Visual Group Theory

This course contains over 40 videos from my undergraduate Abstract Algebra course (Math 4120) at Clemson University. I first taught it in 2010, using Nathan Carter's wonderful book, "Visual Group Theory", which had just been published. Though I love this book, its target audience is below that of an undergraduate abstract algebra course. Thus, I had to supplement it both with content and rigor. After teaching it 4 times during the academic year, the material developed and converged into its present form, which I'm very pleased with.

Examples of topics in this coruse that don't appear in the VGT bok include group presentations, the 2nd 3rd and 4th isomorphism theorems, commutator subgroups, finitely generated abelian groups, finite simple groups, ruler & compass constructions, finite fields, ring theory, and divisibility and factorization. In the end, I suspect that there are very few undergraduate abstract algebra classes that cover this much material.

I love the Visual Group Theory (VGT) approach of introducing the concept of a group first using the Rubik's cube, and then Cayley diagrams, the latter of which is a common theme throughout the course. This allows students to understand the concept of group theory, and see the beauty of this incredible subject. Unfortunately, this is often lost on students in a standard algebra class when most of the examples involve modular arithmetic or permutations.

A common misconception is that the Visual Group Theory approach means that the class is easier or less rigorous. I promise that this is NOT the case. That said, what IS true is that the first 10 or so videos should be widely accessible to people without much math background, such as high school students, art or music majors -- as long as they can think critically and abstractly. Some of the details of the proofs might be lost on them, but they should still be able to understand the main ideas.

I made a course webpage, where I make all content freely available. With each lecture, I post the slides. Additionally, you can find the homework assignments (pdf and LaTeX) for my class, as well as previous exams for practice. It should be very conducive to self-study. Good luck, and I hope you enjoy learning this beautiful areas of mathematics!

http://www.math.clemson.edu/~macaule/math4120-online.html
This course contains over 40 videos from my undergraduate Abstract Algebra course (Math 4120) at Clemson University. I first taught it in 2010, using Nathan Carter's wonderful book, "Visual Group Theory", which had just been publishe...