This class uses ChatGPT in instruction (in mostly non-essential, education enhancing ways).

- Automatic differentiation MATLAB style implemented in Python and C++
- Rounding modes in Python and C
- Reading and printing float32 numbers in Python, round-trip serialization
- Extended precision and accessing it from user code

- Image (signal) restoration 1D - problem formulation, subgradient, comparing methods using MSE, PSNR.
- A derivation of Euler-Lagrange equation
- Commentary on a fatal (in my book) flaw of Python - GIL
- Image restoration 2D - Rudin, Osher, and Fatemi paper; derivation of the fundamental equation.
- Iterative methods for Ax=b - basic descriptions and suggestions of further inquiries.
- Hyperbolic space in dimension 2
- Geodesics derivation in Riemannian Geometry - a demonstration of tensor calculus and Euler-Lagrange approach. Includes the reparameterization argument.
- The theory of connections - a deeper dive into differential geometry. Equation to calculate parallel translation on a manifold. Explanation why Levi-Civita connection is the unique torsion-free connection satisfying natural axioms, thus the "right way" to move vectors around on a curved space. Derivation of gradient.

- Handling Neumann boundary conditions with a circular domain - contains ideas for 'Programming Assignment 3'.
- An exact Helmholtz equation problem - a mostly failed attempt to get ChatGPT to solve $u-f-\lambda\nabla^2u=0$ subject to $\partial u/\partial n=0$, where $f(x,y):=x^2$.
- Newton and Stirling iterated finite difference formulas - a summary of useful formulas to incorporate in a difference scheme.
- 2D Newton-like difference formulas - show how to approximate in 2D using iterated differences.
- Solution of homogeneous Helmholtz with Dirichlet boundary conditions - helpful in proving necessity of the Neuman boundary problem: $(u-f)-\lambda\nabla^2u=0$, $\frac{\partial u}{\partial n}|_{\partial D}=0$ in the image smoothing problem.
- Solution to Helmholtz equation with Neumann BC - one way to solve the problem $\nabla^2u-u = x^2$.
- Series solution to a variant of Bessel equation - the method of Frobenius.
- A bump function argument - Extending $C^\infty$ function on the boundary of the unit disk to the unit disk.
- Another version of the bump function argument - This was done with ChatGPT 3.5.
- Converse of Taylor series, Whitney Extension Theorem - definining functions starting from Taylor series.
- An evaluation of a solution strategy for the Helmholtz equation on the disk - a somewhat tortured chat on the subject.

- Linear Quadratic Regulator (LQR) and The Algebraic Ricatti Equation (ARE) - Formulation of A derivation of ARE from HJB.
- A derivation of PMP = Pontryagin Maximum Principle - a simplified version incorporating the dynamics into the cost function.

- Broyden" s "Good" Algorith - an example of a quasi-Newton method without explicit Jacobian calculation.
- A 2-variable example of Broyden Good Algorithm