NREUP 2016

National Research Experience for Undergraduates Program (NREUP) at University of Michigan-Dearborn: May 9, 2016 - July 24, 2016.

Acknowledgement

This program is an MAA activity funded by NSF grant DMS-1359016.

Faculty mentors: Hyejin Kim and Yunus Zeytuncu

Students: Brook Calhoun (UMD), Aaron Cofield (UMD), Luis Gutierrez (UMD), and Brandi Wingate (UMD) 

Guest students: Brandon Lee (UMD) and Michael Schigelone (UMD)

Program Description: General idea of decomposing a generic function (or a signal) into a superposition of symmetric pieces is a powerful tool in mathematics and science. A few specific areas it is used frequently include differential equations, signal processing, image coding and information theory.

Mathematicians use this tool to solve differential equations, engineers use it to reconstruct unknown parts of a signal from observed parts, and applied mathematicians use it to help researchers to interpolate between parts of various models, such as financial, medical and biological.

In the summer program, we plan to present this general idea using two classical tools of decomposition, Fourier series and spherical harmonics, with applications in different areas of science. 

Outcomes

• Aaron Cofield, Brandi Wingate, and Brooke Calhoun gave an oral presentation, Injectivity of the Numerical Range Function" , at 2016 Summer Undergraduate Michigan Mathematics Research conference  on July 15, 2016 at the University of Michigan-Dearborn.

• Luis Gutierrez gave an oral presentation, Spectrum of the weighted right shift operator", at 2016 Summer Undergraduate Michigan Mathematics Research conference  on July 15, 2016 at the University of Michigan-Dearborn.

• Luis Gutierrez were invited for twenty-minute oral presentation, Spectrum of the weighted right shift operator , at the Young Mathematicians Conference  which was held at the Ohio State University from August 19 to August 21 with full travel support.

• Luis Gutierrez gave an oral presentation, ``Spectrum of the weighted right shift operator'' at the 25th annual session of the Meeting of Minds (MOM) Undergraduate Research Conference on May 12, 2017.

Pictures and Videos: 

2017 CASL Undergraduate Research Showcase: Luis Gutierrez