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

• Resumé, software repositories at GitHub, LinkedIn, Google+, blog.
  
• Lecture notes
• Documents
• Software
• Research
  • Dissertation topic: Critical behavior for the model of random spatial permutations.
    • Research statement, lay version.
    • Doctoral dissertation: Critical behavior for the model of random spatial permutations. PDF format, PostScript format, DVI format; defense slides.
      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.
    • Slides for a job talk: half on general MCMC methods, half on my dissertation research.
    • Slides for 15-minute talk at the February 2010 Workshop of the Center for Simulational Physics at the University of Georgia; manuscript for same.
    • Slides for 15-minute talk at the January 2010 joint meetings.
    • Preprint of condensed version of dissertation, submitted to Journal of Statistical Physics: arXiv:0912.4292 [cond-mat.stat-mech]; local copy.
    • VIGRE proposal for spring 2010; statement of merit and impact; VIGRE report for spring 2010.
    • 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, VIGRE report for fall 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
  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:
    • Course policy, calendar and homework list, math.arizona.edu/~calc.
    • My weekly schedule.
    • 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.
    • Information about the final exam.
  • 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):
    • Course policy addendum, calendar and homework list.
    • My weekly schedule.
    • Exam 4.
  • Fall 2005, Math 110 (college algebra):
    • Course policy addendum, calendar and homework list.
    • My weekly schedule.
    • Exam 4, exam 4 solutions.
  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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