Many or most of the articles here are from class notes, projects, or homeworks that I touched up -

Projects Inspired by Classwork

• building fractals by hand Generates the Mandelbrot set by iterating complex numbers and visualizing convergence boundaries — a clean Python implementation with matplotlib.
• the algorithms behind interpolation & splines Implements and compares 1D interpolation methods from scratch: linear, Lagrangian, Newton’s divided differences, and cubic splines.
• numerical analysis of vector fields Phase portraits, nullclines, and stability analysis for nonlinear systems — numerical exploration of how vector fields behave near fixed points.
• chaotic dynamics and strange attractors Homework assignments from a chaotic dynamics course covering strange attractors, bifurcation diagrams, and sensitivity to initial conditions.
• numerical analysis of one dimensional maps Studies the logistic map and other iterative 1D systems to explore period-doubling and chaos; uses Cython to speed up the orbital calculations.
• ordinary differential equation solving with 4th-order Runge-Kutta Implements 4th-order Runge-Kutta from scratch and applies it to several differential equations — method derivation alongside the code.
• the algorithms behind numerical ootfinding Implements and compares bisection, secant, fixed-point iteration, and Newton’s method for finding function roots numerically.

Class Notes

During college I found it especially effective to write my notes by hand and then transcribe to LaTeX as a study method. Later, I sped up enough in my transcriptions to do it live during class and then only writing down the more complex equations to fully convert later.

• Algorithms
• Applied Analysis
• Calculus 2
• Calculus 3
• Complex Analysis
• Computer Systems
• Differential Equations
• Discrete Math
• Fourier
• Intro To AI
• Markov Processes
• Mathematical Statistics
• Matrix Methods
• Numerical Analysis
• Numerical Computation
• Statistical Methods