COURSE REGISTRATION NOW OPEN FOR WINTER 2025
Students at Canadian PIMS member universities may apply for graduate credit via the Western Deans’ Agreement (WDA). Please be advised, in some cases students must enroll 6 weeks in advance of the term start date and will typically be required to pay ancillary fees to the host institution (as much as $270) or explicitly request exemptions. Please check the individual courses on the PIMS site for registration details.
Winter Courses
January 6, 2025 – April 8, 2025
Advanced studies in Theoretical and Computational Biology
Instructor – Anotida Madzvamuse, University of British Columbia : am823@math.ubc.ca
Abstract: The purpose of this graduate course is to equip graduate students with cutting-edge techniques in data-driven mathematical and computational modelling, analysis and simulations of semi-linear parabolic partial differential equations (PDEs) of reaction-diffusion type. It will cover diverse areas in data-driven modelling using PDEs in biology. I will cover approaches on formulating models from data using first principles, mathematical analysis of reaction-diffusion systems such as linear stability analysis, basic concepts on bifurcation analysis and numerical bifurcation analysis. The second part will focus on numerical methods for PDEs including finite difference methods, and finite elements. This part will also deal with time-stepping schemes and nonlinear solvers for nonlinear PDEs. If time allows, we will look at applications of reaction diffusion theory to cell motility and pattern formation. To support theoretical modelling and numerical analysis, numerical algorithms will be developed and implemented in MATLAB as well as in open finite element source software packages such as FeNiCs, deal.ii and others. Students will be allowed to use packages of their choice as appropriate. Expertise and skills sets to be acquired through this course
- Acquire data-driven modelling skills and techniques in PDEs and their applications to biology
- Acquire techniques and knowledge in mathematical analysis of reaction-diffusion systems
- Acquire expertise and skills in bifurcation analysis, numerical bifurcation, and sensitivity analysis
- Acquire numerical analysis techniques and skills to compute approximate numerical solutions
- Acquire expertise and knowledge in finite difference methods for semi-linear parabolic PDEs
- Acquire expertise and knowledge in finite element methods for semi-linear parabolic PDEs
- Gain some knowledge in bulk-surface PDEs, and their analysis (might be covered if time allows) Key
Mathematical Ecology – Nonlinear PDE Models
Instructor – Rebecca Tyson, University of British Columbia : rebecca.tyson@ubc.ca
Abstract: Mathematical modelling in ecology, including population dynamics, epidemiology, and pattern formation. Theory of such models formulated as difference equations, ordinary differential equations, and partial differential equations.
See here for the complete list of available PIMS Network math-bio & applied math courses for the upcoming term.
Fall Course(s)
September 3, 2024 to December 6, 2024
Topics in Mathematical Biology: biological image data and shape analysis
Instructor – Khanh Dao Duc, University of British Columbia: kdd@math.ubc.ca
Abstract – Advances in imaging techniques have enabled the access to 3D shapes present in a variety of biological structures: organs, cells, organelles, and proteins. Since biological shapes are related to physiological functions, biological studies are poised to leverage such data, asking a common statistical question: how can we build mathematical and statistical descriptions of biological morphologies and their variations? In this course, we will review recent attempts to use advanced mathematical concepts to formalize and study shape heterogeneity, covering a wide range of imaging methods and applications. The main mathematical focus will be on basics of image processing (segmentation, skeletonization, meshing), Diffeomorphisms and metrics over shape space, optimal transport theory with application for image analysis, manifold learning, with some other concepts covered in specific applications (e.g. quasiconformal mapping theory for shape representation, 3D reconstruction in Fourier space…). Students will be encourage to work in groups to present research papers and do a small project to pass the course. This course will also build on the recent BIRS workshop, Joint Mathematics Meetings, and the upcoming SIAM workshops (LSI 2024, SIMODS 2024) on this topic, with some participants to these events invited to contribute to this course and present their research.