My Experience as a 2013 SMART Scholar’s Mentor

Written by Nick Battista, graduate student in the Department of Mathematics

As a Ph.D. student in applied mathematics, when I heard I was going to be a mentor to a SMART student I felt a little nervous. It was not immediately clear to me how much a SMART Scholar would be able to contribute to or understand about my project but, more importantly, I was not sure how effective a mentor I could be. However, within the first few days of meeting Andrea Lane, it was evident that we were going to mutually benefit from one another. 

At first it was a challenge since my research requires extensive knowledge of mathematical modeling and scientific computing/numerical analysis, as well as computer programming across multiple languages and platforms. Andrea started the program not having a strong background, or in some cases any experience, in these things. This was a blessing in disguise. It forced me to learn how to communicate the essential ideas for working on this project and thereby how to transfer my knowledge to Andrea in a way that made sense to her. Furthermore I wrote many tutorials and summaries to describe the basic programming ideas, how to use various software and programming platforms, and the big picture of what research is in general.

Due to Andrea’s unprecedented work ethic, she quickly learned the necessary skills to perform various numerical simulations and analyze their data to produce meaningful results, interesting plots and images, and high quality videos of the simulations. She ran numerical experiments pertaining to the flow of blood, including red blood cells, within embryonic heart tubes for various volume fractions of the red blood cells. She analyzed average flow velocities, pressure, and shear within the heart tube. All of these quantities are thought to be important to the morphogenesis of the heart itself. The simulations that she made, ran, and analyzed helped me answer questions that are pertinent to the aims of my own Ph.D. thesis work.

Beyond the actual embryonic heart modeling research, Andrea expressed an interest in learning more about general scientific computing and programming. Throughout the summer, we made sure to set some time aside to discuss advanced topics in numerical analysis. The goal was for her to see what it is like to develop her own code from the ground up. Eventually Andrea developed her own backward stable nonlinear ordinary differential equation solver, where she had to blend together a bunch of different algorithms she had previously coded with me during the course of the summer.

This was important because, even though the code we use for the heart tube simulations is extremely sophisticated and complex, we could use the ideas she learned from writing her own codes to help her better understand how our heart tube code worked and actually runs simulations.  It was an unparalleled feeling seeing her actually physically finally understand the big picture behind these type of mathematical models and simulations.

All in all, it was a great experience being a SMART scholar’s mentor this summer. It taught me a lot about being an effective mentor and how to competently communicate high level mathematical ideas to someone who hasn’t had as much formal training (or any) in mathematical modeling and scientific computing.  I only hope Andrea got as much out of this research experience as I did.