# CSS.101.1 Mathematical Foundations for Systems Sciences

## Semester:

• 2021 Autumn/Monsoon (Aug - Dec)
• Linear Algebra
• Vector Spaces, Finite-Dimensional Vector Spaces, Linear Maps, Polynomials, Eigenvalues, Eigenvectors, and Invariant Subspaces, Inner Product Spaces, Operators on Inner Product Spaces, Operators on Complex Vector Spaces, Trace and Determinant
•  Analysis
•  Metric spaces, Continuous functions on metric spaces, Uniform convergence, Power series, Fourier series, Several Variable Differential Calculus, Lebesgue measure,Lebesgue integration

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