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

self-study

• illinois, cs 598 evs: tensor computations
  tensor contractions, decompositions (cp/tucker/tt), network states (mps/peps), optimization and sparse kernels, tensor eigenvalues, diagrammatic notation, quantum simulation, electronic structure, hypergraph partitioning