The Mathematical, Computational Statistical Sciences (MCS) capstone experience offers each student an opportunity to learn a subject in great depth, to apply and reflect on previous coursework, and to engage with other disciplines. It also serves to develop further skills in technical exposition, both written and spoken. Graduating students will enjoy the self-confidence and initiative that comes from having successfully conducted an independent research inquiry. Sample topics include: topological field theory and physics; robotics; number theory and cryptography; survival statistics; social network analysis; computer graphics; smartphones as a distributed computing platform; neuroimaging.
In addition to the project, the capstone includes a weekly seminar. Combined, the capstone bears 10 Units.
Identification of project and supervisor:
The MCS Head of Studies (HoS) will announce a list of capstone topics, from which the students should select at least one topic to discuss with the respective potential supervisors. Once a MCS faculty member agrees to supervise a student, the supervisor and student must inform the HoS. Students are allowed to find a topic beyond the list, but they must find an MCS faculty member, who agrees to supervise them. Students are also allowed to have an external main supervisor (non-MCS faculty member), however they have to identify an MCS faculty member who agrees to be their co-supervisor. This supervisor/student matching process must be completed before the end of the academic term of Year 3, Semester 2. All capstone projects must relate to mathematics, computer science and data science, and must be approved by the HoS.
Activities as part of project:
Having identified a supervisor, students are encouraged to begin background work or preparation over the semester break under the guidance of their supervisor. During the whole capstone year, students must follow the timeline for capstone activities announced by the College. One of them is to submit a capstone proposal at the beginning of the first semester of Year 4. This capstone proposal must be written with the advice of the supervisor. Before capstone proposal submission, students must seek approval from their supervisor (and co-supervisor, if applicable). During the whole capstone year, students must participate in the capstone seminars. Students must also update and discuss their progress with their supervisor regularly. By the end of Semester 1 of Year 4, students must submit a report, describing their progress and achievements. By the end of Semester 2 of Year 4, students must complete their project, submit a final thesis and present it orally.
To demonstrate the wide variety of topics that MCS students pursue for their capstone projects, what follows is a sample of capstone titles from past MCS students:
- Polynomial Invariants in Algebra, Combinatorics and Topology
- Formalizing Block Pumpable Language Theory
- Formally Verifying Lookup and Insertion Operations on AVL Trees
- Zoning Out? Detecting Fluctuations in Sustained Attention with Physiological Signals
- Bounding the Number of Spanning Trees in a Bipartite Graph
- Voter Models on Networks with Two Communities
- Building a Certified Program Synthesizer
- The Fixing Number of a Graph
- Phenotypes that affect the Correlation between PF ratio and Mortality for Patients with ARDS: A Retrospective Analysis of ICU Data
