Department

Mathematics

The Department of Mathematics engages in fundamental research at the forefront of knowledge in both pure and applied mathematics. We also offer thoughtfully crafted, timely and relevant academic programmes at both undergraduate and postgraduate levels to prepare students for a wide range of career options, such as in academic research, the financial sector, data science-related industries and any profession that requires quantitative reasoning and clarity of thought.

Shaping
Future Talent

The Special Programme in Mathematics (SPM), one of our flagship offerings, nurtures the most mathematically talented of our undergraduate students, preparing them for Doctor of Philosophy (PhD) studies and possible future careers in academia. We are now seeing the results of our efforts. In Academic Year 2022 / 2023, SPM alumnus Asst Prof TRAN Chieu Minh (below) returned to the department as a tenure track faculty member.

The Master of Science (MSc) in Data Science and Machine Learning (DSML) drew over 2,000 applications and continues to be the most sought-after postgraduate programme in the Faculty.

We updated the curricula of DSML and the MSc in Quantitative Finance (MQF) to enhance their industry relevance. MQF introduced a new core course QF5209 Financial Derivatives: Modelling and Computation and a new elective course QF5211 Monte Carlo Methods in Quantitative Finance, while DSML rolled out two new core courses, DSA5103 Optimisation Algorithms for Data Modelling and DSA5104 Principles of Data Management and Retrieval, as well as a new elective course DSA5206 Advanced Topics in Data Science.

In December 2022, we forged a new collaboration with Tianjin-based Nankai University (NKU), bringing the total number of 3+2 partner universities to five. The joint educational programme allows selected NKU students to complete their last year of undergraduate studies while pursuing studies in the two-year NUS MSc in Mathematics programme.

Shaping
Future Solutions

Our mathematicians continue to push the boundaries in mathematical science research, contributing to advancements in both pure and applied mathematics.

The critical 2d stochastic heat flow

Stochastic partial differential equations are used to describe many physical phenomena involving randomness, such as the evolution of the front of a forest fire or diffusion in random media. However, many of these equations are not mathematically well-defined. In a recent breakthrough with his coauthors, Prof SUN Rongfeng constructed a stochastic process, called the critical two-dimensional (2D) stochastic heat flow, which gives meaning to the long-sought solution of the stochastic heat equation in the critical dimension 2 and in the critical window where a phase transition occurs. This study was published in Inventiones mathematicae (March 2023).

Regularity of the singular set in nonlinear free boundary problems

Many natural phenomena, for instance, glaciers in the ocean, involve multiple phases. It is important to address properties of the interface separating the phases. Previously, the study of free boundary problems was restricted to situations governed by linear equations. Together with his collaborators, Asst Prof YU Hui designed a new strategy which allows the study of nonlinear problems. They achieved the same results for the obstacle problem, a problem arising in multiplayer games as in linear theory. Their work has inspired many studies on related nonlinear problems and was published in the Journal of the European Mathematical Society (March 2023).

Acceleration of iterative methods with machine learning

Iterative numerical methods are ubiquitous in scientific computing. Many approaches based on meta-learning (learning to learn) were recently proposed to accelerate them. Asst Prof LI Qianxiao and his doctoral student Sohei ARISAKA systematically analysed these learning-based acceleration approaches, revealing their differences from ordinary meta-learning problems which can lead to significant performance deterioration. They proposed a principled training approach, demonstrating high performance and versatility in various numerical experiments. The findings underline the necessity of adapting data-driven workflows to better suit the unique demands of scientific computing. This work was covered in the Proceedings of the 40th International Conference on Machine Learning (July 2023).

Smart algorithms to predict the quantum world

Quantum computing is one of the key technologies of the future but our understanding of it is still incomplete. While the interaction between the qubits and their surrounding environment limits their capabilities, can we quantify and predict the limitation? This is challenging because we have to use classical computers to predict the complicated quantum world. Assoc Prof CAI Zhenning’s study of open quantum systems shows that the design of smart algorithms to maximise the capabilities of classical computers can achieve accurate predictions. This work was published in Mathematics of Computation (May 2023).

Our faculty members and students are also recognised for the impact and quality of their research. Prof BAO Weizhu (left) was appointed as a Provost Chair Professor in 2023 for achieving international recognition of his work in modelling and simulating Bose-Einstein condensation, and multiscale methods and analysis for partial differential equations.

Asst Prof Daren WEI (right) was appointed as a Presidential Young Professor and is recognised as a talented young scientist who studies problems related to classification, rigidity and complexity of the dynamical system whose growth of orbit segments is subexponential.

Shaping
Future Society

Our students continue to challenge themselves by pitting their skills and knowledge against their peers, often flying the flag high in international and national competitions.