What Kind of Problems Might I Work On?

While they may differ widely by discipline and job title, one thing remains constant among careers in mathematics—problem solving. Some potential problems that someone with mathematical training might encounter are briefly discussed below. It may be useful to note which of them you find most intriguing, and why.

• How can an airline use smarter scheduling to reduce costs of aircraft parking and engine maintenance?
• How can one design a detailed plan for a clinical trial? Building such a plan requires advanced statistical skills and sophisticated knowledge of the design of experiments.
• Is ethanol a viable solution for the world’s dependence on fossil fuels? Can biofuel production be optimized to combat negative implications on the world’s economy and environment?
• How can automotive systems become more efficient and reduce emissions as mandated by U.S. public policy?
• How do we use major advances in computing power to incorporate knowledge about interactions between the oceans, the atmosphere and living ecosystems into models used to predict long-term change?
• How can automotive and aircraft companies test performance, safety, and ergonomics, while at the same time lowering the cost of construction and testing prototypes?
• 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, and how would it be contained?
• How do you design a robotic hand to grip a coin and drop it in a slot?
• 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 trade-off?
• Can mathematical models be coupled with efficient computational implementations to obtain practical, low-cost simulations to guide computer chip design and manufacture?
• Since a chemical company cannot test potential new products by releasing them into the atmosphere, it must develop models of atmospheric chemistry that simulate the complex chemical reactions in the atmosphere. 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?
• How can genome sequencing analysis help in making clinical decisions based on a personalized medicine approach?
• Recommendation algorithms provide users of e-commerce systems with unique ratings and recommendations of items and products based on their past purchases, behavior and interests. How can mathematics improve rating prediction performance and help enhance the consumer experience?

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 the art of abstraction and advanced computing and programming skills. Preparation for a career in applied mathematics and computational science also involves being able to apply these skills to real-life problems, and achieving practical results. Mathematical and computational skills are a huge career asset that can set you apart and open doors.

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