## Undergraduate Research

Please visit the Mathematics Undergraduate Research page for department wide information about current research opportunities for undergraduate students (including when and how to apply for funding). Below is a snapshot of the undergraduate research being done within the MAC group.

### COMAP Mathematical Contest in Modeling

The COMAP Mathematical Contest in Modeling (MCM) is an annual international contest where teams of three undergraduate students use mathematical modeling to solve a real world problem. Teams have just 4 days to choose one of two posed problems, clarify and make necessary assumptions about the problem, develop and analyze a mathematical model, and compose their findings in a clear and coherent paper. A panel of judges then score the solution papers and prizes are awarded. In 2014, 6,755 teams representing institutions from 18 countries competed in the MCM.

The next contest will be held February 5-9, 2015.

The competition is an excellent opportunity to practice and demonstrate your mathematical skills. Itâ€™s a rewarding and fun, albeit intense, experience. It also is an impressive resume credential when applying for internships or graduate school. Below are some links to more information.

*Informational meeting*: Wednesday, October 22 at 4pm in LCB 323. Please contact Braxton Osting (osting AT math DOT utah DOT edu) for more information.

### Math 4800 - Introduction to Research

These courses provide a research experience in a familiar course setting. There is usually one Applied Mathematics topic every academic year. Here is a list of topics involving the MAC group since the Fall 2012. The complete list is at the Math 4800 archive page.

- Fall 2014. An inverse problem: finding boundary fields which produce breakdown.
*Instructor:*Graeme Milton - Spring 2014. Selected Numerical Algorithms and Their Analysis.
*Instructor:*Yekaterina Epshteyn

## Research Experience for Undegraduates (REUs)

Here is a list of undergraduates doing research within the MAC group (since Fall 2012).

### Fall 2014

- Zhao Jin. Construction of Optimal Portfolio Strategies.
*Mentor:*Jingyi Zhu - Michael Primrose. Imaging with waves in random media.
*Mentor:*Fernando Guevara Vasquez (Supported by NSF DMS-1411577) - Michael Senter. Numerical investigation of First Passage Time through a Fluid Layer.
*Mentor:*Christel Hohenegger (Supported by NSF DMS-1413378) - Wenyi Wang. Imaging in a Homogeneous Aluminum Plate by Using Ultrasonic Waves.
*Mentor:*Fernando Guevara Vasquez - Tao Yu. Construction of Optimal Portfolio Strategies.
*Mentor:*Jingyi Zhu

### Summer 2014

- Logan Calder. Modeling material failure in a triangular lattice.
*Mentor:*Andrej Cherkaev - Trevor Dick. Nonlinear Elasticity: Optimal Climbing Rope.
*Mentor:*Davit Harutyunyan - Alex Henabray. Numerical Solution of 1D Stefan Problems.
*Mentors:*Yekaterina Epshteyn and Jason Albright - Yang Lou. An extension of the PAM method to three dimensions for interface tracking.
*Mentor:*Qinghai Zhang - Michael Senter. Concurrency and GPU Computing in C++ with MATLAB.
*Mentor:*Christel Hohenegger* Kejia Zhu. Modeling material failure in a triangular lattice.*Mentor:*Andrej Cherkaev

### Spring 2014

- Nathan Briggs. General case of 2D and 3D optimal design of optimal composites.
*Mentor:*Andrej Cherkaev - Logan Calder. Fractional Brownian Motion of Prices in the Stock Market.
*Mentor:*Jingyi Zhu - Ryan Durr. The Quantification of Exit Times for varying fluid models.
*Mentor:*Christel Hohenegger - Camille Humphries. Adaptive Numerical Simulation of a 1D Shallow Water Model.
*Mentors:*Yekaterina Epshteyn and Jason Albright - Sage Paterson. Modeling Electrical Breakdown and Fractal Lichtenberg Figures.
*Mentor:*Elena Cherkaev - Michael Primrose. Imaging with waves.
*Mentor:*Fernando Guevara Vasquez - Michael Senter. Numerical investigation of first passage time through a fluid layer.
*Mentor:*Christel Hohenegger - Weny Wang. Uncertainty quantification of acoustic wave propagation in plate material.
*Mentors:*Dongbin Xiu and Fernando Guevara Vasquez

### Fall 2013

- Nathan Briggs. Optimal three material design on the microstructure and macrostructure scale.
*Mentor:*Andrej Cherkaev - Logan Calder. Fractal Models of Finance.
*Mentor:*Jingyi Zhu - Ryan Durr. The Quantification of Exit Times for Varying Fluid Models.
*Mentor:*Christel Hohenegger - Sophia Hudson. Exploring 2D Truss Structures Through Finite Element Simulation.
*Mentor:*Andrej Cherkaev - Camille Humphries. Adaptive Numerical Simulation of 1D Shallow Water Model.
*Mentor:*Yekaterina Epshteyn - Spencer Phippen. Difference Potentials Method for Interface Problems.
*Mentor:*Yekaterina Epshteyn - Michael Senter. Random Motion in Media with Memory.
*Mentor:*Christel Hohenegger

### Summer 2013

- Nathan Briggs. Miscrostructure of three wheel assemblages corresponding to extremal conductivity.
*Mentor:*Andrej Cherkaev - Dylan Frank. Damage propagation in lattices.
*Mentor:*Andrej Cherkaev - Camille Humphries. Adaptive Numerical Simulation of 1D Shallow Water Model.
*Mentor:*Yekaterina Epshteyn - Spencer Phippen. Design of the novel numerical method for one-dimensional Stefan problems.
*Mentor:*Yekaterina Epshteyn - Deni Weeks. Wave Chaos - Wave Scarring in Quantum Billiars.
*Mentor:*Elena Cherkaev

### Spring 2013

- Brady Bowen. Random Fourier Surfaces: Applications to Arctic Melt Pond Modeling.
*Mentor:*Ken Golden - Boya Song. Horizontal fluid transport through Arctic melt ponds.
*Mentor:*Ken Golden - Alessandro Gondolo. Characterization and Synthesis of Rayleigh-damped elastodynamic networks.
*Mentor:*Fernando Guevara Vasquez

### Fall 2012

- Brady Bowen. Continuum Percolation Model for Melt Pond Evolution.
*Mentor:*Ken Golden - Nick Farrenkopf. The Mass-Spring Cantor Set.
*Mentor:*Elena Cherkaev - Alessandro Gondolo. Mass-Spring networks with damping.
*Mentor:*Fernando Guevara Vasquez - Daniel Khoury. Sea Ice and Electrical Measurements.
*Mentor:*Ken Golden

Webmasters: Yekaterina Epshteyn and Fernando Guevara Vasquez.