Teaching experience
Currently at Colorado State, I'm teaching:
• Projects in Applied Mathematics (Spring 2019)
• Introduction to Numerical Analysis (Fall 2018)
During my graduate studies at UNC Chapel Hill, I was the instructor of record for a wide range of classes, including:
• Precalculus
• Introduction to Mathematical Modeling (for non-mathematicians)
• Calculus 1 (single variable, up to the fundamental theorem)
• Calculus 3 (multivariable calculus, up to the divergence theorem)
• Advanced Calculus (mostly following Abbot)
• Numerical Analysis (loosely following Kincaid & Cheney)
I've also helped write worksheets and curriculum for programs aimed at advanced high-schoolers covering non-traditional material:
• Duke TIP; this was an introduction to programming in Matlab, with applications to fractals, self-similarity, chaos and difference equations, etc. For example, students could generate their own Koch-snowflake like fractals using Logo-like instructions around a skeleton code I wrote in Matlab.
• Girls Talk Math; here I wrote a module going in depth about the Mandelbrot set, and guiding them to write their own code from scratch in Mathematica to visualize it.
I'm happy to discuss or share materials from most of these courses; feel free to send me an email.
Gallery
This is a collection of some of the images and interactive visualizations I've produced as a part of my teaching.
1. Portion of the Mandebrot fractal. Brightness corresponds to number of iterations before escape, with a cutoff. Students could go through worksheets towards building the algorithm themself, or just modify parameters, colormap, etc of a finished product. (Used in Duke TIP and Girls Talk Math)
2. Iterative generation of a Koch snowflake using recursive "turtle"-style graphics. These are instructions such as "go forward 2 units," "turn left 30 degrees," "turn right 45 degrees," etc. (Used in Duke TIP)
3. Visualization of the action of matrices in two dimensions. The first figure illustrates the concept of singular value decomposition (rotate, scale, rotate) by coloring the points in the domain by their initial angle. The second figure shows the geometric interpretation of the matrix 2-norm as the length of the semimajor axis of the map of the unit ball. The matrix condition number is the product of these semimajor axes under the forward map Ax and the inverse map A-1x. (Used in Numerical Analysis)
4. Blood-Alcohol content model, where the value follows an exponential decay law (alcohol decays with a half-life in the model). The students could specify what kind of drink(s) to have, and when, by modifying an Excel file and seeing the resulting graph. (Used in Introduction to Mathematical Modeling; for non-math majors)
5. Visualization of Newton's method for finding the root of a function, where arrows follow the tangent line to its zero, then back to the function at that value, visualized similar to a cobweb plot. The user can modify the function, intial guess, and number of iterations. Useful for seeing when things go right, and peculiar functions where things go very wrong. (Used in Calculus 1; Numerical Analysis)
6. Visualization of a two-dimensional Riemann sum. Included capability to change number of rectangles on the fly to demonstrate convergence to the double integral. (Used in Calculus 3)
7. Demonstration of a parameterized surface (u(θ,φ), v(θ,φ), w(θ,φ)), where fixed θ correspond to parameterized ellipses, and fixed φ correspond to helices. Sliders in the demonstration change the values of θ and φ and highlight the corresponding portions of the surface (Used in Calculus 3)