Math 4164 Course Outline

Week 1: Vector spaces, examples, elementary theorems, subspaces, spanning sets
Week 2: Spanning sets, linear independence, bases
Week 3: Dimension, linear transformations, rank/nullity
Week 4: Matrix representations
Week 5: Invertibility, change of coordinates
Week 6: Determinants, eigenvalues
Week 7: Review, first test
Week 8: Diagonalizability
Week 9: Direct sums, Cayley-Hamilton theorem
Week 10: Inner products, norms, Cauchy-Schwarz theorem
Week 11: Projection and the Gram-Schmidt process
Week 12: Orthogonal complements, adjoint of linear operators, normal and self-adjoint
operators
Week 13: Orthogonal diagonalizability
Week 14: Review, second test
Week 15: Projection, spectral theorem