Volume 2, Number 9
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3 March 1997 Vol. 2, No. 9
THE MATH FORUM INTERNET NEWS
AP Statistics Courses | Proof by Induction | Snark Mailing List
ADVANCED PLACEMENT STATISTICS COURSES
Two courses designed to prepare students for
the AP exam in Statistics:
WOODWARD ACADEMY: AP STATISTICS ON THE WEB
- Paul Myers
http://www.mindspring.com/~waus2/apstat/
Comprehensive statistics resources include information
on textbooks, reference materials, software, TI calculator
programs, and the College Board. The site also features
discussions on apstat-l and a selection of online tests.
BB&N: AP STATISTICS - A MEASURE OF EXCELLENCE
http://www.bbns.org/us/math/ap_stats/
Buckingham Browne & Nichols School's course emphasizes
projects that require hands-on gathering and analysis
of real world data. The site provides homework assignments
and makes use of the popular "Workshop Statistics" text.
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FROM THE MATHEDU ARCHIVE: PROOF BY INDUCTION
http://mathforum.org/epigone/mathedu/blinblehhand
Prof. Williams P. Wardlaw [wpw@nadn.navy.mil] writes:
I like to introduce induction with a story about painting
a chain. Given my institution, I prefer an anchor chain:
A First Lieutenant (responsible for painting) orders
a Seaman to paint the anchor chain. Later he asks the
Seaman what color he painted the chain. The Seaman
cannot remember, but is sure that whatever color he
painted a given link, he used the same color for the
next link. The First Lieutenant goes on deck and sees
that the first link, just showing at the top of the
hawse pipe, is chartreuse. What color is (every link
of) the chain?
The story is followed by a formal discussion of induction
and several examples, such as a couple of summation
formulas and a couple of inequalities...
\-|-/
Lou Talman adds:
Sonneborn's Horse Lemma states that all horses are
the same color. Its power lies in its immediate
applicability to proofs by contradiction, which
assume the form "Suppose it were not so. Well, that
would be a horse of another color, wouldn't it."
\-|-/
This searchable thread from the MATHEDU archive cites useful
articles and discusses examples of mathematical proof by
induction at both the high school and the college level.
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