Analytics and Data Science
Due to the exponential growth in the capacity for data storage and steadily decreasing costs over the last 80 years, society has seen an explosion in the accumulation and availability of data. Whereas a century ago, this data could be processed by a few individuals with pen and paper, this proliferation of data has created a growing need for mathematical tools to make it possible to parse large datasets, extract meaningful information, and identify significant trends in order make accurate forecasts and inform and optimize decision making.
This process of using data to making meaningful inferences goes by many names data science, analytics, big data, etc. but essentially it boils down to applying mathematical, statistical and computational tools to the study of real world data. Consequently, mathematicians (and mathematics students) are uniquely positioned to tackle these sorts of problems.
Recent projects in this area have involved using machine learning to reconstruct mathematical models of coupled oscillators from observed time series, using Bayesian methods to identify geospatial trends in the spread of influenza, and a variety of undergraduate projects involving both regression and classification. For more information, see undergraduate projects or papers.
I also have collaborated on a variety of different data-driven applied problems. These projects have included: writing software to analyze proposed athletic schedules to enable college administrators to make informed scheduling decisions, and creating algorithms for optimizing the assembly of fuel cells and for scheduling television advertisements for industry startups. See my github page and papers for more details.