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Zeitgenössische abstrakte Algebra von Joseph Gallian (2016, Hardcover)

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ISBN
9781305657960

Über dieses Produkt

Product Identifiers

Publisher
Brooks/Cole
ISBN-10
1305657969
ISBN-13
9781305657960
eBay Product ID (ePID)
219270925

Product Key Features

Number of Pages
656 Pages
Language
English
Publication Name
Contemporary Abstract Algebra
Subject
Algebra / Abstract, General, Algebra / Elementary
Publication Year
2016
Features
Revised
Type
Textbook
Subject Area
Mathematics
Author
Joseph Gallian
Format
Hardcover

Dimensions

Item Height
9.2 in
Item Weight
33.7 Oz
Item Length
1.1 in
Item Width
6.5 in

Additional Product Features

Edition Number
9
Intended Audience
College Audience
LCCN
2015-954307
Dewey Edition
23
Illustrated
Yes
Dewey Decimal
512/.02
Table Of Content
PART I: INTEGERS AND EQUIVALENCE RELATIONS.Preliminaries. Properties of Integers. Complex Numbers. Modular Arithmetic. Mathematical Induction. Equivalence Relations. Functions (Mappings). Exercises. PART I!: GROUPS.1. Introduction to Groups. Symmetries of a Square. The Dihedral Groups. Exercises. Biography of Neils Abel2. Groups.Definition and Examples of Groups. Elementary Properties of Groups. Historical Note. Exercises. 3. Finite Groups; Subgroups.Terminology and Notation. Subgroup Tests. Examples of Subgroups. Exercises. 4. Cyclic Groups.Properties of Cyclic Groups. Classification of Subgroups of Cyclic Groups. Exercises. Biography of J. J. Sylvester. Supplementary Exercises for Chapters 1-4.5. Permutation Groups.Definition and Notation. Cycle Notation. Properties of Permutations. A Check-Digit Scheme Based on D5. Exercises. Biography of Augustin Cauchy.6. Isomorphisms.Motivation. Definition and Examples. Cayley's Theorem. Properties of Isomorphisms.Automorphisms. Exercises. Biography of Arthur Cayley.7. Cosets and Lagrange's Theorem.Properties of Cosets. Lagrange's Theorem and Consequences. An Application of Cosets to Permutation Groups. The Rotation Group of a Cube and a Soccer Ball. Exercises. Biography of Joseph Lagrange.8. External Direct Products.Definition and Examples. Properties of External Direct Products. The Group of Units Modulo n as an External Direct Product. Applications. Exercises. Biography of Leonard Adleman. Supplementary Exercises for Chapters 5-89. Normal Subgroups and Factor Groups.Normal Subgroups. Factor Groups. Applications of Factor Groups. Internal Direct Products. Exercises. Biography of Évariste Galois10. Group Homomorphisms.Definition and Examples. Properties of Homomorphisms. The First Isomorphism Theorem. Exercises. Biography of Camille Jordan.11. Fundamental Theorem of Finite Abelian Groups.The Fundamental Theorem. The Isomorphism Classes of Abelian Groups. Proof of the Fundamental Theorem. Exercises. Supplementary Exercises for Chapters 9-11.PART III: RINGS.12. Introduction to Rings.Motivation and Definition. Examples of Rings. Properties of Rings. Subrings. Exercises. Biography of I. N. Herstein.13. Integral Domains.Definition and Examples. Fields. Characteristic of a Ring. Exercises. Biography of Nathan Jacobson.14. Ideals and Factor Rings.Ideals. Factor Rings. Prime Ideals and Maximal Ideals. Exercises. Biography of Richard Dedekind. Biography of Emmy Noether. Supplementary Exercises for Chapters 12-14.15. Ring Homomorphisms.Definition and Examples. Properties of Ring Homomorphisms. The Field of Quotients.Exercises.16. Polynomial Rings.Notation and Terminology. The Division Algorithm and Consequences. Exercises.Biography of Saunders Mac Lane.17. Factorization of Polynomials.Reducibility Tests. Irreducibility Tests. Unique Factorization in Z[x]. Weird Dice: An Application of Unique Factorization. Exercises. Biography of Serge Lang.18. Divisibility in Integral Domains.Irreducibles, Primes. Historical Discussion of Fermat's Last Theorem. Unique Factorization Domains. Euclidean Domains. Exercises. Biography of Sophie Germain. Biography of Andrew Wiles. Supplementary Exercises for Chapters 15-18.PART IV: FIELDS.19. Vector Spaces.Definition and Examples. Subspaces. Linear Independence. Exercises. Biography of Emil Artin. Biography of Olga Taussky-Todd. 20. Extension Fields.The Fundamental Theorem of Field Theory. Splitting Fields. Zeros of an Irreducible Polynomial. Exercises. Biography of Leopold Kronecker.21. Algebraic Extensions.Characterization of Extensions. Finite Extensions. Properties of Algebraic ExtensionsExercises. Biography of Irving Kaplansky.22. Finite Fields.Classification of Finite Fields. Structure of Finite Fields. Subfields of a Finite Field.Exercises. Biography of L. E. Dickson.23. Geometric Constructions.Historical Discussion of Geometric Constructions. Constructible Numbers. Angle-Trisectors and Circle-Squarers.
Edition Description
Revised edition
Synopsis
CONTEMPORARY ABSTRACT ALGEBRA, NINTH EDITION is primarily intended for an abstract algebra course whose main purpose is to enable students to do computations and write proofs. Gallians text stresses the importance of obtaining a solid introduction to the traditional topics of abstract algebra, while at the same time presenting it as a contemporary and very much an active subject which is currently being used by working physicists, chemists, and computer scientists., CONTEMPORARY ABSTRACT ALGEBRA, NINTH EDITION is primarily intended for an abstract algebra course whose main purpose is to enable students to do computations and write proofs. Gallian's text stresses the importance of obtaining a solid introduction to the traditional topics of abstract algebra, while at the same time presenting it as a contemporary and very much an active subject which is currently being used by working physicists, chemists, and computer scientists.
LC Classification Number
QA162.G34 2016

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