John Kerl Graduate student Department of Mathematics University of Arizona

E-mail: Phone: Office: Office  hours:

kerl at math dot arizona dot edu (520) 621-1658 MATH 318 by appointment.

• Curriculum vitae
• Employer information
• Research
• Teaching portfolio
• Documents and lecture notes
  Lecture notes for talks:

  Series/conference	Date	Title	Materials
  UA Math Dept. Software Interest Group	Oct. 2009	Python for the working (or aspiring) mathematician	Abstract, slides, hello.py, lorenz.py, plot2.py, projdown.py, tabutil.py, all-in-one.py.
  UA Math Dept. Math. Physics Seminar	Sep. 2009	Critical behavior for the model of random spatial permutations	Abstract, slides.
  UA Math Dept. Graduate Student Colloquium	Aug. 2009	Markov Jabberwocky: fesh, excenture, and the like	Abstract, slides, lay-audience version.
  Stochastic processes and their applications	Jul. 2009	Numerical methods for random spatial permutations	Abstract, slides.
  Workshop on quantum spin systems and applications in quantum computation	Jun. 2009	Lattice quadrupling for percolation in quantum networks	Slides.
  UA Math Dept. comprehensive examination	Jan. 2009	Remarks on interacting spatial permutations and the Bose gas	Paper, slides.
  UA Math Dept. Graduate Student Colloquium	Oct. 2008	Computational methods in percolation	Abstract, slides.
  UA Math Dept. Applied Brown Bag	Oct. 2008	High performance arithmetic	Abstract, slides in PDF, slides in PowerPoint.
  UA Math Dept. Math. Phys. Seminar	Oct. 2008	Lattice quadrupling for percolation in quantum networks	Abstract, slides.
  UA Math Dept. Software Interest Group	Apr. 2008	C for math folks	Abstract, slides.
  UA Math Dept. Math. Physics Seminar	Apr. 2008	Monte Carlo methods for interacting spatial permutations	Abstract, slides, paper.
  UA Math Dept. Graduate Student Colloquium	Mar. 2008	Quantum mechanics for math grads	Abstract, paper, 1D SE solver, 2D SE solver, two-state example.
  UA Math Dept. Graduate Probability Seminar	Feb. 2008	The Metropolis-Hastings algorithm by example	Abstract, paper, code.
  UA Math Dept. Graduate Student Colloquium	Jan. 2008	Numerical Differential Geometry in Matlab	Abstract, slides, Matlab code
  UA Math Dept. Graduate Student Colloquium	Sep. 2007	Is 2 a random number?	Abstract, paper
  UA Math Dept. Graduate Student Colloquium	Feb. 2007	The Householder transformation, Swiss Army knife of numerical linear algebra	Abstract, paper
  UA Math Dept. Software Interest Group	Oct. 2006	Perl for the working (or aspiring) mathematician	Abstract, slides
  UA Math Dept. Graduate Student Colloquium	Sep. 2006	Tensorama	Abstract, paper (see the section titled Tensors)
  UA Math Dept. Software Interest Group	Apr. 2006	Concrete abstract algebra in Python	Abstract, slides, paper
  UA Math Dept. Graduate Colloquium	Mar. 2006	A walking tour through projective spaces	Abstract
  UA Math Dept. Graduate Colloquium	Jan. 2006	Computation in finite fields	Abstract, paper
  UA Math Dept. Software Interest Group	Sep. 2005	Introduction to the vim text editor	Slides
  UA Math Dept. Graduate Colloquium	Sep. 2005	Linear feedback shift registers	Abstract, paper
  Master's thesis defense	Apr. 2005	Codes and Curves	Abstract, slides, thesis
  ASU/Lockheed Martin Seminar Series	Oct. 2004	High performance arithmetic	Slides in PDF, slides in PowerPoint
  ASU Graduate Student Seminar Series	Sep. 2004	An introduction to coding theory for mathematics students	Abstract, paper
  ASU Graduate Student Seminar Series	Apr. 2004	Linear feedback shift registers	Abstract, paper
  DesignCon	Feb. 2004	A reference design for FPGA-based Linux applications
  DesignCon	Feb. 2004	A reference design for embedded ucLinux on a Motorola ColdFire processor
  ASU Graduate Student Seminar Series	Dec. 2003	Computation in finite fields	Abstract, paper

  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: 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.
  • Master’s thesis (May 2005), defense slides.
  Elementary write-ups:
  • 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?
  Miscellaneous (pre-grad school):
  • DDA scaling and shifting formulae.
  • How to solve the Rubik’s cube; a few pretty patterns for the Rubik’s cube.
• Software
• Software-related documents
• Personal
• Math links (mostly to off this site)
• Other links (mostly to off this site)
• Most-used links: Wikipedia, Google calendar, UA calendar, Merriam-Webster Online, Google.

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