Gallian
Editor: Nelson Education
ISBN-10: 1305657969
Size: 1304 kb
Format File: Pdf
Read: 1304

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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.


Lectures in Abstract Algebra I

Lectures in Abstract Algebra I [Pdf/ePub] eBook Author: N. Jacobson
Editor: Springer Science & Business Media
ISBN-10: 1468473018
Size: 1083 kb
Format File: Pdf
Read: 1083

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Lectures in Abstract Algebra I by N. Jacobson Book Summary:

The present volume is the first of three that will be published under the general title Lectures in Abstract Algebra. These vol umes are based on lectures which the author has given during the past ten years at the University of North Carolina, at The Johns Hopkins University, and at Yale "University. The general plan of the work IS as follows: The present first volume gives an introduction to abstract algebra and gives an account of most of the important algebraIc concepts. In a treatment of this type it is impossible to give a comprehensive account of the topics which are introduced. Nevertheless we have tried to go beyond the foundations and elementary properties of the algebraic sys tems. This has necessitated a certain amount of selection and omission. We feel that even at the present stage a deeper under standing of a few topics is to be preferred to a superficial under standing of many. The second and third volumes of this work will be more special ized in nature and will attempt to give comprehensive accounts of the topics which they treat. Volume II will bear the title Linear Algebra and will deal with the theorv of vectQ!_JlP. -a. ces. . . . . Volume III, The Theory of Fields and Galois Theory, will be con cerned with the algebraic structure offieras and with valuations of fields. All three volumes have been planned as texts for courses.

Download or read Lectures in Abstract Algebra I book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc). The present volume is the first of three that will be published under the general title Lectures in Abstract Algebra. These vol umes are based on lectures which the author has given during the past ten years at the University of North Carolina, at The Johns Hopkins University, and at Yale "University. The general plan of the work IS as follows: The present first volume gives an introduction to abstract algebra and gives an account of most of the important algebraIc concepts. In a treatment of this type it is impossible to give a comprehensive account of the topics which are introduced. Nevertheless we have tried to go beyond the foundations and elementary properties of the algebraic sys tems. This has necessitated a certain amount of selection and omission. We feel that even at the present stage a deeper under standing of a few topics is to be preferred to a superficial under standing of many. The second and third volumes of this work will be more special ized in nature and will attempt to give comprehensive accounts of the topics which they treat. Volume II will bear the title Linear Algebra and will deal with the theorv of vectQ!_JlP. -a. ces. . . . . Volume III, The Theory of Fields and Galois Theory, will be con cerned with the algebraic structure offieras and with valuations of fields. All three volumes have been planned as texts for courses.