
Re: [MATHEDU] More from my engineer student
Posted:
Feb 23, 2001 2:09 AM


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 selfgratification. 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 classtime for the sole selfgratification 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 ********************************************************** Matthias Kawski http://math.la.asu.edu/~kawski Department of Mathematics email: kawski@asu.edu Arizona State University office: (480) 965 3376 Tempe, Arizona 852871804 FAX: (480) 965 0461 NOTE: NEW AREA CODES FOR PHOENIX home: (480) 893 0107 **********************************************************
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