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Academics

Mapping GPS Data

I'm a GPS addict. I have a handheld GPS, a computer GPS, a GPS phone, two GPS watches, two GPS cameras, and maybe some others. Wherever I go, chances are pretty good I have at least one GPS with me. Anytime I run/bike/hike/walk/ski I keep a record of where I went using GPS. Now that I have all this data I want to make use of it in a meaningful way. Mathematica is a fantastic tool to analyze all my geographic data. Here's an example from a recent trail run I did at a nearby park. The data is stored in a GPX (GPS exchange format) file, which is a specific type of XML. We can bring the data into Mathematica using Import.
Academics

Not Another Tsunami

Today’s earthquakes near Sumatra fortunately didn’t lead to a major tsunami. But figuring out when tsunamis will develop is a difficult matter---and an interesting exercise in applied mathematics. The main phenomenon is the propagation of so-called shallow water waves---water waves whose wavelength is large compared to the depth of the ocean. Those waves satisfy a partial differential equation (PDE) that was figured out in the 1800s. The equation is a nasty nonlinear one---that can’t be solved exactly. I’ve been working on the numerical differential equation capabilities of Mathematica for more than a decade. Our goal is to automate the solutions of all types of equations---so users just have to enter their equation, and Mathematica then does all the analysis to select and apply the best algorithm. The shallow-water equations are a good test---that I’m happy to say Mathematica passes with flying colors. One essentially just has to type the equations in, and get the solution, which is then easy to visualize---especially using the new visualization capabilities of Mathematica 6. (Click the image below to see the Mathematica animation.) Let me explain a little about what’s involved in getting this.
Academics

Work in the Land of Lakes and Volcanoes (Trabajo en la Tierra de Lagos y Volcanes)

Most of the time I’ve spent working for Wolfram Research has been in the comfort of a climate-controlled office at our Champaign, Illinois headquarters. I’ve had easy access to my great co-workers, multiple computers and a Gigabit local network. I’ve had flexible working hours, a relatively short and pleasant bicycle commute, numerous delicious restaurants nearby and a window overlooking the beautiful campus of the University of Illinois (okay, and the roof of a McDonald’s). All things considered, it’s a pretty good place to be. When I told Theo (my boss) that I wanted to give all this up and spend a year living in a Nicaraguan jungle, there was a bit of hesitation, but not much. We agreed fairly quickly that we could make it work. Here’s where I was headed: