John Kerl Software engineer Mathematician Writer kerl.john.r@gmail.com

• Resumé, software repositories at GitHub, LinkedIn, Google+, blog.
  
• Lecture notes
• Documents
  Formal papers:
  • Doctoral dissertation, March 2010: Critical behavior for the model of random spatial permutations. PDF format, PostScript format, DVI format.
    Frontmatter, Chapter 1: Scientific context, Chapter 2: The model of random spatial permutations, Chapter 3: Random variables, Chapter 4: Markov chain Monte Carlo methods, Chapter 5: The swap-only and swap-and-reverse algorithms, Chapter 6: Band updates, Chapter 7: The worm algorithm, Chapter 8: Delta H computations, Chapter 9: Algorithms for single MCMC runs, Chapter 10: Batching of MCMC runs, Chapter 11: Results, Chapter 12: Future work, Appendix A: Bose-gas derivation of random permutations, Appendix B: Error bars, autocorrelation, and batched means, Backmatter.
  • Dissertation appendix: Notes on exponentially correlated stationary Markov processes.
  • Preprint of proceedings note for the Center for Simulational Physics at the University of Georgia: A worm algorithm for random spatial permutations. The final publication is available in Volume 4, 2010, of Physics Procedia.
  • Preprint of condensed version of dissertation, submitted to Journal of Statistical Physics (December 2009): Shift in critical temperature for random permutations with cycle weights. arXiv:0912.4292 [cond-mat.stat-mech]; local copy. The final publication is available at www.springerlink.com.
  • French language examination: original paper, my translation.
  • Written comprehensive examination paper: Remarks on interacting spatial permutations and the Bose gas (January 2009).
  • Master’s thesis (May 2005): Curves and Codes.
  Expository mathematical papers :
  • Is 2 a random number?
  • The Metropolis-Hastings algorithm by example
  • The Householder transformation, Swiss Army knife of numerical linear algebra
  • Computation in finite fields
  • Concrete abstract algebra in Python
  • Quantum mechanics for math grads
  • An introduction to coding theory for mathematics students
  Course notes:
  • Probability (Math 564, spring 2007).
  • Probability and statistics (Math 564 spring 2007 and Math 567A spring 2008): under construction.
  • Geometry/topology (Math 534A-B, 2005-2006).
  Notes for qualifier preparation (all perpetually under construction):
  • Geometry/topology qual solutions.
  • Complex analysis.
  • Real analysis.
  • Abstract algebra.
  Course/project papers:
  • Project on Berlekamp’s algorithm for incoming graduate students, fall 2009 integration workshop.
  • Some problems in stochastic differential equations (Math 565C, spring 2008): problems and figures. Source code: Brownian motion and bridges with statistical verification, textual output, and graphical output; 2D bridges with graphical output. Damped Brownian motion, Brownian motion on an ellipse, noisy exponential growth, noisy exponential decay, Brownian bridges one way, Brownian bridges another way, complex Brownian motion, exponential growth with multiple noise sources, first martingale problem, second martingale problem, mean-reverting Ornstein-Uhlenbeck process, stochastically forced vibrating string, Feynman-Kac formula.
  • Final project for Theoretical Statistics (Math 567A, spring 2008): paper, source code.
  • Fall 2006 RTG paper: The Discrete Berezin Integral.
  • Poisson summation and the discrete Fourier transform (spring 2006): Math 523B term paper, slides.
  • The DFT and the FFT.
  • Some examples of Fourier approximation, with nice plots.
  Elementary write-ups:
  • Getting hit by lightning ... in the long run.
  • Choice of base in exponential models.
  • Mathematical induction.
  • The cubic formula.
  • Derivation of the sum and differences formulas for sine and cosine.
  • The gamma integral formula.
  • How to manually compute a square root.
  • What’s the difference between probability and statistics?
  • An argument-settling (?) approach to the Monty Hall problem
  HTML:
  • Notes for SWIG talk on Web-page design.
  • Template home-page file (all in one file), instructions.
  • Second template home-page file (uses multiple files), one file you need, another file you need.
  • HTML quick reference, brief introduction to HTML.
  LaTeX:
  • Template PhD dissertation, tar file.
  • Template file for using figures in LaTeX, tar file.
  • Template Beamer presentation with included EPS figure and PDF as output: PDF, main .tex file, auxiliary .tex file, DVI build info, PDF build info, tar file.
  • Template paper with abstract, table of contents, appendices, bibliography, and index, with hyperlinked PDF as output: PDF, tar file. The build script requires kmkidx, which you should download and put in your path.
  • Template quiz file, LaTeX source.
  • A blank template homework file: template.tex, template.pdf.
  • Calculus I exams from spring 2007: Instructions, tar file.
  • A quick how-to for typing up homework in LaTeX: sample.pdf. Source files: sample.tex, isomath.tex, mathenv.tex (download all three).
  • ASU math dept. LaTeX info, Cambridge eng. dept. LaTeX info.
  Typesetting misc.:
  • A table of some special characters in Windows.
  Software misc.:
  • .vimrc (an initialization file for the vim text editor).
  • How to use the Unix command-line mail tool (and you thought Pine was old-fashioned ...)
  • A simple introduction to the make utility
  • A table of the C language’s operator precedence
  • How to do a sprintf in Python: sprintf.html.
  • A reminder for various shell-script syntax
  • A short course in linking and loading
  Rubik’s cube:
  • How to solve the Rubik’s cube (Nourse method), one-face-moves, threefold moves, same, with more verbage.
  Miscellaneous (pre-grad school):
  • DDA scaling and shifting formulae.
• Software
• Research
• Teaching
• Background
  • Resumé
  • Research statement (2010)
  • Teaching statement (2010)
  • PhD coursework (2005-2010)
  • Alma mater: PhD program, Department of Mathematics, University of Arizona.
• Personal
• About this site

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