Mathematica programming – an advanced introduction (2009)

I personally have mixed feelings about Mathematica. Stephen Wolfram has issues, but I don't buy software based on the attitude of the creator. Otherwise, many open source projects that I use with some combination of very cranky, irritable, rude, egotistical, and/or arrogant people involved would be ruled out as well...

Closed source that costs $$$ is definitely an issue - for a while after school it was hard to continue using Mathematica until my employer acquired a site license and I got a home license. In the meantime I tried all of the usual suspects - from open source things (Maxima, Sage, Octave, Julia, and so on...) to other commercial products (e.g., Maple and Matlab). I ended up returning to Mathematica for two reasons: 1) it has a massive standard library, and once you learn the idioms of the library and the language, I found it pretty usable; 2) it has beautiful graphics capabilities.

The open source tools are hit-or-miss on the standard library front - some of the libraries are great, some are missing major features, or their implementations are poor. (Yes, it's OSS and one can either contribute code or feedback, but often I have a problem to solve NOW - I don't have time to wait for the OSS to catch up.)

As for the graphics, I'm not sure what it is about Mathematica visualizations that I like so much, but they look GOOD relative to the others I've tried.

At the end of the day though, Mathematica is just one of the useful tools in my toolchain - the others have their plusses and minuses as well. But one thing I've adapted to over the years is that A) sometimes good software costs money, and B) sometimes jerks are involved in creating good software. Neither case is one that I feel is a valid justification for rejecting a software package outright.

Edit: It's worth noting the time period over which I've been mucking around with Mathematica and the other alternatives I mentioned above. I started seriously using numerical and scientific computing software (including Mathematica) in 1994, so that's a 21 year period of wandering around the space trying out things here and there.

Sage is accumulating a lot of math software. Try it at cloud.sagemath.com. An introduction to sage for undergraduates, using linear algebra as the topic focus is at http://www.gregorybard.com/SAGE.html

I try to avoid Mathematica because Wolfram himself is a self-centered prick and it's closed source - it is a shame, too.

Matlab's strength is doing lots of things for you through its toolboxes; Sage Math is a bloated monster, Maxima is pretty damn good, haven't spent any time with Axiom. Octave is pretty good (none of those delicious toolboxes though) and Scilab just 'felt' wrong (and its Simulink knockoff was atrocious). Mathcad is great, but also expensive and closed - Mathworks kneecapped them by buying the company that made their symbolic engine (and turning it into a toolbox/addon for Matlab).

OpenModelica I never got far with, but I'd like to do some multidomain simulation with eventually.

If I missed a good CAS, let me know.

I wonder why the creators of Mathematica didn't aim for a pure functional language.

Love programming in Mathematica in college but the closed source development and expensive licenses made it a non-starter for me over the years.