The WPI REU program in Industrial Mathematics and Statistics provides a unique educational experience for students of the mathematical sciences by introducing them to research in an industrial environment. It provides a glimpse of the many career possibilities which are open to students with a strong mathematical background.
The students work in teams on problems that come directly from local business and industry. Students work closely with a company representative to define the problem and develop solutions of immediate value to the company. They work closely with a faculty advisor to formulate the problem mathematically and maintain a clear focus on the mathematics at the core of the project. Industrial problems rarely fit into one area of mathematics and this fact is an important part of the research experience. Many projects require some combination of classical analysis, modelling, statistics, optimization, and computer programming.
The results from the projects completed in the REU program are of direct importance to the industrial partners and impact research and development at these companies. Further, projects developed for the REU program are often modified for use in secondary school mathematics curricula in order to improve student motivation and generate interest in careers in the mathematical sciences.
The program provides challenges to students not faced in standard undergraduate programs and develops skills not always developed in traditional educational programs, such as (a) communication at several levels, including reading, writing, speaking, and listening; (b) problem formulation as an interactive, evolutionary process; and (c) the ability to work with a diverse team.
The WPI REU Program in Industrial Mathematics and Statistics has existed since 1998 and, since that time, we have worked with 130 students who have come from 99 different U.S. colleges in 31 states and Puerto Rico; exactly 59 of the 130 students were female. Of the 99 universities that have been represented at the REU program over the last 12 year, half of them do not offer a PhD program in mathematics. Altogether, we have worked on 37 different industrial projects sponsored by 17 different companies. Students from the REU program often go on to pursue graduate degrees in mathematics and in other fields, and they also pursue careers in finance and industry.
This site is supported by the Department of Defense in partnership with the NSF REU program.
provided a unique educational experience for students of mathematics and statistics by introducing them to research on real-world problems come that directly from local business and industry. Students worked closely with a company representative to define the problem and to develop solutions of value to the company. The students worked closely with a faculty advisor to formulate the problem mathematically and maintain a clear focus on the mathematics at the core of the project. The industrial problems rarely fit into one area of mathematics and this fact has been an important part of the research experience. The projects called upon analysis techniques, modelling, statistics, optimization, and computer programming. The program developed the students' oral and written communication skills so that they can communicate their results effectively in industrial and academic settings. The students visited their industrial partners and other companies and were exposed to the sort of work that non-academic mathematicians and statisticians do. The program also provided opportunities for the students to get non-technical professional development from experts. Six faculty members advised projects. There were 36 students in 2010-2012; 15 of them were women. The students came from universities in California, Canada, Connecticut, Florida, Iowa, Idaho, Illinois, Massachusetts, Maryland, Minnesota, Missouri, Montana, North Carolina, New Jersey, New York, Ohio, Pennsylvania, Tennessee, Texas, Utah, and Wisconsin. The students have gone on to pursue graduate degrees in mathematics and in other fields, or are already working in industry. The results from the projects completed in the REU program directly impact research and development at companies and laboratories in the region, and in the relevant mathematical sciences field. Ten research projects were completed on projects coming from companies that focus on insurance, finance, medical research, manufacturing, and geothermal heating: 1. Modeling Multidimensional Tolerance Stackup in Microsoft Excel using Monte Carlo Simulations with Procter & Gamble – Gillette. Created a statistical tool to predict the frequency of defective products for a given manufacturing process. Won award at 2012 Joint Mathematics Meeting. 2. Modeling Cancer Stem Cell and Non-Stem Cancer Cell Population Growth with Center of Cancer Systems Biology at St. Elizabeth's Medical Center. Developed several models to mathematically and numerically investigate the dynamics of the interactions between stem and non-stem cancer cell populations. Presented work at 2012 Joint Mathematics Meeting. Work resulted in peer-reviewed publication, "A Multi-Compartment Mathematical Model of Cancer Stem Cell Driven Tumor Growth Dynamics," Bulletin of Mathematical Biology, 2014, by Weekes, Barker, et al. 3. Incorporating Forward-Looking Signals into Covariance Matrix Estimation for Portfolio Optimization with Wellington Management. Adapted Markowitz portfolio optimization taking financial regime change into account via a method which dynamically estimates the covariance matrix of asset returns. Presented work at 2012 Joint Mathematics Meeting. 4. Geometry and flow effects on the performance of vertical residential geothermal heating systems with New England Geothermal Professional Association. Developed novel mathematical descriptions to inform how different cross-section geometries and geometrical variations of a geothermal heating system affect the harnessing of energy from the soil. Presented work at 2012 Joint Mathematics Meeting. Work resulted in peer-reviewed publication "On thermal resistance in concentric residential geothermal heat exchangers," Journal of Engineering Mathematics, June 2014, vol 86, 103-124, by Frei, Lockwood, et al. 5. Evaluation of Glucose Sensor Simulated Use as a Predictor of Device Performance with Instrumentation Laboratory. Analyzed the performance of the glucose sensor and the lactate sensor in a point-of-care device that estimates blood analyte concentrations using the combined data from sensor card testing and field data of instrument performance. 6. Pricing and Hedging Variable Annuities. Determined fair price for several insurance guarantees and what an insurance company should do to hedge against market risk. 7. Mathematical Modeling of Cobbling Instabilities in Steel Rod Fabrication with Siemens VAI. Developed mathematical models in highly nonlinear geometries in order to help identify the dominant mechanisms of cobbling under different operating conditions. Won award at 2012 Joint Mathematics Meeting. 8. Sharpe Ratio versus the Information Ratio: Capturing Minimum Variance Portfolios with State Street Global Advisors. Constructed a variety of portfolios based on ratio rankings and compare future returns. The performance of these portfolios helped test whether the customary focus on benchmark-driven performance within delegated asset-management creates exploitable investment opportunities. Presented work at 2012 Joint Mathematics Meeting. 9. Conditioning the Capital Asset Pricing Model to Incorporate Macro-Economic Based Variables with State Street Global Advisors. Developed a conditional macroeconomic variable that captures time variation in risk premium across business cycles and tested predictive power of this variable for future market returns. Presented work at 2012 Joint Mathematics Meeting. 10. Re-rating of Auto Insurance Premiums with Hanover Insurance Group. Worked with Hanover's actuaries to design and perform a re-rating and to make recommendations about prospective changes to premiums.
