Before I say anything else about Mathematica, let me just say that I think Wolfram Research are missing out. They've got a Mac version of Mathematica, but it's still called Mathematica, and I feel like it needs a catchy name. Wolfram, if you're reading, how about Mathemactica sometime in the future?
If that paragraph confused you, I'm talking about Mathematica, a powerful and widely-used piece of math software. It does lots of pretty 3D stuff, tables, and tons more, but it will also do Riemann integrals and a bunch of other stuff that you tried to forget from your college math classes. I use it a fair bit, and I'm continually impressed by the power and flexibility it has, so I'm even more excited to play with version 6.0.
Wolfram has just recently released Mathematica version 6.0 and is sending it out the door with a ridiculous amount of new features. They're also promising that one of the new features is "the most important in the 20-year history" of the program. So what are these new features? Well, the big one is something called "Dynamic Interactivity," which sounds like a bad marketing buzzword. Dynamic Interactivity (or DI for the cool kids) looks to be a way of quickly generating interfaces for Mathematica code. As an example, say you're trying to calculate an integral. Using the new DI functionality, you can add sliders for each of the endpoints, and watch a pretty graph of the integral change as you move the endpoints. It sounds like a pretty simple example, and it is, but the same features can be quite powerful when you're working with 3D graphs or other complex structures.
That's not all, though. Mathematica 6.0 comes with lots of other stuff, a full description of which would take up way too much space. There are new and improved 3D graphics and visualization tools, lots of new interface tools, and various expanded integration, statistics, and other functions. There are apparently over 1,000 new functions in this version, so learning them all should keep you busy for a while. Last but not least, there are a bunch of new data tools built into Mathematica, including support for all kinds of data types. You can import molecules, time-series data, maps, and even Apache logs. But even if you don't have lots of data laying around, there's a "Load On Demand" data library provided with the new version, just in case you're bored.
If you're curious about the new features, I'd highly recommend checking out the demos and new features (complete with sample code). Mathematica is a bit pricey for the average user to just play with (but be sure to look for educational prices or site licenses if you're a student); however, it's a very powerful tool and well worth the money if you need it.
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