Here are some resources that may be helpful for the PhD application process, including some notes written by faculty member and graduate students, pre-application support programs, and example statements of purpose. The bulk of this post is focused on the statement of purpose, which is a critical part of an application that is within your control at the time of application.
Worthwhile Reads
Below are some remarks by professors on crafting statements of purpose.
- Graduate school statement of purpose by the MIT EECS Communication Lab.
- From mentoring workshops at COLT: How to write statements of purpose by Boaz Barak and How to write statements of purpose for Ph.D. and fellowship applications by Yisong Yue.
The following reads may be most relevant if you are planning well in advance for graduate applications, as they speak to both short-term and long-term preparation. Of course, take all advice with a grain of salt and only adopt suggestions that resonate with you.
- Applying to Ph.D. Programs in Computer Science by Mor Harchol-Balter.
Support Systems
I'm very grateful to the wonderful people who supported me in my application process and my research journey. Here are a few folks to lean on:
- Research advisors are excellent resources. They can suggest programs and researchers relevant to your interests, research style, and career goals. Moreover, they certainly know what strong grad school applicants look like. Ask them for feedback on your application materials if you feel comfortable doing so.
- Speak to graduate students. Some are part of the admissions committee and have experience reviewing applications, so they have a sense of what works and what does not. More generally, I talked to a lot of students in my lab. I even reached out to alums who went on to schools that I wished to apply to, such as Paul Liu and Eugenie. They provided me a ton of encouragement and strategic advice.
- Bug your friends and family. It is nice having multiple sets of eyes looking for mistakes and ambiguities in your writing. My sister Esther and I always review each other's applications.
- Have a buddy system. It can be quite fun experiencing the application and decision-making process with a friend. (You guys can share findings, joys and sorrows, etc.) My buddy was Wesley Chang whose an absolute powerhouse.
- Participate in or initiate a grad app group. I at UBC initiated by Joice Tang and Prof. Cinda Heeren. We met weekly over the application season, discussing concerns, sharing resources, and keeping one another accountable.
- Your university may have writing centers you can visit.
And the list goes on. The key takeaway is to be resourceful and active in finding support!
Pre-Application Support Programs
Many schools have programs designed to support Ph.D. applicants, especially those underrepresented in the field. For the 2021 application cycle, Jia-Bin Huang compiled a huge list of such initiatives. They typically pair applicants with current or recent grad students to receive feedback on application materials and gain insight into their graduate programs. I was fortunate to connect with wonderful grad students and mentors through several of these initiatives:
- SIGGRAPH Undergraduate Student Mentorship — Mentors this past year included faculty members, industry researchers, and current and recent Ph.D. students. Shoutout to my amazing mentor Ante Qu who, over several meetings, offered an abundance of insight into grad school applications, navigating Ph.D. studies, and the world of computer graphics.
- Graduate Application Assistant Program by MIT EECS
- Equal Access to Application Assistance by the EECS department at UC Berkeley
- University of Washington CSE's Pre-Application Mentorship Service
Example Statements of Purpose
There are plenty of resources online discussing what a statement of purpose should and should not be. I provided some references in an earlier section. Below I share several statements, including my own, as data points. The positions listed are as of Spring 2022.
- Zahid Hossain, Applied Research Scientist & Manager at Facebook Reality Labs, Ph.D. from Stanford
- Eugenie Lai, Ph.D. Student at MIT
- Nelson Lui, Ph.D. Student at Stanford
- Silvia Sellán, Ph.D. Student at the University of Toronto
- Vincent Sitzmann, Assistant Professor at MIT, Ph.D. from Stanford
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My statement of purpose submitted to MIT EECS for Ph.D. studies.
My research interests lie in computational geometry, computer graphics, and mathematical art. Building atop research experiences in these areas, I seek to solve geometric problems arising in computational design and fabrication.
Computational Geometry. My interest in computational geometry stemmed from an independent study in geometric algorithms with Prof. William Evans in Spring 2020. Over the term, I became fascinated with visualizations of geometry and was eager to develop and solve my own geometric questions. One problem I posed was inspired by a study of diffusion in my PDEs class. How would one select k corners of an office to locate heaters so as to warm the space as quickly as possible? Through extensive reading, I discovered my problem to be a novel variant of the geodesic k-center problem on a polygonal domain, which in and of itself is a challenging problem with limited results. This discovery led me into a year-long exploration of combinatorial optimization with applications in geometric facility location. Under the guidance of Prof. Evans, I proved my problem to be NP-hard in general by applying techniques from graph theory and graph embedding. Then I devised a polynomial-time 3-approximation algorithm. Finally, considering restricted instances, I defined and characterized a new family of polygons on which an exact solution can be obtained in polynomial time using dynamic programming. This work resulted in a conference paper to appear at WALCOM 2022. It was rewarding to lead the project from conception to completion. I grew in autonomy, learning to be creative and critical while dissecting problems, synthesizing surveyed results, and communicating my ideas. Furthermore, I fell in love with the curiosity-driven nature of research, which sparked my enthusiasm for pursuing graduate studies. In the coming term, I intend to resolve some of the open problems posed in our paper and continue exploring more sophisticated facility location models that better capture real-world optimization scenarios.
