Daily Reel

Name says it all.

• • Day 1 (Monday)

    • Basic definitions: group/subgroup, abelian/nonabelian.

    • Examples: ((Z/NZ), +), (M_2(R), +), ((Z/2Z) x (Z/2Z), +), ((Z/NZ)^x, *)

    • Order of a group. Order of an element in a group.

    • Think about how to prove two groups are "the same": (Z/4Z) and (Z/2Z) x (Z/2Z) are different. But ((Z/2Z), +) and ((Z/3Z)^x, *) are the same. Why?

  • Day 2 (Wednesday)

    • Definition of isomorphism/homomorphism.

    • "Deep analysis" of dihedral groups.

    • Start of discussion on symmetric groups.

  • Day 3 (Friday)

    • Deeper discussion of symmetric groups. Transpositions/disjoint-cycles

    • Basics about groups (think axiomatic-level proofs).

  • Day 4 (Wednesday)

    • Matrix groups: GL_n(F), SL_n(F)

    • Homomorphisms: in particular, the determinant map

    • Kernel of a homomorphism.