It is unworthy of excellent men to lose hours like slaves in the labor of calculation.
    Gottfried Wilhelm Leibniz

I have often told students that becoming good at math is a lot like becoming good at a sport or at playing an instrument – practice is extremely important. Hours and hours of practice.

However, there is a lot that can be learned from having computer software do math for you, especially if the math is algebra and calculus. The kind of programs that can do this are called Computer Algebra Systems (CAS), and they can actually do much more than just algebra. The most famous CAS is Mathematica from Wolfram Research, and another one called Maple is widely used. The mathematical manipulations these systems can do are remarkable, and the term artificial intelligence seems appropriate to describe them.

Unfortunately, both Mathematica and Maple cost hundreds of dollars, and most students could not justify that much expense. There are a few CAS programs that are free, and for a year or so, I experimented with one called Maxima. However, when Wolfram Research introduced WolframAlpha (W|A) in 2009, it seemed clear it was much superior. As many people know, W|A is web based and free, and it can do much more than just mathematics. My focus here is just on its math capability. W|A gives us access to a substantial subset of Mathematica, and those with an appreciation for math will often be amazed by what it can do.

Of special interest to the student, the page showing the problem solution often has a link called Show Steps. Clicking that will bring up a step-by-step explanation of how the solution was obtained.

An oddity of W|A is that there appears to be no formal documentation – just a series of sample commands that actually don’t cover nearly all of its capabilities. I have found a good many of the “hidden” commands by just trying things, or by looking at the Mathematica documentation for hints about things to try. The table below summarizes my exploration so far, and is more comprehensive than the W|A web site.

I welcome corrections and additions, and may post a revised version of the table later.

This entry was posted on Friday, January 8th, 2010 at 2:27 am and is filed under Learning Math, Thrilling Math, Trig/PreCalculus. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.