Courses: upcoming
The following courses were scheduled for the upcoming academic year:
The following courses were scheduled for the upcoming academic year:
Anotida Madzvamuse : am823@math.ubc.ca
University of British Columbia
Ordinary differential equations
Numerical methods (Numerical Analysis I and II)
Partial differential equations
Matrix theory
Linear systems
This course is available for registration under the Western Dean's Agreement but registrations must be approved by the course instructor. Please contact the instructor (using the email link to the left) including details of how you meet the course prerequisites. Next, you must complete the Western Deans' Agreement form , with the following course details:
Completed forms should be returned to your graduate advisor who will sign it and take the required steps. For students at PIMS sites, please see this list to find your graduate advisor, for other sites, please see the Western Deans' Agreement website .
The Western Deans' Agreement provides an automatic tuition fee waiver for visiting students. Graduate students paying normal required tuition fees at their home institution will not pay tuition fees to the host institution. However, students will typically be be required to pay other ancillary fees to the host institution, or explicitly request exemptions (e.g. Insurance or travel fees). Details vary by university, so please contact the graduate student advisor at your institution for help completing the form. Links to fee information and contact information for PIMS member universities is available below in the WDA section.
Students at universities not covered by the WDA but which are part of the Canadian Association for Graduate Studies (CAGS) may still be eligible to register for some courses under the terms of the Canadian University Graduate Transfer Agreement (CUGTA). Details of this program vary by university and registration is also typically subject to ancillary fees. Both your local and the hosting university must participate in the agreement (e.g. UBC does not participate in CAGS). Please contact the relevant graduate student advisors for more information.
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
We will use zoom for each lecture. Course notes will be distributed in advance and lecture notes will be distributed after each lecture.
This course may be open to students from universities outside of the PIMS network.
Soumik Pal : soumikpal@gmail.com
University of Washington
Young-Heon Kim : yhkim@math.ubc.ca
University of British Columbia
First year graduate course in real analysis and/or probability.
This course is available for registration under the Western Dean's Agreement but registrations must be approved by the course instructor. Please contact the instructor (using the email link to the left) including details of how you meet the course prerequisites. Next, you must complete the Western Deans' Agreement form , with the following course details:
University of Washington Students:
All Other WDA Students:
Completed forms should be returned to your graduate advisor who will sign it and take the required steps. For students at PIMS sites, please see this list to find your graduate advisor, for other sites, please see the Western Deans' Agreement website .
The Western Deans' Agreement provides an automatic tuition fee waiver for visiting students. Graduate students paying normal required tuition fees at their home institution will not pay tuition fees to the host institution. However, students will typically be be required to pay other ancillary fees to the host institution, or explicitly request exemptions (e.g. Insurance or travel fees). Details vary by university, so please contact the graduate student advisor at your institution for help completing the form. Links to fee information and contact information for PIMS member universities is available below in the WDA section.
Students at universities not covered by the WDA but which are part of the Canadian Association for Graduate Studies (CAGS) may still be eligible to register for some courses under the terms of the Canadian University Graduate Transfer Agreement (CUGTA). Details of this program vary by university and registration is also typically subject to ancillary fees. Both your local and the hosting university must participate in the agreement (e.g. UBC does not participate in CAGS). Please contact the relevant graduate student advisors for more information.
The modern theory of Monge-Kantorovich optimal transport is barely three decades old. Already it has established itself as one of the most happening areas in mathematics. It lies at the intersection of analysis, geometry, and probability with numerous applications to physics, economics, and serious machine learning. This two quarter long graduate topics course will serve as an introduction to this rich and useful theory. We will roughly follow the following outline. Fall: Classical theory. Analytic description of solutions. Duality. Displacement convexity. The geometry of the Wasserstein space and Otto calculus. Winter: Entropy-regularized OT. Schroedinger bridges and statistical OT. This is a continuation of the sequence of OT+X courses under the Kantorovich Initiative.
