Group Theory Seminar Online Math Course

Group Theory Seminar

This 7-week seminar is an introduction to the basics of group theory. In this seminar we will focus on defining and understanding groups: how they are constructed and how they interact with the rest of the world. This seminar is not intended to be a complete group theory course (which is a core component of a college undergraduate mathematics curriculum), but rather is intended to give strong high school students a first look at the most important concepts and examples of this very vast subject.

7 weeks


7 weeks ARE YOU READY?  


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AoPS Holidays

There are no classes September 5–7, November 23–29, and December 21–January 3.


Lesson 1 Symmetry
Lesson 2 Examples of Groups
Lesson 3 Cyclic Groups
Lesson 4 Abelian Groups
Lesson 5 Group Actions
Lesson 6 Orbits and Burnside
Lesson 7 Polya Counting and Cayley Graphs

I really enjoyed this class. While taking WOOT, I learned about several interesting areas that I had not previously studied, including functional equations, generating functions, vectors/complex numbers, and convexity. The feedback from the practice Olympiads was useful in that it told me exactly where my solutions failed so I could investigate how to fix them. However, I feel that the most valuable aspect of this class was the problems. WOOT had few problems that could be solved immediately with a standard procedure; instead, the problems took some time to solve, challenging me to consider many solution methods before I found the one that worked.

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