Topics in Modern Algebra

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 (Cayley’s Theorem).
  • Prove Sylow’s Theorems for finite groups.
  • Generate groups given specific conditions.
  • Elaborate the Fundamental Theorem of Galois Theory.

Prerequisites

Recommended Preparation

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