A First Course in Abstract Algebra (3rd Ed.) Rings, Groups, and Fields, Third Edition
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 Edition
- Makes it easier to teach unique factorization as an optional topic
- Reorganizes the core material on rings, integral domains, and fields
- Includes a more detailed treatment of permutations
- Introduces more topics in group theory, including new chapters on Sylow theorems
- Provides many new exercises on Galois theory
The 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.
Numbers, Polynomials, and Factoring. Rings, Domains, and Fields. Ring Homomorphisms and Ideals. Groups. Group Homomorphisms. Topics from Group Theory. Unique Factorization. Constructibility Problems. Vector Spaces and Field Extensions. Galois Theory. Hints and Solutions. Guide to Notation. Index.
Date de parution : 12-2014
17.8x25.4 cm
Thème d’A First Course in Abstract Algebra :
Mots-clés :
Minimal Polynomial; Additive Inverses; Galois Theory; Finite Abelian Groups; Polynomials And Factoring; Gaussian Integer; Vector Spaces And Field Extensions; Quick Exercise; Quintic With Radicals; Sylow Theorem; Ring Homomorphisms And Ideals; Ring Homomorphism; Galois Group; GCD; Abelian Groups; Ring Isomorphism; Commutative Ring; Constructible Numbers; Left Cosets; Group Isomorphism; Irreducible Polynomial; Splitting Field; Normal Subgroups; Principal Ideal; Division Theorem; Algebraic Simple Extensions; Integral Domain; Principal Ideal Domain; Cyclic Group; Unique Factorization Theorem