Course outline

• Background
  • 0.3 - Properties of Z
  • 0.4 - Complex Numbers
  • 0.5 - Matrices
• Groups
  • 1.1 - Examples and Basic Concepts
  • 1.2 - Subgroups
  • 1.3 - Cyclic Groups
  • 1.4 - Permutations
• Group Homomorphisms
  • 0.1 - Sets and Maps
  • 0.2 - Equivalence Relations and Partitions
  • 2.1 - Cosets and Lagrange's Theorem
  • 2.2 - Homomorphisms
  • 2.3 - Normal Subgroups
  • 2.4 - Quotient Groups
  • 2.5 - Automorphisms
• Direct Products and Abelian Groups
  • 3.1 - Examples and Definitions
  • 3.2 - Computing Orders
  • 3.3 - Direct Sums
  • 3.4 - Fundamental Theorem of Finite Abelian Groups
• Group Actions
  • 4.1 - Group Actions and Cayley's Theorem
  • 4.2 - Stabilizers and Orbits in a Group Action
  • 4.4 - Conjugacy Classes and the Class Equation
  • 4.3 - Burnside's Theorem and Applications