Abstract Algebra

Fall 2007

Week 1: Sep 3 - Sept 7

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

Week 2: Sept 10 - Sept 14

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

Week 3: Sept 17 - Sept 21

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

Week 4: Sept 24 - Sept 28

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

Week 5: Oct 1 - Oct 5

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

Week 6: Oct 8 - Oct 12

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

Week 7: Oct 15 - Oct 19

  • 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 22 - Oct 26

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

Week 9: Oct 29 - Nov 2

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

Week 10: Nov 5 - Nov 9

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

Week11: Nov 12 - Nov 16

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

Week 12: Nov 19 - 23

  • Operations of a Group on itself
  • Brainstorming and Catchup Session
  • No Class (THANKSGIVING)
  • No Class (THANKSGIVING)
    • Assign: Problem Set 11

Week 13: Nov 26 - Nov 30

  • Group Operations on Subsets
  • An Example: Class Equation of Icosahedral group
  • -
  • Sylow Theorems
    • No Assignment

Week 14: Dec 3 - Dec 7

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

Week 15: Dec 10 - Dec 14

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