Difference between revisions of "Math 671: Algebra 1."
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| + | #Group Theory | ||
| + | #* Axioms and Examples | ||
| + | #* Homomorphisms and Isomorphisms | ||
| + | #* Subgroups | ||
| + | #* Centralizers and Normalizers | ||
| + | #* Cyclic gorups and subgroups | ||
| + | #* Quotient Groups | ||
| + | #* Lagrange's Theorem | ||
| + | #* Isomorphism theorems | ||
| + | #* Group Actions | ||
| + | #* Permutation Representations | ||
| + | #* Cayley's Theorem | ||
| + | #* The class equation | ||
| + | #* Sylow theorems | ||
| + | #* Direct and semidirect products | ||
| + | #* Solvable and Nilpotent groups | ||
| + | |||
| + | #Ring Theory | ||
| + | #* Definitions and Examples | ||
| + | #* Homomorphisms and quotient rings | ||
| + | #* Ideals | ||
| + | #* Rings of fractions | ||
| + | #* Chinese remainder theorem | ||
| + | #* Euclidean Domains, PID's and UFD's | ||
| + | #* Polynomial Rings | ||
| + | |||
| + | #Module Theory | ||
| + | #* Definitions and Examples | ||
| + | #* Quotient modules and homomorphisms | ||
| + | #* Direct sums | ||
| + | #* Free Modules | ||
| + | #* Tensor Products | ||
| + | #* Exact Sequences | ||
| + | #* Projectives, Injectives, Flats | ||
</div> | </div> | ||
Revision as of 09:33, 20 August 2008
Contents
Catalog Information
Title
Algebra.
Credit Hours
3
Prerequisite
Description
Desired Learning Outcomes
Prerequisites
Minimal learning outcomes
- Group Theory
- Axioms and Examples
- Homomorphisms and Isomorphisms
- Subgroups
- Centralizers and Normalizers
- Cyclic gorups and subgroups
- Quotient Groups
- Lagrange's Theorem
- Isomorphism theorems
- Group Actions
- Permutation Representations
- Cayley's Theorem
- The class equation
- Sylow theorems
- Direct and semidirect products
- Solvable and Nilpotent groups
- Ring Theory
- Definitions and Examples
- Homomorphisms and quotient rings
- Ideals
- Rings of fractions
- Chinese remainder theorem
- Euclidean Domains, PID's and UFD's
- Polynomial Rings
- Module Theory
- Definitions and Examples
- Quotient modules and homomorphisms
- Direct sums
- Free Modules
- Tensor Products
- Exact Sequences
- Projectives, Injectives, Flats
