At the 2023 Columbia Undergraduate Research Symposium, an annual showcase for research from students across Columbia’s Undergraduate schools, Heyuan Yao ‘24GS was among a dozen-plus featured GS students. He shares the collaborative benefits of conducting research within the Department of Statistics and offers advice for students interested in similar experiences.
Tell us about your research: the what, why, and how.
This summer, I participated in the Department of Statistics’ Summer Internship Program, engaging in the project “A comparative study of two indexes of inequality: The Gini coefficient in Economics, and the Gini index in machine learning.” My motivation for selecting this project stemmed from a keen interest in the core research area of probability theory.
Throughout the internship, my primary responsibilities involved conducting literature reviews, developing theoretical frameworks, and performing numerical computations and simulations. Given the inherently mathematical nature of the work, I predominantly carried out the research using traditional tools such as paper and pens.
Why did you want to pursue a research opportunity, and how has it enriched your GS experience?
One of the important reasons I pursue undergraduate research opportunities is to prepare for future graduate applications and research endeavors. You can also check if you really love to do research and are suitable to conduct research. In addition, trying research not only lets me apply my knowledge learned from coursework to some special topics, but also helps shape my choices for major electives and potential subfields within mathematics and statistics.
During my research experience, I received invaluable guidance and suggestions from my groupmates (my supervisors and their PhD students, and some coauthors). The academic interactions within this collaborative environment have enhanced my individual capabilities and fostered a sense of teamwork that extends beyond the confines of short-term projects with my classmates.
What advice would you give to other students interested in research experiences?
The following suggestions are particularly beneficial for students intending to explore research in mathematics and (theoretical) statistics. In addition to fulfilling mandatory coursework requirements in calculus, linear algebra, and ordinary differential equations (ODE), it is highly advisable to enroll in 4000-level courses, especially real analysis and probability theory in the department of mathematics. These measure theory-based courses will establish you a robust foundation, facilitating ease in comprehending scholarly articles and composing essays. Furthermore, both the Department of Mathematics and the Department of Statistics actively welcome historically underrepresented students and those with non-traditional experiences, with GS students often holding a more competitive edge.
I also recommend exploring summer REU programs hosted by various institutions. The American Mathematical Society's website provides a comprehensive list of programs. The programs held by Williams College (SMALL), UChicago, and the University of Minnesota are highly recommended; competitive but rewarding.