Computer Graphics. Having an interest in art and design, I sought applications of geometry in creative contexts. I joined the UBC Digital Geometry Processing Group (DGP) in August 2020 under the supervision of Prof. Alla Sheffer. Alongside Prof. Helge Rhodin and two graduate students, we have been developing computational tools for sketch processing. Many illustration and sketch-based modelling applications require inputs with precisely identified stroke intersections. However, most drawings are inexact: strokes either overshoot or stop short of intended intersections. Therefore, we seek to extract intended stroke connectivity from vector line drawings. My contributions include the design and implementation of an annotation interface for perceptual studies, a necessary ingredient for developing and evaluating our techniques. I learned to craft clear visualizations and intuitive interactions through gathering iterative feedback from my team and study participants. This fall, I am working on curve deformation algorithms to connect over- and underdrawn strokes in drawings while preserving intended stroke shape and continuity. We are preparing a manuscript for SIGGRAPH 2022. Thus far, I have enjoyed the process of synthesizing ideas from geometry, visualization, and optimization in problem-solving. In addition, I appreciate working amongst both diverse and like-minded peers. Witnessing first-hand the innovative developments of geometry processing in art, design, and fabrication has reinforced my desire to pursue research in this area.
Mathematical Art. My experience in the DGP group ignited a curiosity for creating artwork by incorporating ideas from computational geometry and computer graphics. To explore this interest, I joined the Computer Graphics Lab (CGL) at the University of Waterloo last summer, engaging in full-time research with Prof. Craig Kaplan under an NSERC Undergraduate Student Research Award and Waterloo's Undergraduate Research Fellowship. I developed an end-to-end pipeline for the procedural generation of freeform Islamic star patterns. Our method allows users to generate constellations of stars that are impossible by traditional design methods; we achieve such compositions through relaxing symmetry constraints, hence the modifier "freeform". Our key insight is the application of the circle packing theorem, which permits us to encode the shapes and sizes of stars in user-specified complexes. I presented this result to the CGL group, and we are working towards a conference submission in January 2022. Through this experience, I have gained a more rounded understanding of research. Our early work was ambiguous and open-ended, intensified by questions of aesthetics. Through extensive reading and experimentation, I narrowed our investigation, ultimately fusing ideas from perception studies with concepts in mathematics to produce robust results. I remain deeply curious about the interactions between mathematics and art. I hope to continue experimenting with projects like this one as I progress in my research career.
Outreach. I am interested in exploring creative applications of computing as a means to encourage diversity in CS. Since last fall, I have organized and led over a dozen computer art programs for youth through my local community center. My primary goal for these programs has been to foster a sense of belonging in CS amongst my students and volunteers by expanding perceptions of who programmers are and what code can do. In weekly classes, we create digital drawings, animations, generative art, and user interfaces for pattern-making and image processing. At MIT, I aim to continue creating environments conducive to bold, imaginative explorations by encouraging diversity of interest.
Future Work. I am drawn to the geometry-related research at MIT, especially that of Prof. Mina Konaković Luković, Prof. Justin Solomon, and Prof. Erik Demaine. I am excited by Prof. Luković's explorations of discrete differential geometry in the context of digital fabrication, specifically her research on auxetic structures. I would enjoy continuing this line of work—designing deployable and reconfigurable structures. Due to my recent graduate-level coursework in geometry processing, I have also developed a strong interest in Prof. Solomon's research. I am especially curious about developable surfaces, though I am eager to explore a broader range of topics. Lastly, I am very excited by Prof. Demaine's work, which I have followed avidly over the last two years. Many of his projects connect with my love for mathematical problems, particularly those in discrete geometry and graph theory, and my affinity for art and craft. It would be a privilege to investigate algorithms underpinning origami designs, or study geometric folding and unfolding at large, under his guidance.
I am truly excited by the wide-ranging expertise at MIT relating to my interests. After my graduate studies, I aim to pursue research in academia. Having the opportunity to collaborate with and learn from the diverse community of researchers at MIT would grant me access to and clarity in the contributions I wish to make.
Note that the article by the MIT EECS Communication Lab has three annotated examples; the COLT slides contain a statement by Naama Ben David (Postdoctoral Researcher at VMWare, Ph.D. from CMU) with comments.
Acknowledgments
I hope this post is helpful to prospective graduate school applicants, especially those from underrepresented groups in computer science. If you have any suggestions for this write-up or work like to chat about your application beyond what is discussed, then feel free to leave a comment or reach out to me at ryelin@mit.edu.