Mathematics 402A        Autumn 2004

Material covered:

• Wednesday, September 29. Started Section 2.1 in Artin: laws of composition, associativity.
• Friday, October 1. More on 2.1: identity elements, inverses, and groups.
• Monday, October 4. Started Section 2.2: subgroups.
• Wednesday, October 6. Finished Section 2.2. Defined "homomorphism".
• Friday, October 8. More on Sections 2.3 and 2.4: isomorphisms and homomorphisms.
• Monday, October 11. Examples of homomorphisms, kernels, images.
• Wednesday, October 13. Miscellany: properties of kernels, normal subgroups, centers.
• Friday, October 15. Section 2.5: Equivalence relations, partitions, congruence.
• Monday, October 18. Mostly discussed homework. More on congruence, cosets.
• Wednesday, October 20. More on cosets. Lagrange's theorem, classification of groups of prime order, groups of order 4.
• Friday, October 22. More on cosets. Started discussing products of groups.
• Monday, October 25. More on products.
• Wednesday, October 27. Finished products. Started modular arithmetic.
• Friday, October 29. More on modular arithmetic: Fermat's little theorem.
• Monday, November 1. Small group discussions of miniportfolios.
• Wednesday, November 3. Quotient groups.
• Friday, November 5. Quotient groups, the first isomorphism theorem.
• Monday, November 8. Midterm.
• Wednesday, November 10. Symmetries, rigid motions (Sections 5.1 and 5.2).
• Friday, November 12. More on rigid motions.
• Monday, November 15. More on rigid motions: finished Section 5.2
• Wednesday, November 17. Finite groups of motion (Section 5.3).
• Friday, November 19. Started discussing discrete groups of motion.
• Monday, November 22. More on discrete groups of motion.
• Wednesday, November 24. More on discrete groups of motion.
• Monday, November 29. Discussed portfolio problems.
• Wednesday, December 1. Group actions, orbits, stabilizers.
• Friday, December 3. The "Counting formula" from section 5.7, and applications to counting rotational symmetries of three-dimensional figures.
• Monday, December 6. The "Class Equation" from section 6.1.
• Wednesday, December 8. Finished section 6.1. Started discussing the problem of classifying groups, and stated the Sylow theorems.
• Friday, December 10. Discussed applications of the Sylow theorems.

       John Palmieri    Padelford C-538    (206) 543-1785    email    web page