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Re: V9 !!!
Posted:
Dec 3, 2012 3:31 AM


There are two answers to this. One is for Mathematica to have greater "hierarchical density" or "hierarchical depth", i.e., provide lower level routines from which higher level routines are built. Then students might work at the lower levels and "applied production mathematicians" might work at the top levels. But Mathematica does not do a lot of this, which might be considered one of its weaknesses. It is too "toplevel" oriented. However, it does provide basic routines from which one can implement lower level approaches.
So the second answer is to provide third party applications that expand the "hierarchical density" for specific mathematical or technical fields. WRI could not reasonable do this for all technical fields. Do you want a million commands in Mathematica? And WRI people might not even be the best people to do this  they can't be elegant experts in everything. Teachers might want really good additions for teaching undergraduate math, and a graduate student or researcher might want an extensive application for a specific area. But neither of them would want every possible application.
That is why those who say that Mathematica users should never buy a third party application are absolutely wrong. Documented Mathematica applications for communication and collaboration are one of its most powerful features  still much underused and only fitfully supported by WRI itself.
David Park djmpark@comcast.net http://home.comcast.net/~djmpark/index.html
From: Murray Eisenberg [mailto:murray@math.umass.edu]
However, I've always had mixed feelings as Mathematica has grown to build in more and more mathematical functions. At times this has taken the edge off what was a valuable exercise for my undergraduate students: defining more complicated functions  e.g., div in vector analysis or nullSpace in linear algebra  that forced students to understand the precise underlying definitions and algorithms. And it tended to take away a sense of power and accomplishment when students could start by defining the simplest kind of function, such as performing a single elementary row operation, and stepbystep building ever more complicated functions, culminating in something relatively sophisticated, such as finding the orthogonal projection of a vector upon the span of a given set of vectors, and even going further, such as using the latter to find the leastsquares solution to an overdetermined linear system.



