Cross-country Day, Day 2

Last time

Next time

Announcements
- Roll: who's new?
- Reminder: please keep the phones out of sight and sound.
- You have a homework due today -- your one-page summary for the problem "Thad versus Thomas: who's better at cross-country, and why?
  Within your groups you will exchange homeworks. Put your name on your colleagues homework, and you will
  annotate (or amend) that homework throughout today's discussion.
  Then give it to me at the end.
- I got an email this morning about an REU at Auburn, in case anyone is interested.

Last time:

I shared with you some of the projects/problems we'll be considering, and we started working on one problem (cross-country problem). We're using Polya's UPCE strategy to attack it (Here's a handout summarizing his strategy):

Understand
Plan
Carry out
Evaluate

And here's where we left off last time:

Understand Plan Carry out Evaluate

Make different units consistent Calculate Pace and compare
(Would this competition be over if Thomas's were better?) $5000 m = 3.106856 miles$

Weather, Course, etc. Compare to Champions from their time
(or around their time -- a distribution),
and their class?

Same high school? Yes, Bowling Green

How do classes and divisions compare?

We'd like more times from each (a distribution).

Our objective today: to formulate a plan, so that by Friday you should have carried it out to reach our conclusion.

Today:
- We begin with any questions about the Syllabus and approximate schedule.
- A reminder about your course notebooks. Keep one! I suggest loose-leaf binder. It will require pencil and paper (i.e. no computer devices). You can use this on exams.
- Math Modeling is UPCE in disguise (e.g. Charles Collins's Modeling Cycle in his Intro to Modeling handout).
  Collins adds an important unstated part to Polya's strategy: simplification (which would fall into the Planning part of Polya's UPCE).
  - Things should be as simple as possible, but not simpler. (attributed to Einstein).
  - KISS: Keep It Simple Stupid
  - Occam's Razor: I like this formulation: when you have two competing theories that make exactly the same predictions, the simpler one is the better.
- So let's get back to my brother and my nephew, who have agreed to abide by your decision. Data:
  
  Thad (1980) Distance: 2.5 mile course Best time: 13:30
  
  Thomas (2019) Distance: 5000 meters Best time: 17:15
  
  It might help to know Boys State Tournament Individual Champions for Ohio over time.
- Let's get back into our groups, and
  1. share what you've discovered/decided so far.
  2. Consider proposals for a plan at this point.
  3. I'll ask each group to make a short statement about their plan,
  4. and then we'll move to a final Plan.

Website maintained by Andy Long. Comments appreciated.

Thad (1980)	Distance: 2.5 mile course	Best time: 13:30
Thomas (2019)	Distance: 5000 meters	Best time: 17:15