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AiS Challenge

Math Modeling links and comments

I have put together some materials for the Math Modeling course (cobbled together by taking the best of two courses that I found online). (M115 course) (good links) (M110 course : part III Things Change) (Unit 1)
See for the other units, see units 1-5)

Here's a rough syllabus I am proposing: (but am not particilarly attached to)

  1. Intro, goals, expectations, objectives
  2. What is math modeling (open discussion leading into guided examples)
  3. Guided example #1 Living Dangerously (from Unit 1 of M110)
  4. Guided example #2 On the Road (from Unit 1 of M110)
  5. Guided example #3 Shoe Business (from Unit 1 of M110)
  6. Poyla's Four Step Problem Solving Process (what to do when you aren't guided through a problem) Run through process using Round Robin Tournament as an example
  7. Two approaches to problem solving: Empirical modeling vs. Mathematical modeling find examples in this year's Challenge papers of each and discuss what makes them one or the other.
  8. Patterns of Change, section 3.1 problem #1 (from Unit III of M110) Excel mini-lesson and problem #2 using excel to make graphs of the data you come up with problems #3-6 if time allows
  9. Types of growth: basic mathematics background Arithmetic, Quadratic, Exponential, Logistic growth
  10. Linear models (from Unit III Part A of M110) problems 1 & 7
  11. Exponential Models (from Unit III Part B of M110) work through example problem 1 and 7
  12. Logistic Models: Rabbits and Grass example in Starlogo. Carrying capacity
  13. Power Models (from Unit III Part C of M110) #1
  14. Periodic Models (from Unit III Part C of M110) give simple example
  15. Combinations and Systems of Models ( from Unit III Part C of M110) give a simple example
  16. Brief intro into Fourier Transforms and why they are used
  17. Dealing with the issue of mathematical models in Agent-based Models (discussion) Wolfram excerpts example: Civil Violence model and paper by Joshua Epstein (Brookings Inst.)

I don't know how much of this is reasonable to cover in a two-week period. Or if this is what y'all had in mind for a mathematical modeling component..... feedback please. I have emailed the course authors asking permission to use their materials in the STI course.

My thought was that most of these items could be used as jumping off points. The facilitator (online) would set the stage by introducing a problem or concept and problem in the morning. Then students working collaboratively (online) investigate the questions and solve the problems during the day. All the while bantering back and forth with ideas, questions and hopefully inspiration. In the evening the facilitator will review the discussion, solution, and perhaps give more information.