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Algebra Abstract and Concrete 1st Edition by Frederick M Goodman ISBN 0130673420 9780130673428

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Algebra Abstract and Concrete 2.5 Edition Frederick M. Goodman Digital Instant Download

Author(s): Frederick M. Goodman
ISBN(s): 9780130673428, 0130673420
Edition: 2.5
File Details: PDF, 4.72 MB
Year: 2002
Language: english
SKU: EB-879404 Category: Tag:

Algebra Abstract and Concrete 1st Edition by Frederick M Goodman – Ebook PDF Instant Download/Delivery: 0130673420, 9780130673428
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Product details:

ISBN 10: 0130673420 
ISBN 13: 9780130673428
Author: Frederick M Goodman

Addresses the needs of those who often have weak analytic ability, little idea of strategies of problem solving, and less of the patience and confidence needed to work proofs. It introduces readers to the active practice of mathematics — luring them away from the view of mathematics as a system of rules and procedures and helping them learn to think things through for themselves and to explain accurately what they have understood. Uses linear algebra and complex numbers throughout. Highlights all theorems (propositions, lemmas, corollaries) and definitions in boxes. Features an abundance of high-quality exercises.

Algebra Abstract and Concrete 1st Table of contents:

Chapter 1. Algebraic Themes

1. What Is Symmetry?
2. Symmetries of the Rectangle and the Square
3. Multiplication Tables
4. Symmetries and Matrices
5. Permutations
6. Divisibility in the Integers
7. Modular Arithmetic
8. Polynomials
9. Counting
10. Groups
11. Rings and Fields
12. An Application to Cryptography

Chapter 2. Basic Theory of Groups

1. First Results
2. Subgroups and Cyclic Groups
3. The Dihedral Groups
4. Homomorphisms and Isomorphisms
5. Cosets and Lagrange’s Theorem
6. Equivalence Relations and Set Partitions
7. Quotient Groups and Homomorphism Theorems

Chapter 3. Products of Groups

1. Direct Products
2. Semidirect Products
3. Vector Spaces
4. The dual of a vector space and matrices
5. Linear algebra over ℤ
6. Finitely generated abelian groups

Chapter 4. Symmetries of Polyhedra

1. Rotations of Regular Polyhedra
2. Rotations of the Dodecahedron and Icosahedron
3. What about Reflections?
4. Linear Isometries
5. The Full Symmetry Group and Chirality

Chapter 5. Group Actions on Sets

1. Group Actions on Sets
2. Group Actions — Counting Orbits
3. Symmetries of Groups
4. Group Actions and Group Structure
5. Application: Transitive Subgroups of S₅
6. Additional Exercises for Chapter 5

Chapter 6. Rings and Ideals

1. A Recollection of Rings
2. Homomorphisms and Ideals
3. Quotient Rings
4. Integral Domains
5. Euclidean Domains, PIDs & Unique Factorization
6. Unique Factorization Domains
7. Noetherian Rings
8. Irreducibility Criteria

Chapter 7. Field Extensions & Cubic Equations

1. A Brief History
2. Solving the Cubic Equation
3. Adjoining Algebraic Elements
4. Splitting Field of a Cubic
5. Splitting Fields in ℂ[x]

Chapter 8. Modules & Canonical Forms

1. The idea of a module
2. Homomorphisms and Quotient Modules
3. Multilinear Maps & Determinants
4–5. Finitely generated Modules over a PID (Parts I & II)
6. Rational Canonical Form
7. Jordan Canonical Form

Chapter 9. Galois Theory

1. Finite and Algebraic Extensions
2. Splitting Fields
3. Derivative and Multiple Roots
4. Splitting Fields and Automorphisms
5. The Galois Correspondence
6. Symmetric Functions
7. General Equation of Degree n
8. Quartic Polynomials
9. Galois Groups of Higher Degree Polynomials

Chapter 10. Solvability & Radical Extensions

1. Composition Series & Solvable Groups
2. Commutators and Solvability
3. Simplicity of Alternating Groups
4. Cyclotomic Polynomials
5. The Equation xⁿ = b
6. Solvability by Radicals
7. Radical Extensions

Chapter 11. Isometries of Euclidean Space

1. More on Isometries
2. Euler’s Theorem
3. Finite Rotation Groups
4. Crystals

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