Spring 2019

Math 5120 Graduate Algebra II

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General Information, Syllabus, Assessment and Test Dates


  • 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


1.Assigned Work30%
3.Final Examination35%

Test Schedule

  • Test 1: Wednesday, February 13
  • Test 2: Take-home, handed out Wednesday March 20, due Wednesday March 27
  • Final: Take-home, handed out Wednesday April 24, due 10 a.m. Wednesday May 8