Coursework

Convex Optimization

The graduate convex optimization sequence at Berkeley (EE 227B and EE 227C). For EE 227B I worked on a survey of semidefinite programming relaxations of constraint satisfaction problems, with an emphasis on some algorithms which are best-possible if the Unique Games Conjecture is true (and P =/= NP). That report can be found here. For EE 227C, I implemented the aforementioned algorithms (to the extent possible) in Matlab, and tested them along with a natural heuristic generalization of Goemans-Williamson algorithm for max cut. This second report is significantly less polished than the first, but can nevertheless be found here. Code from the second report is available here. Even if you aren’t interested in the rounding schemes described in the report, the code is of use for generating the constraint matrices for the “standard” SDP relaxation of CSPs. Solving such SDPs is a nice way to test performance of SDP algorithms at scale.

Fall 2016 @ Caltech: graduate convex optimization.

Probability and Statistics

The standard undergraduate sequence in probability and statistics for Berkeley IEOR. Graduate level applied stochastic processes and queueing theory (IEOR 263A and IEOR 267). I incorporated the project for queueing theory into my undergraduate senior project, which involved scheduling ambulances for the San Francisco Fire Department. The slides for the queueing theory final project (and hence the stochastic processes component of the ambulance scheduling project) can be found here.

Fall 2016 @ Caltech: graduate stochastic processes.

Graph Theory and Discrete Algorithms

Undergraduate data structures, and algorithms for computational biology. Graduate level graph algorithms and graph theory (IEOR 266). I completed three large projects for the data structures course, but [former] students are not allowed to publicly post their submissions. The graph theory course was mostly theoretical, and introduced ideas such as NP-Completeness, reductions, and approximation algorithms.

Systems and Control Theory

Undergraduate signals and systems, with proof-based mathematics (univariate systems and signals) and computational work in Matlab (univariate and multivariate).  Covered mathematics of multivariate LTI systems (stability, observability, model predictive control) in IEOR 265 at Berkeley.

Operations Research Methods and Application Areas

Linear programming. Integer programming. Semiconductor manufacturing. Service systems design and analysis. Discrete event simulation. My course project for discrete event simulation was simulating stability of an Uber-esque transport system.

Pure Mathematics

Linear algebra and real analysis at Berkeley (upper division, Math 110 and Math 104).

Fall 2016 @ Caltech: undergraduate abstract algebra and graduate linear algebra.