Math 497 — Problem-Solving Projects in Business, Government, and Industry
Math 497 was developed with support of the Preparation for Industrial Careers in Mathematics (PIC Math) program of the Mathematical Association of America (MAA), supported by the National Science Foundation (NSF) Grant Foundation Grant DMS-1345499. In this course, student teams use various mathematical and statistical tools to attack real-world problems, while developing various skills needed to carry a project from the planning phase through a final presentation and report. Past projects have included modeling the spread and mitigation of Ebola in Liberia, and analyzing risk factors for diabetic retinopathy, a leading cause of blindness in working-age adults, for patients in a large data set from the Illinois College of Optometry.
The Guaranteed Automatic Integration Library (GAIL)
When performing a computer simulation to obtain an approximate answer, the amount of computational effort expended typically influences the error. One may expend as much effort as one can afford and hope that the error is tolerable, or one may wish to expend only as much effort as is needed to reach a desired error tolerance. GAIL takes this second view. Our continuing research effort has produced a library containing several Monte Carlo, integration, function approximation, and optimization algorithms that are theoretically guaranteed to meet the specified error tolerance. This sets GAIL algorithms apart from similar algorithms. GAIL is hosted by Github, and was authored by a team of faculty, alumni, graduate students, and undergraduate students: Fred J. Hickernell, Sou-Cheng Choi, Yuhan Ding, Lan Jiang, Da Li, Jiazhen Lu, Jagadeeswaran Rathinavel, Lluís Antoni Jiménez Rugama, Xin Tong, Kan Zhang, Yizhi Zhang, Xiaoyang Zhao, and Xuan Zhou.
Genevieve Hummel, Parker Joncus, Daniel Kosmas, Richard Osborn, Monica Yun, and Tanner Zielinski, undergraduate applied mathematics students, formed a research group for Random Monomial Ideals project supervised by Despina Stasi and Sonja Petrović during summer 2017. The group produced a Macaulay2 computational algebra software package for computation with random monomial ideals and extensions. Richard Osborn was supported, under Stasi's supervision, by the College of Science summer research stipend. Daniel Kosmas was supported, under Petrovic’s supervision, by the McMorris summer research stipend from the Department of Applied Mathematics. The other students were supported by the NSF research grant NSF DMS-1522662 on Randomized and Structure-Based Algorithms in Commutative Algebra.
Dan Kosmas (B.S. MATH '17) and Tim McCollam (B.S. MATH '16, M.S.) worked with Michael J. Pelsmajer during the summers of 2016 and 2017 on an open problem in graph theory on crossing numbers.
Yuanfang Xiang (B.S. MATH '15) and Weronika Swiechowicz (B.S. MATH '16) worked on a summer research project with Sonja Petrović in summer 2014. They studied problems related to effectively and accurately computing maximum likelihood estimates using numerical methods. The joint paper on this project got accepted for publication by the SIAM Undergraduate Research Online (SIURO) journal in 2015.