Honors 391A Discovering Mathematics through Computer Experiments

Instructor: Matthew Dobson (Pronouns: he/him/his)
Class meeting time: M 4:00-4:50pm Elm Room 212
Office hours: Tu 11:10-12:00am, W 11:10-12:00, F 2:30-3:30, or e-mail me to make an appointment.
Office: LGRT 1430 (Tower)
e-mail: dobson@math.umass.edu
Office phone: 545-7194

Course Goals

Modern mathematics makes heavy use of computing for both large-scale complex calculations as well as small-scale experiments to explore a problem and test ideas. This course will use the Matlab computing environment to explore problems where simple rules lead to chaotic behavior and problems where lots of chaotic behavior leads to simple, orderly behavior.

We will develop Matlab programming skills, tools for exploring problems through computing, and techniques for communicating the results.

Grading Policies:

The course grade will be based on attendence and a short, weekly report of additional exploration done outside of class.
Last day to drop with no record is Monday, Sept 17th. Last day to withdraw with a W is Tuesday, October 30th.

Starting code:

Week1:
chaos1_logistic.m
chaos1_logistic_visualization.m
chaos1_logistic_visualization2.m

Week 2:
billiards.m
billiards2.m
billiards3.m
collide_circle.m
collide_rect.m


Week 3:
shuffle.zip
pile.m


Week 4:
Code developed in class.


Week 5:
percolate.m


Week 6:
averaged_polygons.m


Week 8:
Traveling Salesperson Problem


Week 9:
We developed the code in class.
Discussion questions and observations we generated:
  1. It looks like a stock market price.
  2. From the moment we leave zero, how long to return back to zero?
  3. How long to reach zero from a certain value?
  4. If we run j=50, how wide do we expect the span to be?
  5. What does it look like when we average many trials?
  6. What is the highest and lowest for large j?
  7. For j large, how long do they overlap?
  8. What is a better investment strategy for $1 million: Buy at beginning as a lump sum or invest $1k every day
  9. Say we replace coin flip with a die roll, how does that change the path?
  10. Or even bias coin flip, change prob from 0.5 to some other value between 0 and 1


Week 10:
rps.m
rps_video.m
rps_mobile.m



Week 11:
collision2.m
collide_circle.m
DrawTable.m
DrawBumpers.m



Week 12:
ising.m