a first course in abstract algebra rings groups and fields (106 résultats)

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Paperback. Etat : new. Paperback. This advanced undergraduate-level text was recommended for teacher education by The American Mathematical Monthly and praised as a ""most readable book."" An ideal introduction to groups and Galois theory, it provides students with an appreciation of abstraction and arbitrary postulational systems, ideas that are central to automation.The authors take the algebraic equation and the discovery of the insolubility of the quintic as their theme. Starting with treatments of groups, rings, fields, and polynomials, they advance to Galois theory, radicals and roots of unity, and solution by radicals. Thirteen appendixes supplement this volume, along with numerous examples, illustrations, commentaries, and exercises. Students who have completed a first-year college course in algebra or calculus will find it an accessible and well-written treatment. Accessible advanced undergraduate-level text starts with groups, rings, fields, and polynomials and advances to Galois theory, radicals and roots of unity, and solution by radicals. Numerous examples, illustrations, exercises, appendixes. 1971 edition. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

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Paperback. John E Maxfield, Dover Publications Inc. This advanced undergraduate-level text was recommended for teacher education by The American Mathematical Monthly and praised as a ""most readable book."" An ideal introduction to groups and Galois theory, it provides students with an appreciation of abstraction and arbitrary postulational systems, ideas that are central to automation.The authors take the algebraic equation and the discovery of the insolubility of the quintic as their theme. Starting with treatments of groups, rings, fields, and polynomials, they advance to Galois theory, radicals and roots of unity, and solution by radicals. Thirteen appendixes supplement this volume, along with numerous examples, illustrations, commentaries, and exercises. Students who have completed a first-year college course in algebra or calculus will find it an accessible and well-written treatment. Paperback.

Hardcover. Etat : Near Fine. Etat de la jaquette : No Dust Jacket. Fourth Edition; (?). Previous owner's name written in blue pen on the front pastedown and Slight shelf wear. ; Black-and-white mathematical diagrams, illustrations, and formulae. A First Course in Abstract Algebra by John B. Fraleigh is a widely used textbook that provides a clear and comprehensive introduction to abstract algebra. Covering fundamental topics like groups, rings, fields, and homomorphisms, the book balances theory with practical examples and exercises. Its approachable style makes it ideal for undergraduate students, offering a solid foundation for deeper studies in algebra. ; 16.6 x 23.9 x 2.6 cm ; ix, 518 pages.

Paperback. Etat : new. Paperback. This abstract algebra textbook takes an integrated approach that highlights the similarities of fundamental algebraic structures among a number of topics. The book begins by introducing groups, rings, vector spaces, and fields, emphasizing examples, definitions, homomorphisms, and proofs. The goal is to explain how all of the constructions fit into an axiomatic framework and to emphasize the importance of studying those maps that preserve the underlying algebraic structure. This fast-paced introduction is followed by chapters in which each of the four main topics is revisited and deeper results are proven. The second half of the book contains material of a more advanced nature. It includes a thorough development of Galois theory, a chapter on modules, and short surveys of additional algebraic topics designed to whet the reader's appetite for further study. This book is intended for a first introduction to abstract algebra and requires only a course in linear algebra as a prerequisite. The more advanced material could be used in an introductory graduate-level course. Takes an integrated approach that highlights the similarities of fundamental algebraic structures among a number of topics. The book is intended for a first introduction to abstract algebra and requires only a course in linear algebra as a prerequisite. The more advanced material could be used in an introductory graduate-level course. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Hardcover. Etat : new. Hardcover. This is a survey, accessible to junior/senior undergraduate students and containing many examples, solved exercises, and sets of problems, of some parts of abstract algebra that are of use in many other areas of discrete mathematics. Three major themes are particularly relevant to computer science, Boolean algebras and switching circuits, finite fields and algebraic coding, and semigroups and automata. The topics of the book can be studied independently of each other, although the book is a mathematics book, the authors have made great efforts to address the needs of the users of the techniques that are being discussed. There is a special emphasis on fully worked out computational examples. More than 500 exercises accompany the 40 sections. This new edition includes major changes to the first edition: corrections and improvements to the first four chapters, a new chapter on Cryptology, and an enlarged chapter on Applications of Groups. An extensive chapter has been added to survey other (mostly recent) applications, many of which were not included in the first edition, nor are commonly found in undergraduate texts.The book assumes knowledge of the material covered in a course on linear algebra and, preferably, a first course in (abstract) algebra covering the basics of groups, rings, and fields. This is a survey, accessible to junior/senior undergraduate students and containing many examples, solved exercises, and sets of problems, of some parts of abstract algebra that are of use in many other areas of discrete mathematics. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Hardback. Etat : New. Abstract Algebra with Applications provides a friendly and concise introduction to algebra, with an emphasis on its uses in the modern world. The first part of this book covers groups, after some preliminaries on sets, functions, relations, and induction, and features applications such as public-key cryptography, Sudoku, the finite Fourier transform, and symmetry in chemistry and physics. The second part of this book covers rings and fields, and features applications such as random number generators, error correcting codes, the Google page rank algorithm, communication networks, and elliptic curve cryptography. The book's masterful use of colorful figures and images helps illustrate the applications and concepts in the text. Real-world examples and exercises will help students contextualize the information. Intended for a year-long undergraduate course in algebra for mathematics, engineering, and computer science majors, the only prerequisites are calculus and a bit of courage when asked to do a short proof.

