Group representations are where group theory meets linear algebra, and important applications arise in various math subjects (number theory, analysis, algebraic geometry), physics, and chemistry.
We consider the basic representation theory of finite groups. Goals include a look at Fourier series/analysis using groups and elementary character theory.
Category theory is a branch of mathematics that emerged in the 1950s to understand how the different areas of mathematics relate to each other. Today, its influence pervades nearly all of mathematics, in addition to being an important area of study in its own right. This course will cover the basic concepts of category theory, with an emphasis on intuition and examples.
I really enjoyed Modern Algebra, so much so that I decided to make a lecture series explaining all the different topics via examples, proofs, and fun pieces of insight.
This course will cover what is normally covered in two full years of Algebra 1 & Algebra 2. This course will prepare you very well for pre-calculus and topics later on.