Re: annoying documentation in 6 (rant)
- To: mathgroup at smc.vnet.net
- Subject: [mg78974] Re: [mg78940] annoying documentation in 6 (rant)
- From: Murray Eisenberg <murray at math.umass.edu>
- Date: Sat, 14 Jul 2007 02:41:19 -0400 (EDT)
- Organization: Mathematics & Statistics, Univ. of Mass./Amherst
- References: <200707131004.GAA11697@smc.vnet.net> <5349D789-80D3-440D-B016-1A69910A1892@yale.edu>
- Reply-to: murray at math.umass.edu
1. These are not "axioms" Mathematica 6 is adding, functions. Some are implementations of functions used in math; others are functions to facilitate operating upon objects; others are functions that affect the computing environment; etc. In any case, mathematics does have a HUGE inventory of functions -- far more than one ever sees in school and far more than one ordinarily encounters even in college math. As the years pass, mathematics does not get simpler, although certainly significant advances are made when somebody realizes that seemingly disparate ideas are special instances of the same, more general concept that, if sufficiently rich, can be developed itself. 2. That's wonderful -- a teachable moment! This is one of the ways that Mathematica can motivate learning math. Now your 10-year-old may not yet be in a position to grasp what an integral is all about: Does he understand about functions f(x) and their graphs? If not, Mathemtica could help him learn about that. If so, he's ready to begin to grasp the idea of at least the definite integral (probably indefinite integral is harder, since it requires the preliminary idea of derivative, i.e., rate of change). Show the calculation of the area of a rectangle, and represent that as the area under the graph of a constant (positive) function. Next, you could do the same thing for several rectangles -- a step function. Then begin the idea of approximating the area under a "curvy" function via a bunch of rectangles. Etc. J=E1nos wrote: >> >> By far the largest release since Version 1.0 in 1988, Version 6.0 adds >> a remarkable breadth of new functionality. As well as introducing >> several major new fundamental concepts, it adds nearly a thousand new >> functions, and significantly enhances a large fraction of all existing >> Mathematica functions. > > Here are two newbie observations: > > 1. Looks to me tat Mathematica moves in opposite direction to > mathematics. When I was in high school, both my math teachers > emphasized that lots of work went into to give mathematics a solid base, > and for example in Geometry folks spent about 2000 years just to verify > that one basic stone of the foundation was not needed to the standing of > the whole building. I guess it would be terrible for mathematics to add > nearly a thousand new axioms every 100 years. > > 2. My 10 year old wants to learn "programming" and because he still > was not fazed when I told him that his iMac already contained Java, C, > Objective C, C++, python, awk, gawk,... he insisted that I replace > Mathematica 4 on his machine with Mathematica 6 Student edition. After > about 20 minutes I finished the installation he comes and asking what > "Integrate" is doing. He was going over the "introduction to > Mathematica 6" or something similar and the second or third example was > Integrate right there. I am wondering if that is the right steps to be > taken for Students to "fall in love" with Mathematica 6. I myself when= > I see an Integrate anywhere near to me I duck for cover :) > > J=E1nos > > > > > ----------------------------------------- > A newbie is a newbie is a newbie (even if he has Wikipedia to help him)= =2E > > - Andrzej Kozlowski > > > > -- 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:
- annoying documentation in 6 (rant)
- From: Murray Eisenberg <murray@math.umass.edu>
- annoying documentation in 6 (rant)