John Kerl's home page

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.

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Curriculum vitae
Employer information
Research
- Dissertation topic: Critical behavior for the model of random spatial permutations.
  - Research statement, lay version.
  - Draft paper (in progress).
  - Partial dissertation (in progress).
  - Notes on exponentially correlated stationary Markov processes (a dissertation appendix).
  - VIGRE proposal for spring 2010; statement of merit and impact.
  - September 2009 talk for the UA Mathematical Physics Seminar: abstract, slides.
  - July 2009 talk for the Berlin SPA: abstract, slides.
  - VIGRE proposal for summer/fall 2009; VIGRE report for summer 2009.
  - Written comprehensive examination paper; slides for oral comprehensive examination (January 2009).
  - Pseudocode for MCMC simulation of the N2 model (spring 2008).
  - VIGRE proposal for fall 2008.
  - April 2008 talk for the UA Mathematical Physics Seminar: abstract, slides, paper.
- Spring 2008 (follow-up in summer 2009): Independent study under Jan Wehr on a percolation problem arising in quantum networks.
  - Jun. 2009 lecture slides.
  - Oct. 2008 lecture slides.
- Fall 2006 Research Tutorial Group.
  - Paper on the discrete Berezin integral.
- Master’s thesis, May 2005:
  - Thesis: Curves and Codes.
  - Defense slides.
Teaching portfolio
Courses taught:
- Fall 2008, Math 124 (calculus I with applications), section 8:
  - Calendar and homework list, my weekly schedule.
  - Course policy.
  - Links: WebAssign, D2L, math.arizona.edu/~calc.
  - Study guide for the preliminary exam: prep.math.lsa.umich.edu/pmc.
  - Exam 1 study guide, exam 1, exam 1 solutions.
  - Exam 2 study guide, exam 2, exam 2 solutions.
  - Exam 3 study guide, exam 3, exam 3 solutions.
  - Exam 4 study guide, exam 4, exam 4 solutions.
  - Worksheet on optimization and related rates.
  - Worksheet on l’Hôpital’s rule.
- Spring 2007, Math 124 (calculus I with applications), section 8:
- Fall 2006, Math 111 (trigonometry), section 7:
  - Course policy addendum, calendar and homework list.
  - My weekly schedule.
  - Exam 2 study guide, exam 2, exam 2 solutions.
  - Course page: math.arizona.edu/~trig.
- Fall 2006 and spring 2007, Math 511A-B (abstract algebra), super TA:
  - Rob Pawloski’s problem sets.
  - Savitt’s assignments.
- Spring 2006, Math 110 (college algebra):
- Fall 2005, Math 110 (college algebra):
Information for students:
- Documents related to freshman math:
  - Why is the sum-of-consecutive-squares formula true?
  - A brief derivation of the sum and differences formulas for sine and cosine.
  - The gamma integral formula.
  - What’s with the base in exponential models?
  - We have a quadratic formula. Have you wondered if there’s such a thing as a cubic formula? In fact, there is.
  - Why cross the z’s?
- Links: math department home, math department tutoring, math department syllabus information, UA academic calendar, UA General Catalog, University Learning Center, Disability Resource Center.
Notes:
- The exemplar model in mathematics instruction
Notes from the professional-development course, 2005-06 (first teaching year):
- (1) Day one
- (2) Lecture notes
- (3) Organization and presentation
- (4) Classroom management, rapport, and motivation
- (5) Observations of other instructors
- (6) The Rule of Four
- (7) Policies
- (8) Feedback for the professional-development course
- (10) Writing exams
- (11) A lesson plan on word problems
- (12) Grading
- (13) Observations of other instructors
- (14) Semester two compared to semester one

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):

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:

