Undergraduate research opportunities

Each Spring term (May-August) the Department of Applied Mathematics organizes a very active undergraduate research program. Most student participants are supported by NSERC (Natural Sciences and Engineering Research Council of Canada) Undergraduate Student Research Awards (USRA) or the Math Faculty's Mathematics Undergraduate Research Award (MURA) Program. We also welcome international students visiting the department under the Mitacs Globalink Research Internship program. Participants work on a research project under the supervision of a faculty member, and have the opportunity to interact with other participants and with graduate students. At the end of the summer, we organize a mini-conference where all participants give a short presentation on their research project.

Students can also hold research positions in Fall and Winter terms but the mini-conference is only held in Spring and there are fewer undergraduate research students to interact with in other terms.

For inquiries about our undergraduate research opportunities, please contact the Applied Mathematics Undergraduate Office (amug@uwaterloo.ca).

USRA/MURA

The deadline for the next round of applications (for awards in S27, F27, W28) is December 13, 2026.

Additional rounds of applications may be announced in W27 if there are still awards available.

Overview

  • The awards are intended to give undergraduates an opportunity to gain experience in doing research, with a view to subsequent enrolment in a graduate program.

  • The value of an award is $6,000 for the term (16 weeks on a full-time basis). Awardees will receive at least an additional $5,000 as a supplement from the supervisor.

  • Only a limited number of awards are available. Students should have a cumulative average of at least 80% to be eligible.

  • The research topics depend on the availability of supervisors, and typically involve control and dynamical systems (including differential equations), fluid mechanics, mathematical medicine and biology, mathematical physics, data science, machine learning, or scientific computing. For most research areas, it is recommended that students have completed at least their 2B term.

  • USRA is available to Canadian citizens and permanent residents, including those studying at other Canadian or foreign institutions. MURA is available to students in the Faculty of Mathematics at the University of Waterloo who are Canadian citizens or permanent residents or international students on a student visa.

  • Eligible students from other universities are encouraged to apply and to take part in our undergraduate research opportunities.

  • For more details and full eligibility criteria, please visit the NSERC USRA and MURA webpages.

Application process

  • Students are encouraged to contact potential supervisors early on to learn about research groups and projects. This step is optional; you may submit an application without prior contact with supervisors. Please see the list of available projects below. 
  • Submit  an online application form. You will be asked to provide some details about your background, including a CV and transcript, and a short statement of interest. 
  • You may be contacted by potential supervisors to further evaluate your fit with their projects.
  • We anticipate application results to be available by February 2027. If you are matched with more than one supervisor, you can choose which project to join. 
  • If you accept the departmental offer, you will need to submit an additional form specific to the USRA or MURA system for final approval of the award.

Other Opportunities
In addition to USRA and MURA, a number of additional research opportunities are available, including:
Students who have completed exceptional research may be nominated for the Jessie W.H. Zou Memorial Award.

Undergraduate Research Projects

Below is a list of some potential research projects you could participate in under the supervision of an Applied Mathematics faculty member. This list will be updated as new projects become available and it gives an idea of some of the research directions of the department but is by no means exhaustive. Please visit the webpages of our faculty members to learn more about their research activities.

Roberto Guglielmi - Control systems / optimization / PDEs
Roberto Guglielmi 
Topics might focus on more analytical or computational aspects of different control problems in engineering, physics and life sciences.
Terms available: S27, F27, W28
Research areas: Control and Dynamical Systems, Scientific Computing

Marek Stastna-Highly scalable tensor decompositions for four-dimensional fluid simulation data

Group website

Terms available: S27

Project description:The singular value decomposition (SVD) is a well-known matrix factorization used to uncover the dominant components of any dataset that can be represented as a matrix. In applications such as geophysical fluid dynamics, datasets often depend on multiple spatial dimensions and time, and the data are stored in multidimensional arrays called tensors. To perform the SVD on such data, one must first convert the tensor into a matrix, a process that obscures spatial correlations inherent in the data, resulting in a decomposition that is less than optimal. Alternative approaches that factorize tensors directly have recently been derived. This project will implement a high-performance, scalable version of one such tensor decomposition — the “star-M SVD” — as part of an open-source postprocessing tool for large fluid simulation datasets. The successful applicant will apply spatial/geometric intuition to understand tensor structure/data layout in a fluids context; develop proficiency with fundamental concepts of linear and multilinear algebra; extend a prototype star-M SVD code to scale on high-performance computing hardware; and, apply the factorization to a 3+1 (space+time)-dimensional dataset of fluid flow.

Research area(s): Fluid Mechanics, Scientific Computing

Required courses, skills, and experience:  We welcome applicants with a variety of backgrounds. Stream 1 (linear algebra): MATH 136/235 or 146/245 or equivalent, and AMATH 242 or equivalent. Stream 2 (fluid dynamics): AMATH 361/463 or AMATH 362/462, and AMATH 242 or equivalent.
Recommended additional courses, skills, and experience: Experience with C, C++, and/or GPU programming paradigms would be considered an asset.

Henry Shum - Modelling magnetic microrobots
Henry Shum
Terms available: S27, F27, W28
Project description: Microrobots have many potential areas of application, including delivering a drug to a target area in the body, removing kidney stones, or manipulating components to assemble microdevices. Using mathematical models and numerical methods, we can simulate microrobots of various designs moving in a fluid and investigate how we can use magnetic fields to control the robots and how this, in turn, manipulates nearby cargo particles. Students can make use of existing computer programs or create something from scratch. For reference, see this recently published paper in this area.
Research area(s): Control and Dynamical Systems, Fluid Mechanics, Mathematical Medicine and Biology, Scientific Computing
Required courses, skills, and experience: AMATH 250 or similar differential equations course, AMATH 242 or similar course on computational mathematics/numerical methods. The student should have experience with programming in at least one of: Matlab, Python, Rust, or Fortran.
Recommended additional courses, skills, and experience: High school physics and chemistry, AMATH 271 or PHYS 121, AMATH 342, AMATH 361, AMATH 455, AMATH 463

Anita Layton-Mathematics, AI and Data for Health
Terms available: S27, F27, W28
Project description: Modern health research generates enormous amounts of data, but turning those data into useful scientific understanding requires mathematics. Projects will use mathematical, statistical, and computational methods to tackle problems in health and medicine. Depending on the student's interests and background, topics may include machine learning, generative AI and synthetic data, physiological modelling, drug discovery, or the integration of complex biomedical and population-health data. Students may develop predictive models, investigate methods for incomplete or irregular data, explore ways to incorporate biological knowledge into machine-learning models, or combine data-driven and mechanistic approaches. Specific projects will be tailored to the student's interests and preparation.
Research area(s): Mathematical Medicine and Biology, Data Science and Machine Learning, Mathematical Modelling, Scientific Computing
Required courses, skills, and experience: A course in differential equations, probability/statistics, numerical methods, or machine learning. Experience programming in Python, MATLAB, R, or a similar language. Students do not need previous experience in biology or medicine, but should have strong mathematical curiosity and an interest in applying quantitative methods to health problems.
Recommended additional courses, skills, and experience: Additional coursework in differential equations, probability and statistics, optimization, machine learning, scientific computing, or mathematical biology. Experience with data analysis or computational modelling is helpful but not required.