What Kind of Problems Can I Solve?
The careers may differ, but one thing remains constant—problem solving. Listed below are some examples of problems someone with mathematical training might be asked to solve. It may be useful to note which problems you find most intriguing, and why. Examples of organizations doing each type of work are also given.
- How can an airline use smarter scheduling to reduce costs of aircraft parking and engine maintenance? American Airlines; IBM Research
- How can a detailed plan for a clinical trial be designed? Boston Scientific; Medtronic; Wyeth; Pfizer
- Is the replacement of gasoline with ethanol a viable solution to the world’s dependence on fossil fuels? Can biofuel production be optimized to combat negative implications on the worlds’ economy and environment? U.S. government agencies and labs; Amoco Exxon Research and Engineering; Petrobras
- How might the U.S. Social Security system be changed to guarantee the integrity of the system’s future? U.S. Social Security Administration
- How can automotive systems become more efficient and reduce emissions as mandated by U.S. public policy? Ford Motor Company; General Motors
- How can the current uncertainty of nuclear stockpile stewardship and management be estimated for optimum efficiency and safety? U.S. government agencies and labs; Lockheed-Martin Energy Research Corporation; Schatz Energy Research Center (SERC)
- How can climate modeling at the global, regional, and local levels reduce uncertainties regarding long-term climate change, provide input for the formulation of energy and environmental policy, and abate the impact of violent storms? U.S. government agencies and labs such as the National Oceanic and Atmospheric Administration (NOAA)
- How can automotive and aircraft companies test performance, safety, and ergonomics, while at the same time lowering the cost of construction and prototype testing? The Aerospace Corporation; Lockheed Martin; Boeing; General Motors; Ford Motor Co.
- 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 this? GlasoSmithKline; Merck & Co., Inc
- How might disease spread in populated areas in the event of a bioterrorism incident? U.S. government agencies and labs; U.S. Department of Homeland Security
- How do you cram enough data through a high-bandwidth communications network to deliver large data sets reliably? Clear Channel Communications; Qwest Communications; Verizon
- 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? Shadow Robot Company; iRobot Corporation
- How can you mathematically model the spread of a forest fire depending on weather, ground cover, and type of trees? Fire departments; U.S. government agencies such as the National Oceanic and Atmospheric Administration (NOAA)
- How can you allocate an investment among various financial instruments to meet a risk/reward tradeoff? Citibank; Moody’s Corporation; Prudential
- Computer chips are “printed,” much like photographs, from a negative, but manufacturing the “negative” is too expensive to permit cut-and-dry 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? Bell Laboratories, Alcatel-Lucent; Hewlett-Packard; Honeywell; IBM Corp.; Motorola; Philips Research; SGI
- A chemical manufacturer must shift one of its product lines to a new family of compounds that will not harm the ozone layer. 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? U.S. government agencies and labs; DuPont; Kodak
These are just a small sample of the types of problems mathematicians and computational scientists might work on. As you consider your career options, can think how you might parlay your talent into a field that interests you.
Remember: mathematical and computational talent is a huge career asset that sets you apart and opens doors.
Part of the preparation for your future is obtaining a solid foundation in mathematical and computational knowledge—tools like differential equations, probability, combinatorics, applied algebra, and matrices, as well as central skills like the art of abstraction, communicating, and being able to do advanced computing and programming. Preparation for a career in applied mathematics and computational science also involves being able to apply these skills to real-life problems. With preparation in mathematics or computational science and a background in another field, you can enjoy the dual reward of utilizing your skills and achieving practical results. The next question is: where can I work?
Next Page: Where Can I Work?