Representation Theory: We define equivalence of representations and give examples of irreducible representations for groups of low order. Then we use the commutator subgroup to characterize all one dimensional representations of G (characters) in terms of the abelianization of G.
Doctor Bob provides 18 short video lectures on the introduction to representation theory. 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.