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
