Bossy Lobster

A blog by Danny Hermes; musing on tech, mathematics, etc.

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Mathematics

For as long as I can remember, I have had a love of learning math and problem solving. In 7th grade, I participated in my first math competition (MathCounts) and the rest is history.

From August 2013 to August 2018, I spent my time taking classes, teaching and doing research as a graduate student at UC Berkeley. (See my post "Graduated" for a retrospective.) This page is mostly intended as a place to gather some things I made during that time.

Code and Writing:

  • Write-up and some code for generating the "optimal" finite difference stencils to compute a given derivative (November 2013)
  • Discussion of spectral norm as dual to the nuclear norm, in the sense of linear programming. Part of presentation of a paper during student seminar (November 2014)
  • IPython notebook about GMRES (October 2015)
  • Discussion of parametric curves. In particular, how to classify cubics and how implicitization helps with conversion from a parametric curve to an algebraic curve. (April 2016)
  • Math 273 topics course on numerical analysis (GitHub, course ran during Spring 2016)
  • bezier library (GitHub, published in JOSS in August 2017)
  • foreign-fortran project (GitHub, started in Summer 2017, added to readthedocs.org in August 2018)

Papers:

  • Compensated de Casteljau algorithm in K times the working precision (arXiv, GitHub, submitted May 2016 to AMC)
  • A Curious Case of Curbed Condition (arXiv, GitHub, June 2018)
  • UC Berkeley Dissertation (GitHub, submitted August 2018)
  • A 2-Norm Condition Number for Bézier Curve Intersection (arXiv, GitHub, August 2018)

Talks:

  • Butterfly Algorithm for Geometric Non-uniform FFT (slides, GitHub, given February 2015)
  • Paper presentation on WENO survey (slides, given February 2016 in Math 273 topics course)
  • Paper presentation on supermeshing / conservative interpolation (slides, given April 2016 in Math 273 topics course)
  • Thesis talk (slides, given August 2018)

Teaching: