>>>>> Frank Miles <firstname.lastname@example.org> (" fm>" ) says:
fm> I'm was simply trying to point out that the difference between fm> math and engineering can decline as one advances (in some, but fm> definitely not all realms of engineering). Previous postings fm> seemed to indicate that there was some chasm between the two; fm> I'd say there wasn't.
Just to put it clearly: yes, I think there _is_ a chasm, but I don't think it ought to be as deep as it is.
fm> Prolonging the time the 'average' engineer-to-be is willing to fm> tolerate mathematical theory before seeing how it might have fm> relevance to engineering problems is a more difficult matter. fm> This is particularly the case when many lower level jobs, for fm> instance using off-the-shelf digital technology, don't require fm> the same level of skills as, for another instance, analog fm> technologies. Engineers are often attracted to the latest fm> technology de jure; only later will they find out that the basic fm> mathematics and science have a greater long-term payoff in many fm> respects.
Yes, I agree. But I _still_ think there is a difference between math and engineering. Mathematics, in Engineering, is only a tool to _solve_ problems. However, it is much more important for an engineer (or indeed for any scientist) to _chose_ a problem to solve. And this choice is never dictated by scientific or mathematical necessity, but by the society (or firm) a scientist (or engineer) works in.
I agree that math can be a discipline in its own right in coding theory and perhaps also in digital technology. But in analog technology, math is merely used for modelling. Mathematical models are of course very important, but one should never forget that they are only models: a simplified image of reality. It is much more important to know _which_ simplifications are made, and _why_, than to be able to derive a model mathematically.
I did never intend to say that a profound knowledge of mathematics is unnecessary for an engineer. In the contrary, I think it is very important to know one's tools well. However, I think that it should be taught as such, as a tool, in context, and not detached from engineering reality. Everybody can juggle formulas after some training, but the important bit is how to _use_ them. To come back to my beloved trombone metaphor: if you want to play the trombone, you'll not start by learning music theory, but by playing.
After all, if practice is more important than theory in the engineer's work, why should it be otherwise in their education?
In my opinion, practice and theory must go hand in hand, not one one first, the other later. Leraning both `hand in hand' is, in my experience, how students become good engineers. It would help greatly if the curricula would take this into account.
Cheerio, Hanspeter -- Hanspeter Schmid I have no "position". I have opinions Researcher (Analog IC Design) that I defend rather vigorously, and Signal Processing Laboratory, ETHZ. then I find out how silly they are http://www.isi.ee.ethz.ch/~schmid/ and I give them up.