Wolfram|Alpha as a Tool for Mathematics in Education (Part 1)

Wolfram|Alpha launched on May 15, 2009 as a new "computational" engine. Rather than presenting direct search results of a query as Google does, it attempts to present data relevant to your query. Need to know the weather in your hometown on the day you were born? Google might give you a list of 20,000 sites where you can find the information, but Wolfram|Alpha can tell you right away, in the interface, no need to follow any additional links! While this is a novel feature, and certainly has far greater implications than just being an amusing trivia machine, Alpha's access to data isn't terribly important for a mathematics major like me.

When it comes to mathematical software, Maple, MATLAB, and Mathematica are the three big names. At SMU we primarily use MATLAB for scientific computing exercises because it is very easy to manipulate matrices, but Wolfram Mathematica is used in the physics department and offers as many, if not more, features than MATLAB.

What makes Alpha so appealing is that it acts as a front-end to a (only slightly watered-down) version of the Mathematica engine. I say slightly watered-down because Wolfram states that you cannot use the full functionality of the Mathematica engine, but it has proved sufficient for all of the computations I have tried performing on it so far, including Calculus, Ordinary and Partial Differential Equations, and Linear Algebra. Perhaps even more importantly than being freely accessible from any machine with a browser (given that Mathematica is generally available on most engineering/mathematics computers on campus), is that Alpha is much less picky about syntax than the full-fledged version of Mathematica. Need to integrate 1/(x^2)? Any of the following inputs works:

• int 1/(x^2)
• integral 1/(x^2) (note that the dx that calculus teachers are so picky about was left off, but Alpha doesn't care)
• int (1/x^2) dx from x = 1 to 2 (does definite integration)
• integral 1/(x^2) {x, 1, 2}
• Integrate[1/(x^2), {x, 1, 2}] (the official Mathematica syntax)

Unlike most math software, which require precise knowledge of the syntax, Alpha happily accepts nearly any intuitive input you choose to give it and comes out with the right answer, even if Mathematica would have a fit because you used wrong syntax. Even if your intuition is wrong when first trying a query, Alpha can help you correct the problem. For example, int (1/(x^2)) leads Alpha to assume that you're using int() as the floor function rather than an integral, but before it gives you the answer it states "Assuming "int" is a math function | Use as an integral instead," giving the link for you make it interpret your input as an integral instead of a floor function.

The fact that the interface is user-friendly and the syntax is loosely interpreted allowing a variety of users to enter intuitive queries and get the answer they're looking for, in either symbolic or numeric form, makes performing mathematical computations a breeze. Now Alpha is in a position to revolutionize the way students approach math classes. In the past, high school teachers didn't like calculators but they were mostly useless for symbolic computations, and most algebra and nearly all of calculus required a working knowledge of the mathematics behind the process before you could plug into the calculator and get an answer. Upper level mathematics were safe. The TI-89 allowed for symbolic computations of algebra and calculus, but was difficult to use, and differential equations and linear algebra still remained safe. To use software for higher level math required access to a machine with expensive software and a working knowledge of the syntax, and no knowledge of intermediate steps. Alpha changes the game completely: I've input problems from my old Calculus and Differential Equations textbooks into Alpha and it pops out the correct answer just about every time. For most of the calculus problems, it will even show me the steps it took to do the computation.

More on Wolfram|Alpha's potential impacts on high-school/undergraduate college mathematics in the next post.