Whether you're trying to hold together a social network like Facebook, or looking for ways to treat a complex medical condition, mathematical modeling may be able to help find the best solution.

The study of complex networks is an interdisciplinary field where applied mathematicians, physicists, computer and social scientists, and biologists can all make contributions. By reducing a situation to its core essentials through mathematical modeling, applied mathematicians can help to discover the causes and consequences of a condition, says Assistant Professor Juan Restrepo.

Restrepo teaches courses in mathematical modeling and numerical analysis, and conducts research with graduate and undergraduate students on the behavior of heart and brain cells. His research on these dynamic networks has demonstrated that certain proteins regulating the concentration and stability of calcium are important factors in a heart condition known as “alternans,” associated with higher risk for sudden cardiac death.

Restrepo also is working with his students on a study that looks at what happens when certain nodes or connections are removed from a complex social or infrastructure network. The study could be helpful in developing strategies to prevent the collapse of these networks, he says.

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At CU-Boulder, the applied math curriculum prepares you to meet these diverse challenges. Our graduates are very successful in the job market because of our emphasis on both mathematics and computing. The demands of the workplace require that technical employees are able to create a mathematical model and then implement a numerical model to make predications. In addition to our core mathematical curriculum, each applied math major takes six to eight courses in an area of application. This provides our undergraduate majors with excellent preparation for a variety of careers.

Our undergraduate major also provides excellent preparation for graduate programs in engineering, science, business, and medicine. A number of our graduates have attended top-ranked PhD programs at UCLA, Berkeley, Stanford, Johns Hopkins, Cornell, Princeton, etc., and several have earned prestigious National Science Foundation Graduate Research Fellowships.

CU students also have excelled in the international Mathematical Contest in Modeling, which challenges student teams to solve complex, open-ended problems in a 96-hour marathon competition. The Department of Applied Math also offers a broad range of undergraduate research opportunities funded by National Science Foundation grants, and students can gain professional exposure through the student chapter of the Society of Industrial and Applied Mathematics (SIAM) on campus.

Research areas include computational mathematics, probability and statistics, nonlinear phenomena, mathematical biology, and physical applied math. Working with faculty, applied math students have developed solutions to a variety of problems in fluids, dynamical systems, data analysis, networks, signal processing, math biology, math education, and numerics. Applied math students worked with faculty to develop the Mathematical Visualization Toolkit, an award-winning online instructional tool that helps students better visualize calculus concepts.

Undergraduate students, funded by the department’s National Science Foundation MCTP grant, also have worked with faculty advisors on projects ranging from modeling the heating and cooling in a local bakery, to determining the accuracy of an option pricing equation used in financial markets, to developing and analyzing models of early HIV infection in blood cells. Graduate students, with support from various research fellowships, have conducted research on such topics as developing mathematical models that simulate ocean circulation and planetary dynamics, and studying spider webs in comparison to social networks to see if they behave as natural networks or are rather purely the result of social settings.

Applied mathematics graduates can work in a wide range of fields, depending on their interest. CU-Boulder graduates have been hired at Avaya, Deloitte, Goldman Sachs, Great-West Life, the Jet Propulsion Laboratory, Microsoft, Micron Technology, National Instruments, Northrup Grumman, Oracle, and Smith Breeden, to name just a few employers.

Many also choose to go onto graduate school. About 20 percent of CU-Boulder engineering bachelor’s graduates (college-wide) continue onto graduate school, gaining admittance to top schools such as MIT, Princeton, Harvard, Cornell, Stanford, University of California Berkeley, and the University of Texas at Austin.

The job outlook for applied mathematicians is variable depending upon the area of specialty.

The average entry-level salary for applied mathematicians in 2010 was between $40,000 and $60,000, depending upon the graduate's area of specialty.