Difference between revisions of "MAT5173"
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''Contents'' | ''Contents'' | ||
| − | (1) | + | (1) Groups: Cyclic groups, permutation groups and Cayleys theorem, group homomorphisms, normal subroups, quotient groups and Lagrange's theore, the theorems of Euler and Fermat. |
| − | + | (2) Rings: Ring homomorphisms, integral domains and fields, maximal and prime ideals. | |
| − | ( | + | (3) Rings of polynomials: |
| − | (3) | ||
| − | |||
| − | |||
| Line 26: | Line 23: | ||
==Topics List== | ==Topics List== | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
| − | ! Week !! Topic !! Sections from the | + | ! Week !! Topic !! Sections from the Judson-Beezer book !! Subtopics !! Prerequisite |
|- | |- | ||
| − | | 1- | + | | 1-2 |
|| [[Groups]] | || [[Groups]] | ||
| − | || | + | || 3 |
| − | || * | + | || |
| − | * | + | * Definitions and classical examples |
| − | + | * Subgroups | |
| + | * Isomorphisms | ||
|| MAT1313, CS2233/2231, or instructor consent. | || MAT1313, CS2233/2231, or instructor consent. | ||
|- | |- | ||
| 4-5 | | 4-5 | ||
| − | || [[ | + | || [[Cyclic groups]] |
| − | || | + | || 4 |
| − | || | + | || |
| − | + | * Classification of cyclic groups. | |
| − | |||
| − | |||
| − | |||
| − | |||
|- | |- | ||
| + | | 5-6 | ||
| + | || [[Permutation groups]] | ||
| + | || 5 | ||
| + | || | ||
| + | * Permutations | ||
| + | *Cayley's Theorem | ||
| + | - | ||
| 7-8 | | 7-8 | ||
| − | || [[ | + | || [[Cosets and Lagrange's Theorem]] |
| − | || | + | || 10 |
| − | || | + | || |
| + | * Normal subgroups | ||
| + | * Factor Groups | ||
| + | * The theorems of Euler and Fermat | ||
|- | |- | ||
| 9 | | 9 | ||
| − | || [[ | + | || [[Homomorphisms]] |
| − | || | + | || 11 |
| − | || | + | || The Isomorphism Theorem |
| + | | | ||
|- | |- | ||
| − | | 10 | + | | 10-11 |
| − | || [[ | + | || [[Rings]] |
| − | || | + | || 16 |
| − | || | + | || |
| + | * Ring homomorphisms | ||
| + | *Integral domains and fields | ||
| + | *Maximal and Prime Ideals | ||
|- | |- | ||
| − | | | + | | 12-end |
| − | || [[ | + | || [[Rings of Polynomials]] |
| − | || | + | || 17 |
| − | || | + | || |
| + | * The Division Algorithm | ||
| + | * Irreducible Polynomials | ||
| + | * Solving cubic and quartic equations | ||
|} | |} | ||
Revision as of 08:43, 19 March 2023
Introduction to groups rings and fields.
Sample textbook:
[1] Thomas W. Judson and Robert A. Beezer, Abstract Algebra: Theory and Applications, 2008. Freely available online.
Catalog entry
Prerequisite: Algebra and Number Systems (MAT 1313), or Discrete Mathematical Structures (CS 2233/2231), or instructor consent.
Contents (1) Groups: Cyclic groups, permutation groups and Cayleys theorem, group homomorphisms, normal subroups, quotient groups and Lagrange's theore, the theorems of Euler and Fermat. (2) Rings: Ring homomorphisms, integral domains and fields, maximal and prime ideals. (3) Rings of polynomials:
Topics List
| Week | Topic | Sections from the Judson-Beezer book | Subtopics | Prerequisite | |||
|---|---|---|---|---|---|---|---|
| 1-2 | Groups | 3 |
|
MAT1313, CS2233/2231, or instructor consent. | |||
| 4-5 | Cyclic groups | 4 |
| ||||
| 5-6 | Permutation groups | 5 |
- |
7-8 | Cosets and Lagrange's Theorem | 10 |
|
| 9 | Homomorphisms | 11 | The Isomorphism Theorem | ||||
| 10-11 | Rings | 16 |
| ||||
| 12-end | Rings of Polynomials | 17 |
|
