Re: simplify a trig expression

*To*: mathgroup at smc.vnet.net*Subject*: [mg65495] Re: simplify a trig expression*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Wed, 5 Apr 2006 06:55:38 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200603311109.GAA15029@smc.vnet.net> <200604011038.FAA07301@smc.vnet.net> <200604020900.FAA01612@smc.vnet.net> <11D40ADD-9EC9-4DCE-B685-1CA00605B9B2@mimuw.edu.pl> <e0r0c9$mt$1@smc.vnet.net> <paul-C4EC13.21302303042006@news.uwa.edu.au>*Reply-to*: murray at math.umass.edu*Sender*: owner-wri-mathgroup at wolfram.com

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: > > https://calmaeth.maths.uwa.edu.au/ > > 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 math.umass.edu 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

**References**:**Re: simplify a trig expression***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: Re: simplify a trig expression***From:*Murray Eisenberg <murray@math.umass.edu>