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Topic: [MATHEDU] More from my engineer student
Replies: 17   Last Post: Feb 27, 2001 5:18 PM

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Matthias Kawski

Posts: 165
Registered: 12/6/04
Re: [MATHEDU] More from my engineer student
Posted: Feb 23, 2001 2:09 AM
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Let me chip in to tilr the balance a little more towards

I completely agree w/ the student that in many math classes
there is WAY TOO MUCH unenlightening proof -- for the sole
benefit of the teacher's self-gratification. We gotta turn
the boat completely around: The primary concern should be
the student, not the teacher.

A simple criterion: If the teacher can't make a case that
something needs proof -- AS JUDGED BY THE STUDENT -- then
don't waste class-time for the sole self-gratification of
the teacher. Let's even measure the "goodness" of a teacher
by whether/how (s)he can make a compelling case that some-
thing needs proof -- THE JUDGE IS THE STUDENT: If the stu-
dent is not convinced, then the teacher did NOT maske a
good case. ...

Secondly, let's get real -- most of the stuff in any class
is on extremely poor footing. Our calculus classes don't
have real numbers (and we do just fine without proofs of
real numbers), most of our undergraduate courses have very
poorly defined logic (and we just do fine). It is not a
matter of abolishing proof -- recall that most any calculus
STUDENT AND TEACHER wants to do calculus (and not proving
the existence and properties of reals), and any typical
undergraduate course wants to prove exciting thm's about
primes, quotient rings, integrabiltiy, curvature,...(and
not get bogged down in the shaky foundations of logic and
theory) .... in the same way as calculus takes reals for
granted (WITHOUT PROOF) and most other courses take some
reasonably looking logic system for granted (WITHOUT PROOF),
in the same way we should allow our students to take more,
rather obvious/compelling, properties/relations for granted.

This student has every right to "accept" the working of SVD,
just as the advanced calculus teacher accepting that the
logic (s)he uses is OK. Save your proofs for those occasions
where they do provide enlightenment of the STUDENT!
If the teacher can't convince the students that they really
want to work a proof, then (in the majority of cases) either
a "rigorous proof" is inappropriate, or the teacher is simply
not good (or has not done her/his homework).

Matthias
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Matthias Kawski http://math.la.asu.edu/~kawski
Department of Mathematics e-mail: kawski@asu.edu
Arizona State University office: (480) 965 3376
Tempe, Arizona 85287-1804 FAX: (480) 965 0461
NOTE: NEW AREA CODES FOR PHOENIX home: (480) 893 0107
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