Abstract algebra : an interactive approach /: an interactive approach. ([2018?])

• Record Type: Book
• Further Information: Note: William Paulsen.
• Authors: Paulsen, William
• Contents: Preliminaries; Integer Factorization; Functions; Modular Arithmetic; Rational and Real Numbers; ; Understanding the Group Concept; Introduction to Groups; Modular Congruence; The Definition of a Group; ; The Structure within a Group; Generators of Groups; Defining Finite Groups in Sage ; Subgroups; ; Patterns within the Cosets of Groups; Left and Right Cosets; Writing Secret Messages; Normal Subgroups; Quotient Groups; ; Mappings between Groups; Isomorphisms; Homomorphisms; The Three Isomorphism Theorems; ; Permutation Groups; Symmetric Groups; Cycles; Cayley's Theorem; Numbering the Permutations; ; Building Larger Groups from Smaller Groups; The Direct Product; The Fundamental Theorem of Finite Abelian Groups; Automorphisms; Semi-Direct Products; ; The Search for Normal Subgroups; The Center of a Group; The Normalizer and Normal Closure Subgroups; Conjugacy Classes and Simple Groups; The Class Equation and Sylow's Theorems; ; Solvable and Insoluble Groups; Subnormal Series and the Jordan-Hölder Theorem; Derived Group Series; Polycyclic Groups; Solving the PyraminxTM ; ; Introduction to Rings; The Definition of a Ring; Entering Finite Rings into Sage ; Some Properties of Rings; ; The Structure within Rings; Subrings; Quotient Rings and Ideals; Ring Isomorphisms; Homomorphisms and Kernels; ; Integral Domains and Fields; Polynomial Rings; The Field of Quotients; Complex Numbers; Ordered Commutative Rings; ; Unique Factorization; Factorization of Polynomials; Unique Factorization Domains; Principal Ideal Domains; Euclidean Domains; ; Finite Division Rings; Entering Finite Fields in Sage ; Properties of Finite Fields ; Cyclotomic Polynomials; Finite Skew Fields; ; The Theory of Fields; Vector Spaces; Extension Fields; Splitting Fields; ; Galois Theory; The Galois Group of an Extension Field; The Galois Group of a Polynomial in Q; The Fundamental Theorem of Galois Theory; Applications of Galois Theory; ; Appendix: Sage vs. Mathematica®; ; Answers to Odd-Numbered Problems Bibliography
• Edition: Second edition
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2018
• Copyright Date: 2016
• Extent: 1 online resource, illustrations
• Subjects: 512.02; Algebra, Abstract
• Languages: English
• ISBNs: 9781498719797; 1498719791
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.