Road to Research

While I didn’t actually meet him at the time, I first came into contact with my mentor, Dr. Ming Chen, when I attended a math department seminar in the Fall of 2021. I had seen fliers around the mathematics building about the talk titled: Understanding Nonlinear Surface Water Waves on Deep Water. I was fascinated, despite my lack of understanding of the material, so I went. I recall Dr. Chen being there and asking the speaker a question. Afterwards I looked over the department website and saw Dr. Chen’s research was primarily on water waves as well.

I formally met Dr. Chen in the Spring of 2022 when he taught my section of MATH 0413, Introduction to Theoretical Mathematics. I enjoyed the class immensely. Historically the math department at Pitt has been focused on analysis, which is roughly speaking the theoretical foundations of calculus, because of this MATH 0413 frequently is focused on analysis. Dr. Chen is an applied analyst so the insight and depth he brought to the course was very enriching. Since I was aware of his research from the previous semester, I mentioned my interest to him over email towards the end of the semester. He responded enthusiastically and we set up a meeting to go over the project he had in mind. This project, on dispersive wave quantization, appealed to me because it synthesized ideas from analysis and theoretical mathematics with a concrete real-world phenomenon in the Talbot effect. I have enjoyed the opportunity to do this research very much.

I knew I was interested in undergraduate research when I transferred to Pitt in the Fall of 2021. However, like many others, I was initially uncertain as to how to get involved. I had very limited advanced coursework and doubted my own ability to understand, let alone contribute to, math research. I mentioned my interest to a general academic advisor in Dietrich and he suggested I take ARTSC 0101, First Approaches to Research. The course was an introduction to the process of getting involved, much of it consisted of resume writing and how to contact potential research mentors. I drew two important takeaways from the course. Firstly, the expectations for undergraduate researchers are reasonable: you are there to learn, not to already know everything. Don’t let your lack of experience discourage you from reaching out to get experience. Second, research experience for undergraduates (REU) programs exist, and are an excellent opportunity. Even after the course I felt like I didn’t fully understand how undergraduate research worked, what my options were, and so on. I learned how the system functions much more clearly by actually taking part in it.

Now, over a year later, I feel as if I understand the ways to get involved with undergraduate research much more. Here I will describe the general lay of the land as I understand it, in the most direct way possible. There are four ways to get involved:

Cold emailing: Look on the website of the department(s) you’d like to do research in, find professors who are doing work which sounds interesting, read a few of their papers, then send them an email. In the email you can express general interest in their work and ask to set up a meeting. You can also directly ask about research opportunities, but this is not always appropriate. Some professors will have information for interested undergraduates online. If they ask you to include particular information such as a resume or transcript then make sure you do. While this is potentially the most direct way it can also result in rejection, don’t let it discourage you!

Former or current professors: This is a great way to get involved with research at your university. A current or former professor will understand your capabilities and will frequently be happy to extend an invitation to do research. This does potentially limit your options since you won’t necessarily take a class with every professor at your university who you would like to do research with.

Intermediaries: At least in the math department at Pitt, departments are very excited to offer you research opportunities and connect you with mentors. If you take initiative and reach out to the director of undergraduate studies and ask about opportunities, they can generally help.

Applying to a program: Most universities have research fellowships which you can apply to. Some would necessitate you already have a project in mind, while others will connect you with research mentors. The most competitive of these opportunities are REUs. I am surprised more people don’t know about REUs. As soon as I learned about them, I knew I had to apply. They are usually funded by the National Science Foundation. If accepted, you receive a stipend over the summer, and typically accommodations at the hosting University. Note that due to funding constraints most REUs, but not all, are limited to U.S. citizens. The general structure is you apply to a particular REU site. Numerous universities host them in a wide variety of topics, not just limited to math. You can find more information on the NSF website. Applications are generally due in February and March. A typical application will consist of a personal statement, a copy of your unofficial transcript, and two letters of recommendation from professors or research mentors. I would stress contacting your letter writers as soon as possible in order to give them time. My experience at the Elon and North Carolina A&T Joint REU in mathematical biology has been highly impactful for my own research experience. I can’t stress the importance of REU’s enough, they expand your academic network significantly and usually have a strong component of career development. The majority of REUs in STEM strongly encourage applicants from diverse backgrounds typically not represented in the field. If this sounds like you, or if it doesn’t go for it! These opportunities are out there, and they make a huge difference. I particularly enjoyed getting to engage with a group of other passionate and motivated undergraduates. Plus, the stipends are significant, they range from $3,000-$6,000, so if finances are what is limiting your ability to participate in research over the summer, an REU can be a great option.

Regardless of which method you choose I would encourage you to establish relationships with your professors. In doing so you will learn about what academia is like. Furthermore, letter writers who know you well are essential for future academic success. Go to office hours, ask questions that surpass the bounds of the course, and so on. I also think going to colloquia or seminars as I did can be a great way to get exposure to current research topics. Even if you don’t understand everything, that immersion will help you understand the field in a global sense. Learning how to do research is directly applicable to my professional goals. I ultimately want to teach and research mathematics in a university setting, so getting experience doing research is critical to my ability to get into graduate school and excel there. My research experiences have also allowed me to explore my interests outside of the classroom and better understand what I would ultimately like to do. Lastly, research, especially in mathematics, is a distinct way of learning. When I began working with Dr. Chen I had hardly any of the background required to even phrase the problem we were studying. In fact, I am only now taking a course in ordinary differential equations. I had to quite literally learn and understand numerous topics from different courses I had yet to take. This completely altered the way I learned this content and gave me background in topics other undergraduates have minimal exposure to.

A poster I created as part of my REU program.

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