Introduction to Group Theory: As devices for measuring symmetry, groups occupy a central role in several areas of mathematics. This course begins with the definition of a group and finishes with the Sylow Theorems for finite groups and the Fundamental Theorem of Finite Abelian Groups. Emphasis is placed on teaching through examples.
- no lectures added
To do the problem sets: some proofs, but heavy on example-oriented problems. For those looking for a more functional and less theoretical understanding of finite groups, the basics of integers and primes should be enough.
To follow the lectures: Basic knowledge of proofs, set theory, and the integers. The focus will be on finite groups, with the occasional infinite example. Most linear algebra exercises are labeled advanced; we use mostly 2x2 matrices, with occasional 3x3 cases.
Base list: Sets, bijections/one-one correspondences, equivalence relations, and equivalence classes. Factorization of integers into primes. A video playlist for the prerequisites can be found here.
Office Hours: I'll be running the course out of the subreddit GroupTheory2012. Questions and comments can be posted there.
Videos: The complete video list is available in the Abstract Algebra section, GT series at mathdoctorbob.org.
Book: I'm using Herstein's Topics in Algebra for an outline. He doesn't do group actions, and it is not a great book for beginners. I'm a big fan of Schaum's Outlines for beginners. Dixon's Problems in Group Theory is also affordable with many solved problems.
This is a video course with supplemental problem sets. The 30+ videos are already shot and available through the above links. Although the class is finished, I will keep an eye out for questions or comments.
Prerequisite videos are available as noted above.
(Bob Donley) I'm an ex-academic with over a decade of teaching experience. My research area is the representation theory of semisimple Lie groups. As a grad student and a postdoc, one of my specialties was running problem sessions to help PhD students get through quals. I've been cited twice by students as a most influential professor.