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Topic: [MATHEDU] Arnold's problem
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Terence Gaffney

Posts: 45
Registered: 12/6/04
[MATHEDU] Arnold's problem
Posted: Jun 12, 1997 10:51 AM
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i agree with David Epstein that you can embed Arnold's problem in a collection
of problems which will make it easier for the studk it, and more

enjoyable to work on it.

But i believe it is better for the students if we can give them problems in
which the constellation of associated questions unrolls before the students
as they work on the initial problem, instead of handing them
the constellation at the beginning or feeding it to them in steps.

learning to see the constellation is as important as solving the problem
you started with.

A proof of the theorem (ascribed to Artin) that a positve valued polynomial
is a sum of squares can be found in lang's algebra book in the section on
Real Zeros and homomorphisms p279 in the '65 edition. Of course, this is a key
result in trying to move results in algebraic geometry from C to R.

best,
Terry Gaffney

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