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Higher Mathematics Made Easy December 17, 2009

Posted by Peter Varhol in Software tools.

I have a graduate degree in applied mathematics.  I was never very good in mathematics, but my love of the subject matter managed to sustain me through three-plus years of advanced calculus, differential equations, statistics, forecasting, queuing theory, FFTs, Laplace transforms, and the like.  When I’ve taught these subjects, I’ve always stressed that they are both easier to understand, and more relevant, than people have been led to believe.

I didn’t mean that as hyperbole, but rather as a firm notion that useful mathematics didn’t have to be obtuse and out of reach of all but the nerds.  Maplesoft, with Maple 13 and MapleSim 3, have demonstrated that I must have been on to something.  I had the opportunity to examine these products and speak with Tom Lee, Vice President of Applications Engineering and Chief Evangelist at MapleSoft.

Maple, whose technology originally came out of Canada’s University of Waterloo, is the godfather of the symbolic mathematics engines.  That means that it can manipulate not only numbers, but also variables as parts of equations.  Those equations can be just about anything you would like, from integral calculus to differential equations.  You simply type in the equation, and Maple will solve it.

It may seem like little more than an intellectual exercise, except that there are plenty of fields where higher-level mathematics is needed to analyze and solve technical problems.  This includes design engineering (civil, structural, aerospace, mechanical; really, just about any type of engineer), financial modeler, forecaster, operations research analyst, and economist.

What did these professionals do in the era before Maple and its competitors?  “Estimated, guessed, or over-engineered,” according to Tom Lee.  It’s not that the math was particularly hard, but there was a lot of it, and with deadlines and other tasks requiring less concentration, a ballpark approach was used more often than not.

MapleSim is a simulation package that takes Maple equations and simulates a system based on those equations.  It includes both predefined equations and many components and examples that can be pieced together in different ways to build different systems.  This can be anything from an automobile carburetor to a bridge.  A simulation of a carburetor can test gasoline consumption or engine efficiency, for example, under different types of gasoline-air mixtures.  The savings in time and money over building actual prototypes in some cases can be measured in years and millions of dollars.

I’ve been away from mathematics for a while, as have many professionals who learned it as a part of their education but don’t have the opportunity to use it in practice.  Lee points out that there can be a learning curve for Maple in such circumstances, but that ultimately it may bring back a resurgence in math-based analytics.

Mathematics.  Good stuff.  Not always easy, but accessible.  With symbolic math engines like Maple, today you can almost call it easy.



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