Math 31
Topics in Algebra

Resources

Below are links to various documents and resources for the course.

Resources on proof-writing:

• Introduction to mathematical arguments by Michael Hutchings
• Book of Proof by Richard Hammack

About Cayley diagrams:

• Visual Group Theory: Cayley graphs is a video that discuss Cayley diagrams by thinking of generators of groups as actions (flip, turn, etc.) that can be applied to group elements to reach all the different states (horizontal, up/down, solved).

Strategy for building a Cayley diagram for a group G:

1. Identify a set of generators for G. Assign to each a type of arrow (solid line, dotted line, red, green, etc.)
2. Start by writing the identity element.
3. Multiply the identity element by each generator. Draw the corresponding type of arrow from the identity to the result of the multiplication.
4. Multiply each result by each generator. Draw the corresponding type of arrow from each element to the result of the multiplication.
5. Repeat Step 4 until all group elements are listed.

Note: Every group element should show up in the end, and you should have an arrow of each type leaving each group element.