Matthew L. Wright
Assistant Professor, St. Olaf College

Modern Computational Math

Math 242 ⋅ Spring 2019

Prof. Wright's office hours in RMS 405: Mon. 10:30–11:30, Tues. 1:30–2:30, Wed. 8:00–9:00, Thurs 10:15–11:00, Fri. 2:00–3:00, whenever the door is open, or by appointment

Help sessions: Wednesdays, 7–8pm, in RNS 204

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Friday
February 8
Introduction; Mathematica basics
Do the following before next class:
Monday
February 11
Computing the digits of \(\pi\)
Do the following before next class:
  • Start the \(\pi\) Project. Implement two of the methods for approximating digits of \(\pi\).
  • For an explanation of why the sum of reciprocals of squares converges to \(\pi^2/6\), watch this video. For an explanation of why the product formula from last time converges to \(\pi\), watch this video.
Wednesday
February 13
Fibonacci numbers
Do the following before next class:
Friday
February 15
Fibonacci identities
Do the following before next class:
  • Verify the identity \(F_n^2 - F_{n+r}F_{n-r} = (-1)^{n-r}F_r^2 \) for several values of \( r \) and lots of values of \( n \). Bring observations and questions to class on Monday.
Monday
February 18
Do the following before next class:
  • Catalan's Identity says \(F_n^2 - F_{n+r}F_{n-r} = (-1)^{n-r}F_r^2 \). Verify this for at least three values of \(r > 2 \). For each value of \( r \), check at least 100 values of \( n \). Submit a Mathematica notebook containing your verifications to Assignment 2 on Moodle. Please put your name at the top of your notebook. (Note that this is an Assignment, not a Project.)
  • Take a look at this paper, which gives various identities for the Pell numbers. Try to generate several other polynomial identities similar to those described in Proposition 1. For example, can you directly conjecture and verify the identity for \(n=11\)?
  • Take a look at the Pell Project, which is due Friday.
Wednesday
February 20
Pell numbers
Do the following before next class:
Friday
February 22
Iterated functions
Do the following before next class:
  • To be announced...
Monday
February 25
Iterated functions; Collatz conjecture
Do the following before next class:
  • To be announced...
Wednesday
February 27
Iterated functions; Collatz fractals
Do the following before next class:
  • To be announced...
Friday
March 1
Mean-median map
Do the following before next class:
  • To be announced...
Monday
March 4
Mean-median map
Do the following before next class:
  • To be announced...
Wednesday
March 6
Mean-median map
Do the following before next class:
  • To be announced...
Friday
March 8
Primes
Do the following before next class:
  • To be announced...
Monday
March 11
Prime sieves
Do the following before next class:
  • To be announced...
Wednesday
March 13
Prime powers
Do the following before next class:
  • To be announced...
Friday
March 15
Mathematics of RSA cryptography
Do the following before next class:
  • To be announced...
Monday
March 18
Encrypting text with RSA cryptography
Do the following before next class:
  • To be announced...
Wednesday
March 20
Prime patterns and the Riemann zeta function
Do the following before next class:
  • To be announced...
Friday
March 22
Prime patterns and the Riemann zeta function
Have a great spring break! No class March 25 – 29.
Do the following before next class:
  • To be announced...
Monday
April 1
Introduction to Python
Do the following before next class:
  • To be announced...
Wednesday
April 3
Yahtzee in Mathematica and Python
Do the following before next class:
  • To be announced...
Friday
April 5
Yahtzee in Mathematica and Python
Do the following before next class:
  • To be announced...
Monday
April 8
Trouble simulation
Do the following before next class:
  • To be announced...
Wednesday
April 10
Random walks
Do the following before next class:
  • To be announced...
Friday
April 12
Random walks
Do the following before next class:
  • To be announced...
Monday
April 15
Random Walks
Do the following before next class:
  • To be announced...
Wednesday
April 17
Random walks
Do the following before next class:
  • To be announced...
Friday
April 19
Random walks
TBA
  • To be announced...
Monday
April 22
Markov chains
Do the following before next class:
  • To be announced...
Wednesday
April 24
Markov chain inverse problem
Do the following before next class:
  • To be announced...
Friday
April 26
Markov Chain Monte Carlo (MCMC)
Do the following before next class:
  • To be announced...
Monday
April 29
MCMC function minimization
Do the following before next class:
  • To be announced...
Wednesday
May 1
Combinatorial optimization: simulated annealing
Do the following before next class:
  • To be announced...
Friday
May 3
Magic squares
Do the following before next class:
  • To be announced...
Monday
May 6
Traveling salesperson problem
Do the following before next class:
  • To be announced...
Wednesday
May 8
Traveling salesperson problem
Do the following before next class:
  • To be announced...
Friday
May 10
Final projects
Do the following before next class:
  • To be announced...
Monday
May 13
Final projects
Do the following before next class:
  • To be announced...
Wednesday
May 15
Final projects
TBA
Saturday
May 18
2–4pm: Final exam/presentations for Math 242 A
Tuesday
May 21
2–4pm: Final exam/presentations for Math 242 B