Class meets Monday & Wednesday, 75 minutes per session.
Important Dates¶
First day of classes: Thursday, January 29
Presidents’ Day (no class): Monday, February 16
Thursday, February 19: Monday schedule followed
Spring recess: March 15–22
Patriots’ Day (no class): Monday, April 20
Friday, April 24: Monday schedule followed
Last day of classes: Friday, May 8
Final exams: May 11–15
Schedule¶
| # | Date | Day | Topic | Notes |
|---|---|---|---|---|
| 1 | Feb 2 | Mon | Approximation Theory - Taylor’s theorem with remainder | |
| 2 | Feb 4 | Wed | Finite Differences | |
| 3 | Feb 9 | Mon | Error & Stability - Floating point | |
| 4 | Feb 11 | Wed | Condition Numbers | |
| 5 | Feb 18 | Wed | Fast-Inverse Square Root | |
| 6 | Feb 19 | Thu | ODEs Forward Euler Method Quiz 1 | Mon schedule |
| 7 | Feb 23 | Mon | Snow-day | |
| 8 | Feb 25 | Wed | Stability of Euler’s method | |
| 9 | Mar 2 | Mon | Nonlinear Equations - Bisection | |
| 10 | Mar 4 | Wed | Euler-Maruyama | |
| 11 | Mar 9 | Mon | Nonlinear Equations - Bisection | |
| 12 | Mar 11 | Wed | Fixed Point Methods + Quiz 2 | |
| Mar 15-22 | SPRING BREAK | |||
| 13 | Mar 23 | Mon | QR & Least Squares - Norms, conditioning | |
| 14 | Mar 25 | Wed | Orthogonality, Gram-Schmidt | |
| 15 | Mar 30 | Mon | QR factorization | |
| 16 | Apr 1 | Wed | Least squares via QR | |
| 17 | Apr 6 | Mon | TBD | |
| 18 | Apr 8 | Wed | SVD, pseudo-inverse, low-rank approximation + Quiz 3 | |
| 19 | Apr 13 | Mon | Interpolation - Lagrange | |
| 20 | Apr 15 | Wed | Chebyshev polynomials | |
| 21 | Apr 22 | Wed | Values ↔ coefficients, FFT | |
| 22 | Apr 24 | Fri | Calculus using polynomials | Mon schedule |
| 23 | Apr 27 | Mon | Spectral accuracy & Gibbs | |
| 24 | Apr 29 | Wed | Neural Networks - Universal approximation + Quiz 4 | |
| 25 | May 4 | Mon | Barron spaces | |
| 26 | May 6 | Wed | Deep networks | |
| May 11-15 | FINAL EXAM |
Topic Summary¶
| Topic | Classes | Content |
|---|---|---|
| Approximation Theory | 3 | Taylor’s theorem, finite differences |
| Error & Stability | 3 | Floating point, forward/backward error, condition numbers |
| ODEs | 2 | Euler’s method, Euler-Maruyama |
| Nonlinear Equations | 3 | Bisection, fixed-point, Newton, convergence analysis |
| QR, Least Squares & SVD | 6 | Norms, Gram-Schmidt, QR, least squares, TBD, SVD |
| Interpolation | 5 | Lagrange, Chebyshev, FFT, calculus via polynomials, spectral accuracy |
| Neural Networks | 3 | Universal approximation, Barron spaces, deep networks |
Assessment¶
Quizzes (4): 15-20 minutes at end of class, checking homework understanding
Final Exam: During finals week (May 11-15)