Updated November 16, 2017

## Welcome

James Madison University (JMU) has been chosen for a National Science Foundation Research Experiences for Undergraduates (REU) site in mathematics. All interested undergraduates (who are US citizens or permanent residents) are encouraged to apply for this eight week program, in which students will work in groups of 2-4 under the supervision of their faculty mentors.

## Dates

May 21 2018 - July 13 2018.

## Projects

The optimal boundaries for the perfect steak: A perfectly cooked steak is one of the most sought-after meals, but there is very little agreement on how this fundamental dish should be prepared. Should you place the steak on a hot pan and flip it frequently? Or should you flip it only once? Should you sear it in the pan and then roast it in the oven? Or should you roast it first and sear it last? In this project, we will tackle this problem using partial differential equations. Each of these cooking techniques represents different boundary conditions for the modeling differential equation. Given a desired temperature distribution, we will identify processes using numerical and analytical techniques that will cook a steak to these specifications. This will involve mathematically modeling heat conduction and mass transfer in a theoretical slab of beef as heat is applied in different ways, evenly around the surface such as in an oven, or intensely heat applied one side, such as in a pan. It is also an optimization problem, searching for the optimal path to the desired distribution. Beyond differential equations, students with a background in programming are encouraged to apply. (And we don't discriminate against vegetarians.)

Mentors: Hala AH Shehadeh and John Webb

Making sequential decisions with combinatorics and algebra: The game of best choice, also known as the secretary problem or game of googol, has been studied since at least the 1950's and was widely popularized in a 1960 column of Martin Gardner. In the classical setup, a player conducts "interviews" with a fixed number N of "candidates." After each interview, the player ranks the current candidate against all of the candidates that have been considered so far (without ties). The player must then decide whether to accept the current candidate and end the game or, alternatively, whether to reject the current candidate forever and continue playing in the hope of obtaining a better candidate in the future. Most researchers who have studied this problem assume that all N! permutations of candidate rankings are equally likely. In this program, we use combinatorics and algebra to relax this constraint and study how various non-uniform distributions of permutations can affect the optimal strategy for the game of best choice.

Mentors: Brant Jones and Laura Taalman

Housing and a \$4,500 stipend are supplied, as well as full use of university facilities and travel expenses.

## Applications

This REU participates in the Mathematical Sciences REU Common Reply Date agreement. Any student who receives an offer from an REU that participates in the Common Reply Date agreement, including this REU, is not required to accept or decline the offer until March 8, 2018 (or later). The goal of the Common Reply Date agreement is to help students make informed decisions, particularly when faced with the potential of receiving offers from multiple REUs.