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
Python:
- A plotter, sending tabular file data to pylab: documentation, main script, required I/O module.
- SACK: A simple algebra calculator. Includes some elementary group routines, some linear-algebra functionality, and some support for computation in real tensor algebras. Documentation, source tree, tar file.
- Matrix arithmetic (using SACK’s matrix module sackmat_m.py): Matrix multiply, matrix add, matrix subtract, matrix inverse, matrix power, determinant, trace, real matrix exponential, complex matrix exponential, real matrix square root (Denman-Beavers), complex matrix square root, real matrix A^*A, complex matrix A^*A, row reduction, row echelon form, row rank, kernel basis, kernel basis, Gram-Schmidt orthonormalization, Jacobi eigensolver for real symmetric matrices, tester for the Jacobi eigensolver, Householder-matrix generator, another Householder-matrix generator, another Householder-matrix generator, rotation-matrix generator, QR decomposition, real polar decomposition, complex polar decomposition.
- Misc. matrix generators: oneeye, tridiag, discrete Laplacian with Dirichlet boundary conditions, discrete Laplacian with periodic boundary conditions.
- Numerical calculus: 1-D numerical differentiation, 1-D numerical integration, contour integrals, another contour integral, streamlined complex integration.
- Taylor polynomials, Lagrange interpolation module, program.
- Real and complex I/O.
- Fourier processing: Fourier-series approximation, Fast Fourier Transform module and program. (Uses pyrcio_m.py.)
- Probability: some Markov chain hackwork, 1D and 2D Brownian motion and Brownian bridge, beta-distribution PDF, beta-distribution PDF plotter. The latter uses Tom Loredo’s special functions.
- Gaussian normal routines normalpdf, normalcdf, invnorm, erf, erfc, and inverf: normal_m.py.
- Real/complex abstraction layer for conj(), real(), imag(), phz(): cplxreal_m.py.
- Random-scalar-complex generator: module, tester.
- Real random-matrix generator (m × n, GL(n), SL(n), O(n), SO(n), symmetric, skew-symmetric): program randmat, module randmat_m.py.
- Complex random-matrix generator (m × n IID mean-square-1, GUE, IID mean-square-1 XX^t): program randmatc, module randmatc_m.py.
- Statistics: module, 1D histogram, 2D histogram, mean, standard deviation, pair covariance, pair correlation, covariance matrix, correlation matrix, univariate linear regression, noisy-line generator, noisy-sine generator, stratified random sampling.
- Sliding-window data smoother: program, module.
- Routines for printing images, cycle decompositions, and orders of moves on the Rubik’s cube: module, demo, demo output.
- A utility module: kerlutil.py; float to hex: float2hex_m.py; how to do a sprintf in Python: sprintf.html.
- Tar file of Python programs: python.tgz.
Matlab:
- Vector calculus / differential geometry: An illustration of the Jacobian, tangent planes to S2 using graph and spherical coordinates.
- Final project for Math 537A (Riemannian geometry): gdgproj.m, lectures notes, complete directory listing. (You need gdgproj.m and all the other *.m files.)
- Binary I/O: fbinread, fbinwrite.
- Plot animation: param_movie.m.
- Misc.: cmpvecs, vecrange.
Perl:
- Makefile generator: kbld, sample program 1 for kbld. Many more programs using kbld are in my source directory.
- Substitute for makeindex which correctly handles alphabetization of text including \mathbb etc. in LaTeX files: kmkidx.
- Tools for formatting and manipulating tabular data in plain ASCII: colprint, mwxprint, parside, interleave, creach, twoper, xpose, cpick, dashes, caytex, mattex.
- Tools for large-scale search and replace: krepl, mrepl. Variants of familiar tools: bffind, mgrep.
- Windows workalikes for familiar Unix tools: kbc, grep.pl, head.pl, tail.pl, uniq.pl, wc.pl, whereis.pl, My_win_glob.pm, w.pl, notes about Perl and Windows file associations, toc.pl which works around the Windows association/redirection bug.
- Unix workalikes for familiar Windows tools: grepr, lsr, rmr.
- fixrlinks: When I rsync -rtlz between hosts on which the spelling of my home directory differs (e.g. /u5/kerl on one and /home/kerl on the other), rsync doesn’t change the symlink referents. This script can be run after an rsync to fix that.
- finddang: Reports on dangling symlinks.
- Miscellaneous text manipulation: upcase, downcase, scrunch, printtwice, printtwicej, printthricej, chop, dspc, dspcw, linesort, detab, retab, fdiff, nocolon, wordfreq.
- Numerical calculus: series estimation, another series estimation, 1-D numerical differentiation, 1-D numerical integration, 2-D numerical integration, path integral one way, same path integral another way.
- Floating-point matrix arithmetic: Matrix multiply, matrix add, matrix inverse, determinant, row reduction, row echelon form, row rank, kernel basis, Gram-Schmidt orthonormalization, Jacobi eigensolver for real symmetric matrices, elementwise vector sum, elementwise vector difference, elementwise vector product, vector times scalar, dot product, vector-to-scalar sum, vector-to-scalar sum of squares, matrix library file PMATLIB.pm.
