Students will study group-theory questions using the computer algebra system GAP, and learn the underlying algorithms it uses and why they work. For example: what are all the groups of order 16? What are the simple groups of small order? Which groups act transitively on 7 points? What are the transitive actions of the alternating group on 7 letters? Why do these questions matter?
Class time will be approximately 50% lecture and 50% labwork, and there will also be homework and a final project (but no final exam). GAP will be installed on the classroom computers, and students will have access to the math department computer lab. It is freely-available software that runs on all major platforms, so students can also install it on their personal machines. Students are expected to understand the basics of group theory (e.g., actions by permutations, subgroups, normal subgroups); M373K or M343K will be enough. They are also expected to have some experience programming in any language. (GAP is its own language, and I don't assume any experience with it. But I will assume familiarity with using variables, control structures, etc.) In place of a text, I will distribute notes and lab instructions.