Abstract Algebra

Fall 2006

Week 1: Aug 28 - Sept 1

  • Linear Review and Extension I
  • Linear Review and Extension II
  • Groups
  • Brainstorming and Catchup Session
    • Assign: Problem Set 1

Week 2: Sept 4 - Sept 8

  • Subgroups
  • Brainstorming and Catchup Session
  • Isomorphisms
    • Assign: Problem Set 2

Week 3: Sept 11 - Sept 15

  • -
  • Brainstorming and Catchup Session
  • Homomorphisms
  • Equivalence Relations and Partitions
    • Assign: Problem Set 3

Week 4: Sept 18 - Sept 22

  • Cosets
  • Brainstorming and Catchup Session
  • -
  • Restriction of Homomorphisms
    • Assign: Problem Set 4

Week 5: Sept 25 - Sept 29

  • Brainstorming and Catchup Session
  • Exam 1
  • Products of Groups
  • Modular Arithmetic
    • Assign: Problem Set 5

Week 6: Oct 2 - Oct 6

  • Quotient Groups
  • Brainstorming and Catchup Session
  • -
  • Linear Review and Extension III
    • Assign: Problem Set 8

Week 7: Oct 9 - Oct 13

  • Linear Review and Extension IV
  • Brainstorming and Catchup Session
  • Linear Review and Extension V
  • Linear Review and Extension VI
    • Assign: Problem Set 7

Week 8: Oct 16 - Oct 20

  • No Class (FALL BREAK)
  • No Class (FALL BREAK)
  • Linear Review and Extension VII
  • Linear Review and Extension VIII
    • No Assignment

Week 9: Oct 23 - Oct 27

  • Symmetry of Plane Figures
  • Brainstorming and Catchup Session
  • Group of Motions in the Plane
  • Finite Groups of Motions
    • Assign: Problem Set 8

Week 10: Oct 30 - Nov 3

  • -
  • Brainstorming and Catchup Session
  • Discrete Groups of Motions
  • Abstract Symmetry (Group Operations)
    • Assign: Problem Set 9

Week11: Nov 6 - Nov 10

  • Brainstorming and Catchup Session
  • Exam 2
  • Operations on Cosets
  • The Counting Formula
    • Assign: Problem Set 10

Week 12: Nov 13 - 17

  • Operations of a Group on itself
  • Brainstorming and Catchup Session
  • -
  • An Example: Class Equation of Icosahedral group
    • Assign: Problem Set 11

Week 13: Nov 20 - Nov 24

  • Group Operations on Subsets
  • Sylow Theorems
  • No Class (THANKSGIVING)
  • No Class (THANKSGIVING)
    • No Assignment

Week 14: Nov 27 - Dec 1

  • -
  • Brainstorming and Catchup Session
  • Example: Groups of Order 12
  • Free Groups
    • Assign: Problem Set 12

Week 15: Dec 4 - Dec 8

  • Generators and relations
  • Review
  • Review
  • No Class (End of Semester)