- Generators of special-purpose matrices: Hilbert matrix (famously near-singular), identity, DDA A, DDA Q.
- Fast Fourier transform and associated tools: radix-2 FFT, complex rectangular-to-polar, complex polar-to-rectangular, power sum (for discrete Parseval).
- Data generators for testing FFT implementations: pcisgen, pspikegen, phatgen, prampgen, prandgen.
- Misc. numerical routines: Lagrange interpolation, partial sums, binomial coefficients and Pascal’s triangle, extended GCD using Blankinship’s algorithm.
- Tar file of Perl programs: perl.tgz.
Fortran:
- Simple programs: hello in F77, hello in F90, F90 I/O examples, how to find machine epsilons.
- Some library routines: Simpson adaptive quadrature, LU decomposition, matrix arithmetic, matrix I/O.
- Some library routines: Crout, back-substitution,
- Drivers: matrix arithmetic, single-precision Simpson, double-precision Simpson, LU decomposition, LU solver.
- Makefile.
- Tar file.
C/C++:
- SPFFL, a small-prime finite-field C++ library: documentation, source code tree, source code tar file.
- Misc. general-purpose C/C++ routines: tree, tar file.
- Some simple X11 C++ programs: xgr documentation, xfim documentation, tree, tar file.
PHP:
- Collapsible trees, such as for the page you are looking at; source code here.
- A frivolous cycle decomposer; source code here.
Software-related documents
HTML:
LaTeX:
- Template file for using Matlab plots and Inkscape drawings in LaTeX, 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, directory listing.
- 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.
Other:
- .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
Personal
- Photos (mostly of family)
- People I have been
- People and things which I am not
- My heroes in the media
- Exercise log, calendar, quotes.
- Woodworking
- Motto — Quidquid latine dictum sit, altum videtur — and other quotes.
- Unit-quaternionic description of myself: jk=i. :)
- Frivolity
Math links (mostly to off this site)
- Encyclopedias: Mathworld, Planetmath, xbeta, PlanetMath DG page, MacTutor (biographies), Mathematics Genealogy Project, Random Math Quotation, Matthias Beck’s quote list, Math Atlas, Sloane’s sequences, The Data Analysis BriefBook.
- arXiv (preprints): front.math.ucdavis.edu:, AC, AG, CO, DG, GM, GR, MP, NT, PR, RA, RT, SG.
  arxiv.org: stat, cs.AR, cs.CG, cs.CG, cs.DM, cs.DS, cs.IT, cs.MS.
  math-ph, cond-mat, quant-ph, hep-th, comp-ph.
- Mathematical directories: Center for Commutative Algebra, Number Theory Web, CBEL/NT, Finite Geometry Web, Young Mathematicians’ Network
- On-line journals: Sonoran Journal of Graduate Mathematics, AMS Notices, AMS Bulletin, AMS ERA, Chronicle of Higher Education, MAA, SIAM, ACM, AIP News, MCOM, IEEE/IT, Probability Surveys.
- Search: MathSciNet, Citeseer, Scirus, Google Scholar.
- Software: Pari/gp (algebraic number theory), GAP (group theory), Macaulay 2 (algebraic geometry)
- U.S. math department web pages
- LaTeX: http://en.wikibooks.org/wiki/LaTeX/Mathematics
- National laboratories.
- Industrial research groups: AT&T Labs, Bell Labs, Bell Labs Math, Intel Labs, Xerox PARC, Cisco ARTI, HP Labs, Sun Labs, Siemens Corporate Research, Philips Labs, Microsoft Research, IBM Watson Research Center. See also MSRI.
- Terry Tao’s blog
- Milne
- Don’t quit grad school (or, don’t give up on applying) until you read ...
- Josh Chesler’s 2009 notes on the academic job search.
- Job listings: AMS, Mathjobs, jobs.phds.org, MAA Math Classifieds, Chronicle of Higher Education, Higher Ed Jobs, Academic Keys, SIAM.
- Math jokes, thanks to AMS Notices, January 2005: J. Verhagen, A. and E. Cherkaev, workjoke.com, Oxford Invariant Society, UW Madison
Other links (mostly to off this site)
Languages:
Programming:
- Matlab: Primer by Fosdick et al., Matlab Central, Cleve’s Corner (Matlab column)
- Python: www.python.org, Prabhu Ramachandran’s intro, local copy.
- C++: www.cpp4u.com
- Fortran: Jack Ponton’s intro
- Mathematica: some tutorials.
- Quick-reference cards for HTML, CSS, vim, Python, and more: www.digilife.be/quickreferences/quickrefs.htm
Physics:
Running:
- General information: Runner’s World Online, www.time-to-run.com.
- Arizona calendars etc.: www.azroadrunners.org, www.arizonaroadracers.com.
- Distances: www.gmap-pedometer.com, UA area, www.mapmyrun.com (routes etc.).
- Energy consumption: calculator.
- Sports medicine: U. Mich. Health System pages; Merck Medical Dictonary.
- Starting: John “The Penguin” Bingham.
- The anthropology of running: Bramble and Lieberman.
Triathlons, biking, etc:
Cooking:
- Epicurious,
- Bittman,
- Pirello.
Most-used links: Wikipedia, Google calendar, UA calendar, Merriam-Webster Online, Google.

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You must be the change you want to see in the world. — Mohandas Gandhi