What Kind of Problems Do You Want to Solve?

The careers may differ, but one thing remains the same -- problem solving. Listed below are some potential industrial problems that a mathematician or computational scientist would solve at his/her place of work. Take note of which of the following sample problems you find most intriguing, and why.

• A pharmaceutical company wants to search a very large database of proteins to find one that is similar in shape or activity to one they have discovered. What's the most efficient way to do so?
• How might disease spread in populated areas in the event of a bioterrorism incident?
• How do you cram enough data through a high-bandwidth communications network to deliver large data sets reliably?
• When we pick up a quarter, our brain sends complicated signals to our nerves and muscles. How do you design a mechanical hand to grip a coin and drop it in a slot? An automobile production plant is falling far short of the capacity for which it was designed. Why? How can you mathematically model the spread of a forest fire depending on weather, ground cover, and type of trees?
• How can you allocate an investment among various financial instruments to meet a risk/reward tradeoff?
• How does a protein, like an enzyme, fold into a molecular shape? Where are the active sites on the molecule?
• Computer chips are "printed", much like photographs, from a negative. But manufacturing the "negative" is too expensive to permit cut-and-try testing of proposed layouts and the corresponding "print." Are there accurate mathematical models of the exposure process? Can they be coupled with efficient computational implementations to obtain practical, low-cost simulations to guide chip design and manufacture?
• A chemical manufacturer must shift one of its product lines to a new family of compounds that will not harm the ozone layer. Since it cannot test possible new products by releasing them into the atmosphere, it must develop models of atmospheric chemistry that simulate the complex chemical reactions in the atmosphere, the action of the sun, etc. Can computational simulations show sufficient detail to capture the effects of the chemicals, but still be fast enough to permit studies of many different chemicals?

These problems are just a sample of what industry has to offer. Your career search should involve deciding how you'll parlay your interest in mathematics into your eventual career path.

Part of the preparation for your future is mathematical knowledge-tools like differential equations, probability, and matrices, as well as central skills like the art of abstraction, good communication skills and the ability to program computers. Another part of preparation is experience using these ideas in real applications, experience in finding the general patterns among specific problems in engineering, science, finance, medicine, and many other areas. With preparation in mathematics and a background in another field, you can enjoy the dual reward of applied mathematics: using your skills and seeing the results.