Notes

Below is a collection of notes from various coursework and self-study. These notes are taken either live during lecture or during my free-time, so they are very prone to mistakes. Feel free to reach out with any questions or corrections.

Illinois

• MATH 447: Real Variables
  metric spaces, compactness, connectedness, uniform continuity, \(C(K)\) completeness, dini's theorem, differentiation, integration, fundamental theorem, power series
• MATH 466: Applied Random Processes
  discrete/continuous-time markov chains, recurrence, invariant distributions, kolmogorov equations, martingales, brownian motion, queueing, mcmc, population models.
• ECE 498: Quantum Information Processing Theory
  quantum states, operators, \(\text{SU}(2)\), tensor products, entanglement, unitary evolution, projective measurements, density matrices,\( \text{CPTP}\) maps, kraus operators, quantum channels, error correction, \(\text{POVMs}\), \(\text{LOCC}\), teleportation, entanglement measures and distillation