STEP Reflection

Name: Michael Heinz
Type of Project: Undergraduate Research

1. Please provide a brief description of your STEP Signature Project

My STEP Signature Project was conducting research in mathematical physics under Professor Ovidiu Costin. In this research, I analyzed methods of resummation of divergent series and applied a new method of resummation to the divergent asymptotic series of a particular differential equation, the Painlevé equation PII. I conducted a lot of numerical analysis of the accuracy and precision of our method and documented my results on Maple, a computing machine.

2. What about your understanding of yourself, your assumptions, or your view of the world changed/transformed while completing your STEP Signature Project?

First, I assumed that doing research while conducting coursework was much easier than it actually is. In all of my previous research endeavors, either I didn’t have much coursework or the research I did was not very time-consuming (requiring around three hours per week). This was completely blown out of the water in the research project. I started the project during the summer while taking courses to satisfy GE credits, and the coursework was much more time-consuming than I had expected. Because of this, the beginning of my research was extremely slow, and it took me about a month to really get into the swing of things. My course load this autumn semester was relatively light, and therefore research went much smoother, but I have definitely gained a lot more respect for how research is conducted in tandem with coursework and how you have to manage your time to do so properly.

Second, and more importantly, I loved this research. It was extremely stimulating and interesting, and it made me want to go back and work on it over and over again. This was something I had not experienced with my previous research positions, so it was very refreshing to be working on something I actually love. It has definitely confirmed my desire to attend graduate school with a long term goal of becoming a professor, as both the research and teaching aspects appeal to me. I was hoping I would find an answer to the question,”Is graduate school the right thing for me?” and I believe I have.

3. What events, interactions, relationships, or activities during your STEP Signature Project led to the change/transformation that you discussed in #2, and how did those affect you?

I think the largest cause of this transformation was my relationship with my research advisor, Professor Ovidiu Costin. He has been a great mentor throughout this whole process and has been very understanding concerning my workload throughout both the summer and autumn semesters. He has shown me a great deal about mathematical physics and asymptotics over the last seven months, but he also really helped me understand what it meant to do research in these areas. I am very grateful to have Professor Costin as my advisor, and I attribute some of the reason why I fell in love with this research to him.

Additionally, many of my friends in the math and physics programs who also do research have been a great help in finding my love for research in this project. I was very close to a friend over the summer who was also taking classes and doing research, and he really helped me figure out how to balance out these two aspects of my academic life. When I entered autumn semester, there were many of my other friends in the math program that I could talk to my research about. Simply being able to talk to others at a similar math level about some of the concepts really helps clarify them for myself, and that was very useful in making progress in my research.

Finally, I think one of the best experiences I have had throughout this STEP project has been presenting at the 2018 Autumn Research Festival. The presentation itself was not satisfying since there were no judges, and most of my friends/colleagues had classes. Hence, there was nobody really to present to at the festival. However, the preparation for the presentation was amazing. Not only did it really make me have to understand all the details to my research and how they build onto one another so that I could compile it into a poster, but being able to give mock presentations to my professors, friends, and family was extremely rewarding. Seeing how interested some of these people were in my research (although they knew very little about the field) made the work I did throughout the project so much more worthwhile. I think this rewarding experience really made me fall in love with this research and the idea of doing research in general, and I expect the Denman in Spring of 2019 to be a similarly positive experience.

4. Why is this change/transformation significant or valuable for your life?

This transformation is very valuable to my life because it has helped me decide what I want to do in the future. I was debating between doing an REU or an internship over the next summer (the latter for more work experience), but due to this project I have little desire to gain an internship experience to be able to go into the industry as I would rather go to graduate school for math or physics to become a professor. This project has clarified a big question mark in my professional goals and future plans as I was very split between going to graduate school and going into the industry. I am very grateful that STEP gave me the opportunity and the funding to work on this extremely worthwhile project.