Claremont Mathematics REU 2012

 

UPDATE: The NSF has declined to fund the Claremont Colleges Mathematics REU this Summer, so the program as described below will not be happening this summer. Please check back next year for updates on the status of the Claremont Colleges Mathematics REU.


Pending funding, the Claremont Colleges Mathematics REU (Research Experience for Undergraduates) in beautiful Claremont, California will host nine undergrad student researchers from June 4 through July 27, 2012. Student researchers will collaborate with Claremont faculty on one of three research projects, gaining hands-on experience with modern mathematical research methods and writing tools including LaTeX and Beamer, culminating in a conference-style talk and poster session. A weekly colloquium series will expose student researchers to the culture of mathematics, and a series of workshops will provide training and answer questions on topics from authoring scholarly publications to the graduate school application process.

Students selected for the REU will receive travel funding, room and board and a stipend and will return with a research talk and poster suitable for presenting at their home department or at a research conference. Like other summer internships, the Claremont Mathematics REU offers serious students of mathematics summer pay, valuable on-the-job experience and networking opportunities; unlike other internships, however, the REU offers a unique opportunity to experience firsthand the life of research mathematician as well as a chance to make a lasting contribution to human knowledge in the form of publication in a professional journal.

Projects for Summer 2012 are in the areas of applied mathematics, analysis and differential equations:

Running faster in lower dimensions with professor
Deanna Needell (Claremont McKenna College)

Is a fast MRI possible? Data in the modern world like the measurements that create an MRI image is so voluminous that storing, viewing, and analyzing it is often extremely difficult both physically and computationally. Dimension reduction addresses this issue by projecting high dimensional data onto a low dimensional space in such a a way that the geometry of the data is preserved. This technology can be used in digital photography, medical imaging, computational biology and many more applications. In this project, we will harness the power of randomized dimension reduction to accelerate methods in applications which require high computational costs.

Interested students should be comfortable with linear algebra. At least one semester of statistics or probability would also be helpful. No previous
exposure to dimension reduction or randomized algorithms is needed. A well balanced team will include a mix of students with and without programming experience (preferably in Matlab).


Lengths of Lemniscates with professor
Michael O'Neill (Claremont McKenna College)

Let P(z)= zn + ... be a monic polynomial of degree n and consider the curve


 
γ(P) = { z : |P(z)| = 1 }.

Erdős, Herzog and Piranian conjectured in 1958 that the length, L(γ(P)), of γ(P) is maximized when P= zn - 1, the case where the lemniscate is a symmetric flower shape. The problem is still open and cash prizes are offered by Erdős and Eremenko for the solution. In this project we will study recent progress on the problem and attempt some of our own. Interested students should have had courses in multivariable calculus and beginning complex variables.  Participants can expect to improve their technique in analysis and function theory and to learn something about the calculus of variations.


Nonlinear Boundary Value Problems and Applications with professor
Alfonso Castro (Harvey Mudd College)

This project shall familiarize the students with techniques such as quadrature, phase plane and energy arguments for the solvability of nonlinear boundary value problems. Fixed point theorems derived from the generalized intermediate value theorem and Brouwer degree will be studied. Applications to equations arising in Mathematical Biology, Mathematical Physics will be investigated.

 



We are accepting applications at
www.mathprograms.org; a complete application will require a copy of your transcripts and letters of recommendation from two professors familiar with your work as well as filling out an online questionnaire. Look for us soon on facebook and google+!

Please direct questions to REU program director Sam Nelson at Sam (dot) Nelson (at) cmc (dot) edu.