This is course 1A in my DIY graduate program, a year-long course on foundational concepts and techniques from mathematical analysis. This will include abstract vector spaces and inner product spaces, metric spaces, manifolds, measures, and integration.
| # | Chapter | HW | Lab |
|---|---|---|---|
| 1 | Abstract Vector Spaces | Notes | - |
| 2 | - | Problem Sets | - |
| 3 | Linear Transformations and Matrices | Notes | Linear Transformations |
| 4 | - | Problem Sets | Linear Systems |
| 5 | Inner Product Spaces | Notes | The QR Decomposition |
| 6 | - | Problem Sets | Least Squares and Computing Eigenvalues |
| 7 | Spectral Theory | Notes | - |
| 8 | - | Problem Sets | Image Segmentation |
| 9 | Metric Space Topology | Notes | - |
| 10 | - | Problem Sets | The SVD and Image Compression |
| 11 | Differentiation | Notes | - |
| 12 | - | Problem Sets | Differentiation |
| 13 | Contraction Mappings and Applications | Notes | - |
| 14 | - | Problem Sets | Newton’s Method |
| 15 | Integration I | Notes | - |
| 16 | - | Problem Sets | Conditioning and Stability |
| 17 | Integration II | Notes | - |
| 18 | - | Problem Sets | Monte Carlo Integration |
| 19 | Calculus on Manifolds | Notes | - |
| 20 | - | Problem Sets | - |
| 21 | Complex Analysis | Notes | - |
| 22 | - | Problem Sets | Visualizing Complex-valued Functions |
| 23 | Spectral Calculus | Notes | - |
| 24 | - | Problem Sets | The PageRank Algorithm |
| 25 | Iterative Methods | Notes | - |
| 26 | - | Problem Sets | Iterative Solvers |
| 27 | Spectra and Pseudospectra | Notes | - |
| 28 | - | Problem Sets | The Drazin Inverse |
| 29 | Rings and Polynomials | Notes | - |
| 30 | - | Problem Sets | GMRES |
Written on: December 1, 2024