National University

MTH441 Abstract Algebra

Lead Faculty: Dr. Igor Ya Subbotin

Course Description

This course continues and advances the work done in MTH 416 Algebraic Structures, discussing selected fundamental algebraic structures. The main concepts of Sylow Theory of finite groups, finite permutation groups (Cayley's Theorem), Galois Theory, Lattices Theory, Coding Theory and Cryptography, Boolean Algebra and Switching Theory are studied.

Learning Outcomes

  • Discuss vector spaces, subspaces, extension fields, algebraic extensions.
  • Extend group structure to finite permutation groups (Cayley's Theorem).
  • Discuss Sylow's Theorems.
  • Generate groups given specific conditions.
  • Investigate symmetry using group theory.
  • Operate discrete frieze groups, particularly plane crystallographic groups.
  • Identify plane periodic patterns (lattices).
  • Understand the base of the coding theory as an application of finite fields.
  • Discuss the Fundamental Theorem of Galois Theory.
  • Discuss the three major concrete models of Boolean algebra: the algebra of sets, the algebra of electrical circuits, and the algebra of logic.
  • Describe other applications of abstract algebra such as in avoiding problems of round off in computations.