Students at Canadian PIMS Member Universities may register through the Western Deans Agreement for the “shadow course” offered at UBC (see registration details above). Students at UW may register directly for the UW course. Course codes and other registration details for students in either of these cases are listed in the registration section above. Students at other institutions should contact one of the instructors to attend the course as a non-registered student.
Online instructions over Zoom. Written on a tablet. Notes will be provided. A Slack channel will be created for answering student questions. Weekly in person office hours will be held at UW and UBC.
Lecture notes will be distributed over Slack. Recorded lectures may be viewed on our YouTube channel.
This course may be open to students from universities outside of the PIMS network, and those coming from industry/government.
Ben Williams : tbjw@math.ubc.ca
University of British Columbia
a first course in real analysis, and some point-set topology, including quotient topologies, connectedness, path-connectedness.
Homotopy of maps and homotopy equivalence of spaces will be assumed, but the necessary background here can be quickly covered by self-study.
Fundamental groups and covering spaces, while helpful, are not necessary.
the theory of abelian groups, isomorphism theorems and the classification of finitely generated abelian groups.
Ring theory and the theory of modules over commutative rings is extremely helpful, but not formally required.
This course is available for registration under the Western Dean's Agreement but registrations must be approved by the course instructor. Please contact the instructor (using the email link to the left) including details of how you meet the course prerequisites. Next, you must complete the Western Deans' Agreement form , with the following course details:
Completed forms should be returned to your graduate advisor who will sign it and take the required steps. For students at PIMS sites, please see this list to find your graduate advisor, for other sites, please see the Western Deans' Agreement website .
The Western Deans' Agreement provides an automatic tuition fee waiver for visiting students. Graduate students paying normal required tuition fees at their home institution will not pay tuition fees to the host institution. However, students will typically be be required to pay other ancillary fees to the host institution, or explicitly request exemptions (e.g. Insurance or travel fees). Details vary by university, so please contact the graduate student advisor at your institution for help completing the form. Links to fee information and contact information for PIMS member universities is available below in the WDA section.
Students at universities not covered by the WDA but which are part of the Canadian Association for Graduate Studies (CAGS) may still be eligible to register for some courses under the terms of the Canadian University Graduate Transfer Agreement (CUGTA). Details of this program vary by university and registration is also typically subject to ancillary fees. Both your local and the hosting university must participate in the agreement (e.g. UBC does not participate in CAGS). Please contact the relevant graduate student advisors for more information.
This is a course in homology and cohomology of topological spaces. We study spaces and continuous functions by means of abelian groups and their homomorphisms. Topics will include cellular homology of spaces, calculation techniques and applications (e.g., fixed point theorems, invariance of domain), homological algebra, and cohomology, including the cup product and Poincaré duality.
Remote access for this course will be provided via zoom. The instructor intends to lecture from handwritten notes on a tablet. Lecture notes will be provided after the lectures have been delivered.
This course may be open to students from universities outside of the PIMS network, and those coming from industry/government.
Assessment will be via homework, midterm and final exam.
N.B. The syllabus is also available as a pdf document.
UBC Vancouver is located on the traditional, ancestral, and unceded territory of the Musqueam people. The land it is situated on has always been a place of learning for the Musqueam people, who for millennia have passed on their culture, history, and traditions from one generation to the next on this site.
You must be able to work with abelian groups. This prerequisite can be sometimes overlooked. Beyond this, the course is actually two, crosslisted courses.
There are some topics that will be helpful to know about, but should not be strictly necessary for the development of the theory.
If you are a graduate student who wants to take this course, but are concerned you may lack some prerequisite, please contact me directly.
The course will follow [[https://doi.org/10.1142/12132][Lectures on Algebraic Topology]] by Haynes Miller. This book is a bound version of the notes that are available [[https://math.mit.edu/~hrm/papers/lectures-905-906.pdf][online]]. We will follow the notation and terminology of this book for the most part. The course may also refer to the exercises from [[https://pi.math.cornell.edu/~hatcher/AT/ATpage.html][Algebraic Topology]] by Alan Hatcher, which is freely available online.
