I will assume that you studied Math 340 or Math 341.
The main source for the course are the lecture notes.
Topics to be covered:
2) Dual Spaces, Quotient Spaces, Tensor Spaces.
3) Invariant Subspaces and Diagonalization.
4) Inner Product Spaces, Spectral Theorem.
5) Quadratic Forms.
6) Canonical Forms.
7) Groups, Rotations, and Symmetries of Platonic Solids
8) Basics of Representation Theory of Finite Groups.
9) Possibles Projects and Presentations in Mathematics.
You are welcome!
Dr. Shamgar Gurevich,