Day 4 in Mat120

Distribute Worksheet 2.1
Distribute additional calculators
Collect 1.1 problems.
Small error on Worksheet 1.3: in the first note,
(e.g. Example 5, p. 27)
should have been written (e.g. Example 5, problem #27)
Role
Quiz "opportunity"
Questions on problems?
Additional Comments on Math modeling (from yesterday)
- "All models are wrong; some models are useful." As the text notes, models are idealizations.
- Occum's razor: William of Occum (1285?-?1349). If there are several possible explanations for some observation, and no significant evidence to judge the validity of those hypotheses, you should always use the simplest explanation possible. Occum's razor is also known as the principle of parsimony -- scientists should make no more assumptions or assume no more causes than are absolutely necessary to explain their observations. (from this source)
  Example: the dots in Ex 4, p. 16 were connected by a smooth, monotonic (that is, decreasing) curve. It's simple, and consistent with the data.
- I mentioned George Polya's Principles of Problem Solving: they're outlined and demonstrated on pages 59-65 of our text.
A comment on linear regression (yesterday's problem #15):
Regressing ulcers on income, i.e.
U=mI+b,
and regressing income on ulcers, i.e.
I=nU+c
do not give "equivalent" results. If you solve U=mI+b for I as a function of U, you do not get I=nU+c!
Upshot: it really does matter which variable is treated as dependent, and which as independent.
A comment on section 1.4 (which we're skipping):
Those unfamiliar with their calculators may want to follow along in section 1.4; check to see if you can reproduce the plots.
A comment on trig:
There's a refresher in Appendix D.
Section 1.3 Worksheet
Questions?
To the problems:
- At seats: 1, 3, 54
- At board: 6, 7, 20

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