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MTH610 Topics in Modern Algebra

Lead Faculty: Dr. Igor Ya Subbotin

Course Description

Examines the algebra of various mathematical structures with the goal of gaining a broader and more sophisticated understanding of algebraic structures. Topics include groups, rings, fields and other main algebraic structures.

Learning Outcomes

  • Construct and evaluate finite and infinite fields
  • Apply main properties of vector spaces for construction of extension fields, elaborate algebraic extensions
  • Elaborate main properties of rings, subrings, ideals and quotient rings, rings of polynomials and formal power series, division in rings
  • Extend group structure to finite permutation groups (Cayleyandapos;s Theorem)
  • Prove Sylowandapos;s Theorems for finite groups
  • Generate groups given specific conditions
  • Elaborate the Fundamental Theorem of Galois Theory