ESP Biography
JAMES CAMACHO, MIT student focused on math & cs.
Major: 64 College/Employer: MIT Year of Graduation: 2024 

Brief Biographical Sketch:
James Camacho believes everything made sense to somebody, and wants more things to make sense to more bodies. Past Classes(Clicking a class title will bring you to the course's section of the corresponding course catalog)M15911: Numerical Methods: Solving Equations w/ Computers in HSSP Spring 2024 (Mar. 02, 2024)
Most problems cannot be computed exactly, and even those that can might be very expensive. Numerical methods try to find good enough approximations efficiently.
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Tentative Schedule:
1. The derivative, fixed point iteration, Newtonâ€™s method, Euler, RungeKutta, and multistep methods.
2. Quadrature a.k.a. numerical integration, finite difference methods and correctors.
3. Linear differential equations, matrix fundamentals, the QR algorithm, Newtonlike methods, stiffness.
4. Finite element methods, various bases, Fourier/DCT transforms, Fourier analysis (faster solvers), Fourier analysis (stability).
5. Optimization: Binary and goldensection search, the simplex method, gradient descent, conjugate gradient descent, and Adam.
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Class website: https://programjames.github.io/hsspspringnumericalmethods/
C15794: Steering Large Language Models in Splash 2023 (Nov. 18  19, 2023)
Learn how to manipulate the inner activations of a neural network to generate text in different styles.
C15795: Computers: From NAND Gates to Assembly in Splash 2023 (Nov. 18  19, 2023)
An overview of the modern computer. Why are semiconductors so dope? What's the obsession with flipflops? How do bits and bytes become programs? Learn here!
M15488: Numerical Methods in HSSP Spring 2023 (Feb. 25, 2023)
Solving integrals is hard, wouldn't it be better to get a computer to do that for you? Here we explore numerical methods, beginning at "What is a derivative? (20 min. edition)" and using that answer to solve impossible problems quickly and accurately.
Lecture schedule (tentative):
1. The derivative, fixed point iteration, Newton's, Euler & RungeKutta methods.
2. GaussLegendre quadrature, solving PDE's (e.g. heat equation). Finite difference methods & correctors.
3. Matrices: finding eigenvalues/vectors, Broyden's method, condition number & stiffness. Common bases and their condition numbers (i.e. why polynomials are bad).
4. Finite element methods w/ Chebyshev polynomials or sines/cosines. Fourier/DCT transforms, Fourier analysis (faster solvers) & Fourier analysis (determining convergence rate).
5. Optimization: golden section, simplex, gradient descent, conjugate gradient method, Adam.
6. Different ideas, maybe a combination of them: Image recognition w/ Bayes' theorem, the Lagrangian w/ the simplex method, image compression w/ principal component analysis.
