On 25/05/2013 10:34, Andrzej Kozlowski wrote: > Well, to disappoint everyone I have to confess that here, at Warsaw > University, we are going to have a university wide course in > Mathematica, open to all students of mathematics, natural sciences, > economics and finance and even (oh horror!) computer science (in fact, I > am not in the process of trying to "sell" this course to my the students > in my analysis for computer science class). We have actually received a > grant, quite substantial by Polish standards, to implement such a > course, and, of course, since everyone likes extra money, this has meant > that there has been no opposition or grumbling about it from any "old > fogies" (except perhaps one guy who complained that Mathematica was not > open source but we quickly stifled him). > > An even greater heresy: the course also is going to involve some > knowledge of Wolfram Alpha: in fact it is entitled "Mathematics with > Mathematica and Wolfram Alpha". (To RJF - no, we are not going to teach > anything about any other CAS. If anyone likes to use something other > than Mathematica they can learn it itself, but won't get any credit for > it). Actually, our course is going to be a "supervised, self-study and > Internet based course". In other words, we (the project authors, who are > getting paid for designing and realising it) will prepare study > materials (scripts, videos, problems in different disciplines that can > be solved with the help of Mathematica or Wolfram|Alpha, tests, etc. but > there won't be any lectures. There will however be tests and students > will be able to get credit for passing them - otherwise, of course, it > would be hard to get them interested. >
I think that is an absolutely wonderful decision. I wish I was of student age (and spoke Polish!) to avail myself of it, and the associated maths courses.
I think mathematicians, and more particularly, users of maths, have a range of styles of thought, and the every concrete approach, which Mathematica encourages, would certainly have appealed to me.
To give a specific example, I remember trying to learn about group theory. For a long time, groups seemed somehow vague to me. I learned the axioms of what counted as a group, and thought "Yeah well - so what!". I learned (or tried to learn) assorted other definitions, such as "normal subgroup", and of course, I looked at various tiny examples of groups. However, what I really needed was software which would let me make examples that were big enough to begin to see why all those definitions were any use - software that let me explore. I am the sort of person who finds it hard to learn something that doesn't seem any use - even if I know that everyone says it really will be useful once I get to understand it!
As to the issue of alternative CAS software, I did chemistry, and nobody worried about the fact that all our NMR machines were Varian, or that the infra red machines were made by Perkin Elmer, or that we learned to program the type of computer owned by the university - a technical university course inevitably focuses its students on certain products.
You say the focus will be on graphics rather than symbolic computation, but I must say, I think symbolic computation is the more exciting part - because it opens up entirely new possibilities.
Take symbolic integration as an example. I know there are those who would say students should be told to solve all their integrals with Mathematica (and take a calculator to add their bills when they shop) but I am not thinking that way. It is easy to make a construct in Mathematica that displays like an integral, but doesn't evaluate. Using this, students could explore strategies such as change of variable - simply using pattern replacement and simplification. Mathematica would be contributing no skills that the students didn't already know - simply adding some muscle to help explore more substantial problems.