Powers and Roots: Definitions and Properties

Explains the independence of events and sets in an algebraic context.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

Covers the polar form of complex numbers and its applications in mathematical calculations.

Covers antiderivatives, fundamental theorems, integration techniques, and rational functions.