Q: How did you first become interested in mathematics?
A: I declared sometime toward the end of sophomore year, but I think I realized I wanted to be a math major at the beginning of sophomore year.
Q: What do you think drew you toward the math department?
A: I came in just having taken AP calculus in high school and I honestly thought that was going to be the last math class I ever took because it was a stressful experience and I was really looking forward to trying something new. But I figured, if I’ve gone all the way up to AP calculus, I might as well take multivariable calculus. And then, if I’ve taken multivariable calculus, I might as well take linear algebra. And then I started getting hooked, especially with linear algebra. From there, I decided I might as well major.
Q: What is your thesis about?
A: I’m writing a thesis on network analysis, specifically social network analysis. Social network analysis — a lot of people think it’s like analyzing Facebook or Twitter. It’s sort of related to that, but [it’s] network analysis. “Social” is the adjective, it’s not “social network” analysis. It’s the science of examining networks of relationships between people or business or countries or any sort of entity and trying to figure out how the different actors in the network are going to behave based on the relationships between them.
Q: Could you give me an example?
A: I worked as a research assistant for Professor Clemans in the psychology department the summer before this year. She had just done the APEX study — the Amherst Peer Experience study — for the class of 2017. She was looking at how peer networks change over time, and she was trying to figure out if certain attributes of people make them more likely to attract people as time goes on. A lot of that comes down to social network analysis. For example, there’s a concept called ‘centrality’ in social network analysis, which is what I’m focusing on, which is essentially how much power or influence they have. By converting the network into a matrix of numbers, you can basically calculate who has the most power in all these different ways.
Q: By doing this, do you expect to find people with the strongest networking abilities?
A: Yes. I’m writing a program in Python that will figure out who’s the most central based on an algorithm I’ve developed. What I’m looking at is basically ease of communication among different members of the network, and also the ability of the network to isolate someone else. If you can isolate someone else — you only have one friend in that network, and that person decides to stop talking to you — then all the sudden you have no more access to that network. The person who has the ability to cut you off has a lot of social influence in that way.
Q: So far, what has been the hardest part of writing a thesis?
A: Probably figuring out exactly how I wanted to write this algorithm. It’s hard to make something up. It’s almost coming out to be like a creative thesis. I already have the introduction, which is sort of a review of past research and past measures, but at some point I had to sit down and think, “What do I want to make up?” It was sort of a daunting challenge, and I went through a lot of different drafts of what key factors in a network I wanted to be targeting. No one method [for which] I could code could account for every single part of a network, so I had to really focus on a few specific things in order for it to be a feasible project.
Q: What has been the most enjoyable part?
A: What I really like about my thesis is the extent to which it’s accessible to people who aren’t math majors. It’s a little embarrassing that my senior math thesis is that accessible, but I really like that it has real-world applications. That’s what drew me to the subject in the first place. It’s a general topic that I’m interested in also, so being able to apply my math background to this thing that I’m interested in is very fun.
Q: Do you plan on using this work or continuing it in the future?
A: Ideally, yes. I don’t know at what point it’ll come back in. Network analysis is a burgeoning field, but also hasn’t totally been implemented in a lot of different contexts just yet. But I’m hoping that I will have the opportunity in the future, when presented with a problem, to be like, “Hey, I actually know a little bit about this area. Let me try and look at it from a network perspective”—as opposed to an individual case-by-case perspective.
Q: Do you have any advice for students considering writing a thesis?
A: Don’t be afraid to make up your own subject. Often students, especially in the sciences, will work with a professor on their own project, and there are a lot of really cool professor projects in the math department as well, but I had the gut feeling that I wanted to do this. It’s been a little bit scary to write a thesis where someone else won’t necessarily have the answer if I can’t figure it out, but it’s been a lot more rewarding because it’s something that I came up with. I didn’t invent it, but I came up with it on my own.
Q: Now that you’re well underway, is there anything you would have changed or done previously before you started your thesis now that you know what the process is like?
A: It would have been nice to have been working on my thesis over the summer becauseI would have been able to make a lot more headway and I’d have more time to focus on it, but really during the summer was when I was figuring out what I wanted to be doing. I couldn’t have changed it if I wanted to, but — this is another thing for future thesis writers: if you can, stay at Amherst before your senior year and start working on your thesis, “it’ll be a very good decision.”
This is less from my experience and more from the experience of being a senior, but if you’re going to write a thesis, make sure you’re doing it for the right reasons: because you’re interested in the topic, or because you want the research experience.
