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Newsletter: Math Forum Internet News, No. 2.9 (March 3)
Posted:
Mar 2, 1997 2:05 AM


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 apstatl 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 handson 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://forum.swarthmore.edu/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...
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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."
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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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The Math Forum ** 3 March 1997
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