There will be fortnightly homework, of which your lowest-scoring assignment will be dropped. Homework will constitute 15% of the overall grade.
Grading of homework will be based on correctness, completeness and readability. That is, points may be taken off for answers that are confusing, poorly presented, poorly explained, or devote a great deal of attention to irrelevant points.
You are encouraged to work with each other on the homework assignments, but the work you turn in must be your own. The use of AI tools for anything other than checking spelling, grammar and LaTeX formatting is prohibited.
There is an in-class midterm, worth 20% of the grade. This will be held at a time to be settled later.
The final is worth the rest of the grade, 65%. The time of final will be set by UBC scheduling during the term.
The course covers the first three chapters of Miller’s book.
The following is an approximate weekly schedule of the course.
UBC provides resources to support student learning and to maintain healthy lifestyles but recognizes that sometimes crises arise and so there are additional resources to access including those for survivors of sexual assault. UBC values respect for the person and ideas of all members of the academic community. Harassment and discrimination are not tolerated nor is suppression of academic freedom. UBC provides appropriate accommodation for students with disabilities and for religious, spiritual and cultural observances. UBC values academic honesty and students are expected to acknowledge the ideas generated by others and to uphold the highest academic standards in all of their actions.
Details of the policies and how to access support are available on the UBC Senate website.
Miranda Holmes-Cerfon : holmescerfon@math.ubc.ca
University of British Columbia
Good upper level undergraduate or early graduate knowledge of:
This course is available for registration under the Western Dean's Agreement but registrations must be approved by the course instructor. Please contact the instructor (using the email link to the left) including details of how you meet the course prerequisites. Next, you must complete the Western Deans' Agreement form , with the following course details:
Completed forms should be returned to your graduate advisor who will sign it and take the required steps. For students at PIMS sites, please see this list to find your graduate advisor, for other sites, please see the Western Deans' Agreement website .
The Western Deans' Agreement provides an automatic tuition fee waiver for visiting students. Graduate students paying normal required tuition fees at their home institution will not pay tuition fees to the host institution. However, students will typically be be required to pay other ancillary fees to the host institution, or explicitly request exemptions (e.g. Insurance or travel fees). Details vary by university, so please contact the graduate student advisor at your institution for help completing the form. Links to fee information and contact information for PIMS member universities is available below in the WDA section.
Students at universities not covered by the WDA but which are part of the Canadian Association for Graduate Studies (CAGS) may still be eligible to register for some courses under the terms of the Canadian University Graduate Transfer Agreement (CUGTA). Details of this program vary by university and registration is also typically subject to ancillary fees. Both your local and the hosting university must participate in the agreement (e.g. UBC does not participate in CAGS). Please contact the relevant graduate student advisors for more information.
This course will introduce the major tools in stochastic analysis from an applied mathematics perspective. Topics to be covered include Markov chains (both discrete and continuous), Gaussian processes, Ito calculus, stochastic differential equations (SDEs), numerical algorithms for solving SDEs, forward and backward Kolmogorov equations and their applications. It will pay particular attention to the connection between stochastic processes and PDEs, as well as to physical principles and applications. The class will attempt to strike a balance between rigour and heuristic arguments: it will assume that students have seen a little analysis, particularly in the context of studying PDEs, but will generally avoid measure theory. The target audience is graduate students in applied mathematics or related fields, who wish to use these tools in their research for modelling or simulation. The course will be divided roughly into two parts: the first part will focus on stochastic processes, particularly Markov chains, and the second part will focus on stochastic differential equations and their associated PDEs.
Remote access will be provided via zoom. The lectures will be delivered mostly on blackboards with occasional slides. PDF lecture notes will be handed out.
This course is open to students from within the PIMS network of universities.