John Kerl's home page

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

Resumé, software repositories at GitHub, LinkedIn, Google+, blog.
Lecture notes
Documents
Software
Github repositories: http://johnkerl.github.com

Ruby:
- RUFFL, a Ruby finite-field library (ported from SPFFL, below, which I wrote and used for my master’s thesis): documentation, source code.
- hashrun: a little script which executes the first hash-commented line in a file.
Python:
- pgr, a plotter which sends tabular file data to pylab: documentation, main script, required I/O module.
- Matrix arithmetic (using the 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.
- Simple MCMC (Metropolis-Hastings) sampling for the 2D Ising model.
- 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.
- 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.
- 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.
Java:
- Data plotter Plot, using AWT. Supporting classes: PData.java, TextFileReader.java.
- Brownian motion and Brownian bridges: Brownian motion, test routine, Brownian bridges, test routine, I/O module, statistics module.
Perl:
- Makefile generator (“yet another make-make”): yamm, sample program 1 for yamm. More programs using yamm are in the tar file gen.tgz.
- 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.
C/C++:
- C project for enumerating constrained (e.g. self-avoiding) walks on the plane integer lattice: README file, tar file.
- C/bash project for bond percolation on the two-dimensional square lattice (used for my PhD computational exam at UA): PDF with mathematical background, source code.
- SPFFL, a small-prime finite-field C++ library (used for my master’s thesis): documentation, source code.
- Misc. general-purpose C/C++ routines: tree, tar file.
- Some simple X11 C++ programs: xgr documentation, xfim documentation, tree, tar file.
- Examples of using function pointers in C: without typedefs, with typedefs.
LISP:
- Cycle decomposition etc. for the Rubik's cube.
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.
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, lecture notes, tar file of complete directory. (You need gdgproj.m and all the other *.m files.)
- Binary I/O: fbinread, fbinwrite.
- Plot animation: param_movie.m.
- Misc.: cmpvecs, vecrange.
PHP:
- Collapsible trees, such as for the page you are looking at; source code here.
- A frivolous cycle decomposer; source code here.
Research
Teaching
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
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