Re: if using Mathematica to solve an algebraic problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg109014] Re: if using Mathematica to solve an algebraic problem*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Sat, 10 Apr 2010 06:54:13 -0400 (EDT)

An instructive example when one is teaching techniques of integration: Integrate[ Exp[-x^2],x ] Why this is instructive is left as an exercise to the reader. On 4/9/2010 3:34 AM, Bill Rowe wrote: > On 4/8/10 at 8:03 AM, dave at removedbailey.co.uk (David Bailey) wrote: > >> I also think that if Mathematica had been available to me back then, >> I would have felt it was a bit like an addictive substance - very >> interesting in small doses, but also terribly dangerous. There would >> have always been the possibility of becoming skilled in answering >> questions through Mathematica, rather than actually learning the >> subject! > > While I think I understand the concern you express here, I still > wonder. If one becomes very skilled at using Mathematica to > solve problems correctly wouldn't there have to be some > corresponding gain in understanding of how the same problems > would be solved without Mathematica? > > The point I am trying to get at is areas Mathematica fails or > shows limitations invariably require understanding of details of > the problem and computer arithmetic. It seems becoming highly > skilled at getting correct results from Mathematica requires > mastery of these details to a large degree. And it also seems > understanding those details are exactly what is required to > solve the problem without Mathematica. -- 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