Research Experience for Undergraduates (REU) in Computational Mathematics at Illinois Institute of Technology

Date: 
Monday, May 19, 2014, 9:00am - Friday, July 25, 2014, 5:00pm

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Our Site 

We are a small REU site in Chicago, now in its sixth year of operation. Among other things, our students have been successful in presenting their work at the Joint Mathematics Meeting and getting results published in student-oriented or peer-reviewed math journals.

Problem 

For computer experiments one has a collection of data, \((\bx_1,y_1), \ldots, (\bx_n,y_n)\), where each \(y_i=f(\bx_i)\) represents the output of sophisticated computer code given the \(d\)-vector of input parameters, \(\bx_i\).  One desires a good approximation to \(f\), sometimes called a surrogate, that is faster to evaluate than the function \(f\) itself.  A popular way to construct the surrogate is to use radial basis function methods, also known as kriging methods [Fas07,FSK08,Ste99].  See this link for some interactive examples.  Important practical questions include: i) how to choose the family of basis functions and their tuning parameters to get the best approximation, ii) how well these methods perform for a large number of scalar inputs, \(d\), iii) how to avoid numerical instabilities, and iv) data-driven error estimation.

[Fas07] G. E. Fasshauer, Meshfree approximation methods with MATLAB, Interdisciplinary Mathematical Sciences, vol. 6, World Scientific Publishing Co., Singapore, 2007.
[FSK08] A. I. J. Forrester, A. Sóbester, and A. J. Keane, Engineering design via surrogate modelling, Wiley, Chichester, 2008.
[Ste99] M. L. Stein, Interpolation of spatial data: Some theory for kriging, Springer-Verlag, New York, 1999.

Solution

Two REU students will endeavor to solve these and related problems, working together with faculty (Profs. Greg Fasshauer and Fred J. Hickernell) and graduate student mentors. Subject to available funding, this project will span ten weeks in the summer of 2014 (starting and ending dates can be negotiated - especially for students from universities following the quarter system).  Students will attend tutorials given by faculty and graduate students to describe the problems in detail and introduce the numerical software to be used.  Students will also perform a literature search, read recent literature related to the research problems, derive possible algorithms to solve the problems, and develop computer programs to implement and test their solutions.  Work will be done independently and in groups. Students will meet regularly with faculty to report and discuss their results.  Each  student will receive a stipend of $5000.  Students will be encouraged to present their results at the Joint Mathematics Meetings in San Antonio in January 2015 or in another conference.  Travel support is anticipated.

Apply

REU students should know calculus, matrix algebra, and computer programming.  Experience with numerical methods and MATLAB is an asset. Students must be US citizens or permanent residents, who have not yet completed their bachelor's degrees.  To apply, submit your curriculum vitae, including your name, gender and ethnicity (optional), whether you are a US citizen or permanent resident, and details of your relevant coursework and experience.  You should also submit transcripts of college/university courses taken.  A cover letter should describe what you find interesting about mathematics and any experience you have had with programming (C, Java, etc.) and mathematical software (MATLAB, Mathematica, Maple, etc.).  A confidential letter of recommendation from a professor is required.  All materials should be submitted to Prof. Fred Hickernell, Department of Applied Mathematics, Illinois Institute of Technology, 10 W. 32nd St., Chicago, IL 60616, hickernell@iit.edu.  Applications received by March 15, 2014 will receive priority.  Selection of successful applicants is expected to be towards the end of March.  Women and underrepresented minorities are especially encouraged to apply.

Due to our current funding status, the upcoming REU is subject to available funding.

If you have questions, please contact Prof. Hickernell.