For the last For Math’s Sake column of the semester, I interviewed fellow mathematics PhD student Marissa Whitby. Completing her undergraduate studies at Towson University in Maryland, Marissa now works in Professor Kathrin Smetana’s research group, and has previously been a teaching assistant for many mathematics courses at Stevens. I really enjoyed getting some alternate perspectives on mathematics, and I hope you will enjoy reading about them. The interview transcript below is edited for conciseness and clarity.
Charlie: I wanted to start by asking about your background in mathematics. In particular, what experiences made you excited about the subject growing up?
Marissa: I was really lucky to have some great teachers in mathematics growing up. My first favorite math teacher was in middle school algebra, and he really made me realize that math is actually pretty cool and not as scary as you’d think. I had another fantastic math teacher for precalc in high school, who explained things in a very straightforward and fun way that wasn’t intimidating. My parents also really supported my interest in math, and took me to little workshops at nearby colleges that would talk about complicated subjects in really cool ways. One workshop had us use pipe cleaners to better understand topology, and another was on cryptography, which made me think that high-level mathematicians are also international spies. Seeing all these applications of mathematics, I figured that basically you could jump into any STEM field you wanted, since you can do so much with math.
C: Did those positive experiences continue during your undergrad?
M: Yes! My undergrad advisor ran the applied math lab at Towson, and we got a contract from an energy company looking to improve their natural gas forecasting. We introduced this pretty basic mathematical idea but it greatly improved the model they were using. It was so cool to get to play with these cool features and apply it to other fields, which is why I wanted to continue diving into the subject in grad school.
C: Very cool! What kind of research projects do you work on currently? And I’m guessing they also have an applied focus – what’s the application?
M: I work with Prof. Smetana on reduced order modeling, where the goal is to solve equations that describe something we’re interested in measuring, like fluid flow or temperature, and solve those equations very efficiently using a computer. In particular, I’ve been interested in solving multiscale problems that arise in modeling wind turbines. In that application, we have composite structures whose properties on tiny scales have a big effect on the behavior on the overall structure, so I’m running simulations to figure out if one material is going to be better than another. The reduced order modeling is important here because we are trying to test many types of materials so we need a way to simulate the turbine and also get the solutions in a reasonable time.
C: Indeed! So, what software are you using for running these simulations?
M: Right now I’ve been running things on MATLAB to do tests of the algorithms and make sure they work, and then for larger real-world applications I’d likely be using C++.
C: Got it. Is that something you’d like to work on after the PhD? What do you have in mind for a career in mathematics afterward?
M: I really love the idea of trying to work somewhere like NASA, there’s so much math involved in projects like Perseverance or the James Webb Telescope, and it helps us understand our entire universe which is mind blowing. Beyond that though, I really like the application for wind turbines or other green energy projects, since it’s also really important to take care of our climate and work on projects there that will benefit the greater good. Anything like that, sign me up!
C: Switching gears, I also was curious if you have a favorite math problem or puzzle. This can be totally unrelated to your research.
M: Yes! I thought I’d share about the Tower of Hanoi, which is a puzzle about reordering blocks or discs of different sizes, and the pieces represent levels of a “tower” that you’re supposed to move from one place to another according to a specific set of rules. It started in a Hindu temple where the religious leaders would test the patience of their students; there were 64 golden discs in the original version. But then, a French mathematician visited and was fascinated by this problem, so he came up with a way to determine how many moves it would take to solve the problem using what’s called a generating function. He found out that, with 64 discs, it would take 585 billion years to finish! I just think it’s very cool that you can use math here to figure out how long something will take and whether it’s feasible based on the constraints you have in the problem.
C: That is really cool! I didn’t know about the historical origins, but that’s an awesome story. All right, as a last question, do you have any advice or recommendations for people studying math who may be struggling, or feeling frustrated or scared by the subject?
M: A few things. I think it helps to try and make the problem as concrete as possible, drawing a picture if you can or doing something that makes it less abstract. Being able to work with things and make them more tangible really helps. Also, some people get overwhelmed with the specific formulas they have to use, but there’s no one way to solve a problem – a lot of the time you can solve a problem in so many different ways. Lastly, having a good mentor or good teacher and asking for help when you’re confused is really important: you’ll get different perspectives on the subject and eventually there will be one that resonates with you or makes everything click. So go to office hours and ask for help if you’re stuck and nothing else is working!
C: That’s all great advice! Thanks for your time Marissa!
M: No problem!