Hardcover. Etat : new. Hardcover. Like its popular predecessors, A First Course in Abstract Algebra: Rings, Groups, and Fields, Third Edition develops ring theory first by drawing on students familiarity with integers and polynomials. This unique approach motivates students in the study of abstract algebra and helps them understand the power of abstraction. The authors introduce groups later on using examples of symmetries of figures in the plane and space as well as permutations.New to the Third EditionMakes it easier to teach unique factorization as an optional topic Reorganizes the core material on rings, integral domains, and fieldsIncludes a more detailed treatment of permutationsIntroduces more topics in group theory, including new chapters on Sylow theoremsProvides many new exercises on Galois theoryThe text includes straightforward exercises within each chapter for students to quickly verify facts, warm-up exercises following the chapter that test fundamental comprehension, and regular exercises concluding the chapter that consist of computational and supply-the-proof problems. Historical remarks discuss the history of algebra to underscore certain pedagogical points. Each section also provides a synopsis that presents important definitions and theorems, allowing students to verify the major topics from the section. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Hardcover. Etat : Fine. No Jacket. 4th Edition. One of the favorite introductions to Abstact Algebra. Strikes the delicate balance between rigor and breadth, putting the math in historical context. Historical notes by Victor Katz. Chapters Included: 0 A Few Preliminaries. 1 Introduction to Groups. 2 Homomorphisms and Factor Groups. 3 Advanced Group Theory. 4 Introduction to Rings and Fields. 5 Factor Rings and Ideals. 6 Factorization. 7 Extension Fields. 8 Automorphisms and Galois Theory. Appendices include bibliography, notation, answers to odd numbered problems & an index. ix + 518pp. Hardcover with plastic coated boards, but no dust jacket. Minor storage-marks exterior. Opens as if seldom read. Interior is tight, complete, clean, and unmarked. Always privately owned with no ownership markings. Fine (As New) condition. Copyrights 1989, 1982, 1976, and 1967. Printed in U.S.A. Print-line indicates "A" printing of 1988, 1st Thus copy implied. Stated 4th edition. ISBN: 0-201-16847-2. LCCN: 88-22171. No MSR found. No Ownership Markings.

Taschenbuch. Etat : Neu. Neuware -At first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common. However, reduction to Smith normal form, named after its originator H.J.S.Smith in 1861, is a matrix version of the Euclidean algorithm and is exactly what the theory requires in both cases. Starting with matrices over the integers, Part1 of this book provides a measured introduction to such groups: two finitely generated abelian groups are isomorphic if and only if their invariant factor sequences are identical. The analogous theory of matrix similarity over a field is then developed in Part2 starting with matrices having polynomial entries: two matrices over a field are similar if and only if their rational canonical forms are equal. Under certain conditions each matrix is similar to a diagonal or nearly diagonal matrix, namely its Jordan form.The reader is assumed to be familiar with the elementary properties of rings and fields. Also a knowledge of abstract linear algebra including vector spaces, linear mappings, matrices, bases and dimension is essential, although much of the theory is covered in the text but from a more general standpoint: the role of vector spaces is widened to modules over commutative rings.Based on a lecture course taught by the author for nearly thirty years, the book emphasises algorithmic techniques and features numerous worked examples and exercises with solutions. The early chapters form an ideal second course in algebra for second and third year undergraduates. The later chapters, which cover closely related topics, e.g. field extensions, endomorphism rings, automorphism groups, and variants of the canonical forms, will appeal to more advanced students. The book is a bridge between linear and abstract algebra.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 396 pp. Englisch.

Taschenbuch. Etat : Neu. Neuware -This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory. The journey starts with the basic idea that new number systems arise from solving different equations, leading to (abstract) algebra. Along this journey, the reader will be exposed to important ideas of mathematics, and will learn a little about how mathematics is really done.Starting at an elementary level, the book gradually eases the reader into the complexities of higher mathematics; in particular, the formal structure of mathematical writing (definitions, theorems and proofs) is introduced in simple terms. The book covers a range of topics, from the very foundations (numbers, set theory) to basic abstract algebra (groups, rings, fields), driven throughout by the need to understand concrete equations and problems, such as determining which numbers are sums of squares. Some topics usually reserved for a more advanced audience, such as Eisenstein integers or quadratic reciprocity, are lucidly presented in an accessible way. The book also introduces the reader to open source software for computations, to enhance understanding of the material and nurture basic programming skills. For the more adventurous, a number of Outlooks included in the text offer a glimpse of possible mathematical excursions.This book supports readers in transition from high school to university mathematics, and will also benefit university students keen to explore the beginnings of algebraic number theory. It can be read either on its own or as a supporting text for first courses in algebra or number theory, and can also be used for a topics course on Diophantine equations.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 364 pp. Englisch.

