Re: mathematica use

*To*: mathgroup at smc.vnet.net*Subject*: [mg2576] Re: mathematica use*From*: bruck at mtha.usc.edu (Ronald Bruck)*Date*: Tue, 21 Nov 1995 09:26:13 -0500*Organization*: University of Southern California, Los Angeles, CA

In article <DIBv0D.BnI at wri.com> harkerj at coral.indstate.edu (roadrunner) writes: > >What are your feelings about using mathematica and other computer aids in >mathematics classrooms? > Try answering the following question: how many local maxima are there of f(x) = sin(x + sin(3x)) in the interval [0,2\pi]? Try it first on your graphing calculator. Do it next with pencil and paper. Do it next with Mathematica or other CAS (preferably in conjunction with what you just finished). Assuming the Empire State Building is 1000 feet high, and has a blackboard attached to its side, and you plot this function with x = 0 being at ground level and the maximum occurring at the top of the blackboard, how much of a dip is there between the first two local maxima? Nikolaus Vonessen showed me this problem. It's an excellent lesson that human beings need to think about problems and not just blindly compute; but that symbolic or computational programs can be of tremendous help in DIRECTING those thoughts. --Ron Bruck