Past Courses

  • 2017
    • Fall: Calculus with Apps (Math 11A - UCSC).
      Topics: the first quarter of the calculus sequence.
    • Spring: Complex Analysis (graduate) (Math 207A - UCSC)
    • Winter: Real Analysis (Math 105A - UCSC).
      Topics: Chapters 1 through 6 of Strichartz' "The way of Analysis".
    • Winter: Partial Differential Equations I (graduate) (Math 213A - UCSC).
      Topics: Laplace, heat and wave equations, studied using various techniques: classical solutions, potential theory, distributions and Fourier analysis, stationary phase, weak formulations, L2 Sobolev spaces and other Hilbert space methods.
  • 2016
    • Winter: Introductory Differential Equations (Math 216, two sections, U. Michigan) - (Course website). Additional material specific to the sections I taught available here.
  • 2015
    • Winter: Complex Analysis II (Math 428 A, U. Washington) - Course website.
      Draft of lecture notes here. (topics similar to Winter '14)
    • Winter: Introductory Real Analysis I (Math 327 B, U. Washington) - Course website.
      (topics similar to Autumn '13)
  • 2014
    • Summer: Introductory Real Analysis II (Math 328 B, U. Washington) - Course website
      Topics: power series, continuity, uniform continuity, theory of integration, improper integrals, the Gamma function, Stirling's formula. Emphasis on proofs.
    • Summer: Seminar in Analysis (Math 530 C, U. Washington)
      Preparatory problem-solving sessions for graduate students toward taking the "Linear Analysis" Preliminary Exam. Topics: distributions, linear algebra, spectral theory, Fourier analysis, numerical methods for ODEs.
    • Summer: Special Lecture on math and origami, taught at SIMUW 2014 and at the 2014 discovery seminar on "Left brain, right brain: creative thinking in the sciences and in the arts.". Slides (Warning: 47MB file).
    • Winter: Complex Analysis II (Math 428 A, U. Washington) - Course website
      Topics: Some applications of residues, Rouché's theorem, conformal mappings, linear fractional transformations, Riemann mapping theorem, complex dynamics of rational maps.
  • 2013
    • Autumn: Introductory Real Analysis I (Math 327 A, U. Washington) - Course website
      Topics: sequences of real numbers, limits, point set theory, uniform continuity.
    • Autumn: Complex Analysis I (Math 427 A, U. Washington) - Course website
      Topics: making our way from the algebra of complex numbers to residue theory, omitting no proof.
    • Summer: Computer Labs at MSRI Summer School on "The mathematics of seismic imaging".
    • Summer: Computer Labs at UW RTG IPDE Summer School - Detail of sessions
      Topics: Implementation and inversion of the thermoacoustic tomography problem. Illustration of the principle of propagation of singularities for the wave equation. Generalized X-ray transforms.
  • 2012
    • Autumn: Linear Analysis (Math 309 B&C, U. Washington) - Course website
      Topics: systems of ODE's, solutions to PDE's using Fourier series and separation of variables. Emphasis on problem-solving.
  • 2011
    • Summer '11: Computer Labs at UW RTG IPDE Summer School - Detail of sessions
      Topics: The fast fourier transform. Implementation of the Radon tranform and attenuated Radon transform, and their inversion. Partial data problems. Generalization to other families of integration curves.