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Re: simplify a trig expression

  • To: mathgroup at
  • Subject: [mg65495] Re: simplify a trig expression
  • From: Murray Eisenberg <murray at>
  • Date: Wed, 5 Apr 2006 06:55:38 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <> <> <> <> <e0r0c9$mt$> <>
  • Reply-to: murray at
  • Sender: owner-wri-mathgroup at

Actually, we have a system here called OWL that is similar to CalMaeth 
and employs Mathematica and MathLink as its back-end engine.  We use it 
in a calculus course aimed at students in biological sciences, social 
sciences, and business; several units are on methods of integration. 
Curiously, in our mainstream course (for students in math, computer 
science, physical sciences, and engineerings) we cannot currently employ 
that system mainly for logistical reasons (no lab space available) and 
partly because we'd need to develop a richer set of exercises.

So I completely agree that using a CAS behind an on-line learning 
management system is a sensible thing to do.  So is using CAS in a 
different way, as a tool directly employed by students, to do more 
interesting things (as I explained in another message).  As I originally 
said, all I wanted to do was produce a demonstrably correct set of 
answers to a handful of integration exercises that would be in a form 
similar to what students would get by hand.  And although I have no 
doubt that each and every one of the graduate teaching assistants who 
will be grading our symbolic integration exam is capable of converting, 
say, a student's answer of Cos[x]/(Sin[x] + 1) to Mathematica's result 
of 2 Log[Cos[x/2] + Sin[x/2]], and vice versa, I did not want them to 
have to waste time doing so: each grader has to read a question on 366 
papers!  Hence my little exercise in trying to coerce Mathematica's form 
into the paper-and-pencil form.

Paul Abbott wrote:
> There is another aspect to this exercise: at my University there is a 
> project called CalMaeth:
> This uses Mathematica (via pattern-matching and other tricks behind the 
> scenes) to compare exact answers to those obtained by students with the 
> goal being to attempt to automatically determine exactly which step (or 
> at least the first one) in the "standard paper-and-pencil technique" 
> that the student got wrong, and giving appropriate feedback. To me, this 
> is particularly sensible use of CAS and better than "forcing" 
> Mathematica and the student to get the "same" answer.
Murray Eisenberg                     murray at
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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