Textbooks: Axler, "Linear Algebra done right" and Tao, "Analysis II."

Syllabus

1 Vector Spaces 2 Finite-Dimensional Vector Spaces 3 Linear Maps 4 Polynomials 5 Eigenvalues, Eigenvectors, and Invariant Subspaces 6 Inner Product Spaces 7 Operators on Inner Product Spaces 8 Operators on Complex Vector Spaces 9 Trace and Determinant 10 Metric spaces 11 Continuous functions on metric spaces 12 Uniform convergence 13 Power series 14 Fourier series 15 Several Variable Differential Calculus 16 Lebesgue measure 17 Lebesgue integration