Fall 1999
MT-A511 Graduate Algebra I
Syllabus, Assessment and Test Dates
Syllabus for Graduate Algebra I & II
Groups: Isomorphism theorems, group action, simplicity of alternating groups, solvability of p-groups, Sylow theorems, Jordan-Hšlder theorem, direct and semidirect products, finitely generated abelian groups
Rings: Chinese Remainder Theorem, Euclidean domains, PIDs, unique factorization, Gauss lemma, irreducibility criteria
Fields and Galois Theory: Field extensions: algebraic, finite, separable, normal. Finite fields, ruler and compass constructions, fundamental theorem of Galois theory, cyclotomic extensions, solvability by radicals, symmetric functions, computation of Galois groups of cubics and quartics, transcendental extensions
Modules: Introduction, direct sums, free modules, modules over principal ideal domains and/or other topics from module theory
Assessment| 1. Homework | 25% |
| 2. In-class presentation | 5% |
| 3. Tests | 35% |
| 4. Final Examination | 35% |
Test Schedule
Test 1: Wednesday, September 29
Test 2: Take-home, handed out Monday, November 8, due Monday November 15
Final: Monday, December 6 from 8 a.m. to 9:50 a.m.
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