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• 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

• Test 1: Wednesday, October 1
• Test 2: Take-home, handed out Wednesday November 12, due Wednesday November 19
• Final: Monday, December 15, at 8 a.m. + oral exam to be scheduled individually between December 10 and December 12