Taschenbuch. Etat : Neu. Neuware -This textbook offers an innovative approach to abstract algebra, based on a unified treatment of similar concepts across different algebraic structures. This makes it possible to express the main ideas of algebra more clearly and to avoid unnecessary repetition.The book consists of two parts: The Language of Algebra and Algebra in Action. The unified approach to different algebraic structures is a primary feature of the first part, which discusses the basic notions of algebra at an elementary level. The second part is mathematically more complex, covering topics such as the Sylow theorems, modules over principal ideal domains, and Galois theory.Intended for an undergraduate course or for self-study, the book is written in a readable, conversational style, is rich in examples, and contains over 700 carefully selected exercises.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 340 pp. Englisch.

Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.

Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory. The journey starts with the basic idea that new number systems arise from solving different equations, leading to (abstract) algebra. Along this journey, the reader will be exposed to important ideas of mathematics, and will learn a little about how mathematics is really done.Starting at an elementary level, the book gradually eases the reader into the complexities of higher mathematics; in particular, the formal structure of mathematical writing (definitions, theorems and proofs) is introduced in simple terms. The book covers a range of topics, from the very foundations (numbers, set theory) to basic abstract algebra (groups, rings, fields), driven throughout by the need to understand concrete equations and problems, such as determining which numbers are sums of squares. Some topics usually reserved for a more advanced audience, such as Eisenstein integers or quadratic reciprocity, are lucidly presented in an accessible way. The book also introduces the reader to open source software for computations, to enhance understanding of the material and nurture basic programming skills. For the more adventurous, a number of Outlooks included in the text offer a glimpse of possible mathematical excursions.This book supports readers in transition from high school to university mathematics, and will also benefit university students keen to explore the beginnings of algebraic number theory. It can be read either on its own or as a supporting text for first courses in algebra or number theory, and can also be used for a topics course on Diophantine equations.

Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - This textbook offers an innovative approach to abstract algebra, based on a unified treatment of similar concepts across different algebraic structures. This makes it possible to express the main ideas of algebra more clearly and to avoid unnecessary repetition.The book consists of two parts:The Language of AlgebraandAlgebra in Action.The unified approach to different algebraic structures is a primary feature of the first part, which discusses the basic notions of algebra at an elementary level. The second part is mathematically more complex, covering topics such as the Sylow theorems, modules over principal ideal domains, and Galois theory.Intended for an undergraduate course or for self-study, the book is written in a readable, conversational style, is rich in examples, and contains over 700 carefully selected exercises.

Paperback. Etat : new. Paperback. Thinking Algebraically presents the insights of abstract algebra in a welcoming and accessible way. It succeeds in combining the advantages of rings-first and groups-first approaches while avoiding the disadvantages. After an historical overview, the first chapter studies familiar examples and elementary properties of groups and rings simultaneously to motivate the modern understanding of algebra. The text builds intuition for abstract algebra starting from high school algebra. In addition to the standard number systems, polynomials, vectors, and matrices, the first chapter introduces modular arithmetic and dihedral groups. The second chapter builds on these basic examples and properties, enabling students to learn structural ideas common to rings and groups: isomorphism, homomorphism, and direct product. The third chapter investigates introductory group theory. Later chapters delve more deeply into groups, rings, and fields, including Galois theory, and they also introduce other topics, such as lattices. The exposition is clear and conversational throughout. The book has numerous exercises in each section as well as supplemental exercises and projects for each chapter. Many examples and well over 100 figures provide support for learning. Short biographies introduce the mathematicians who proved many of the results. The book presents a pathway to algebraic thinking in a semester- or year-long algebra course. Presents the insights of abstract algebra in a welcoming and accessible way. The book succeeds in combining the advantages of rings-first and groups-first approaches while avoiding the disadvantages. The exposition is clear and conversational throughout. The book has numerous exercises in each section. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - At first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common. However, reduction to Smith normal form, named after its originator H.J.S.Smith in 1861, is a matrix version of the Euclidean algorithm and is exactly what the theory requires in both cases. Starting with matrices over the integers, Part 1 of this book provides a measured introduction to such groups: two finitely generated abelian groups are isomorphic if and only if their invariant factor sequences are identical. The analogous theory of matrix similarity over a field is then developed in Part 2 starting with matrices having polynomial entries: two matrices over a field are similar if and only if their rational canonical forms are equal. Under certain conditions each matrix is similar to a diagonal or nearly diagonal matrix, namely its Jordan form. The reader is assumed to be familiar with the elementary properties of rings and fields. Also a knowledge of abstract linear algebra including vector spaces, linear mappings, matrices, bases and dimension is essential, although much of the theory is covered in the text but from a more general standpoint: the role of vector spaces is widened to modules over commutative rings. Based on a lecture course taught by the author for nearly thirty years, the book emphasises algorithmic techniques and features numerous worked examples and exercises with solutions. The early chapters form an ideal second course in algebra for second and third year undergraduates. The later chapters, which cover closely related topics, e.g. field extensions, endomorphism rings, automorphism groups, and variants of the canonical forms, will appeal to more advanced students. The book is a bridge between linear and abstract algebra.