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

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Schedule

There are no classes currently scheduled.

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AoPS Holidays

There are no classes May 23–25, July 3–5, September 5–7, and December 21–January 3.

Lessons

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

This was the best and most enjoyable math course I have ever taken (and this is coming from an engineering major who sat through a lot of math/engineering classes). I had never learned geometry well back in high school and was only really good at the Pythagorean theorem/SAT geometry type stuff, so I really wanted to finally address this weak area of mine. Needless to say, this course went above and beyond my expectations. I have learned so much that I can now solve almost any Alcumus geometry problem, as well as most AMC geometry problems I've encountered, where just 5 months ago I could barely do any slightly tricky geometry problem.

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