Do You Really Grok It?

This is a new one for me. This is meant to provide slightly more challenging problems (or perhaps, better stated: more unifying problems) than those typically seen in the homework. Going through these problems is completely optional, and I cannot say how many there will be throughout the semester. However, you are more than welcome to talk to me about any of the material in these, and they certainly will help deepen your understanding of algebra.

NOTE: THESE MAY NOT GO IN ORDER OF OUR LECTURES. THE ORDER IS BASED SOLELY ON WHAT I'M THINKING ABOUT.

• Grok It #1 (showing groups are isomorphic)

• Grok It #2 (finite index subgroups and modular forms)

• Grok It #3 (Automorphism groups of (Z/pZ))

• Grok It #4 (Intro to Algebraic Geometry--requires ring theory)

• Grok It #5 (Why the A in A_n stands for Alternating)

• Grok It #6 (Power Sets as Boolean Rings)

• Grok It #7 (Quaternions--as rotations, and as number theoretic objects)

• Grok It #8 (An example of a PID that is not an ED--really, just showing that it's not an ED)