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### General Information, Syllabus, Assessment and Test Dates

### Objectives

- To gain additional knowledge of basic abstract algebra concepts
- To further develop techniques of precise mathematical proof
- To further develop clarity of thought regarding the abstract algebra concepts studied through examples and theorems

Syllabus for Graduate Algebra I & II (major topics are listed; other topics will be covered.):

- Groups: Isomorphism theorems, group action, simplicity of alternating groups, solvability of p-groups, Sylow theorems, Jordan-Hölder 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. | Assigned Work | 30% |

2. | Tests | 35% |

3. | Final Examination | 35% |

### Test Schedule

- Test 1: Monday, February 13
- Test 2: Take-home, handed out Monday March 27, due Monday April 3
- Final: Take-home, handed out Wednesday April 26, due 10 a.m. Wednesday May 10