Advanced courses Winter 2021

Alexander Bihlo (Memorial University)

This course will provide a short overview of classical methods of machine learning before providing an introduction to the areas of deep learning, reinforcement learning, and deep reinforcement learning. An introduction to TensorFlow and Keras will be provided.

Prerequisites include: undergraduate linear algebra, multivariate calculus, elementary probability, and elementary experience with Python.

James Watmough (University of New Brunswick Fredericton)

This course will provide an advanced introduction to differential equations and dynamical systems. Our approach to the subject will be largely geometrical and based on applications in ecology, epidemiology, and immunology. Topics to be covered include local stability of equilibria, Lyapunov functions, bifurcations of equilibria, limit cycles, bifurcations of limit cycles.

A good grounding in basic linear algebra and analysis is required, and some familiarity with Maple, Matlab, or R will be helpful. No previous exposure to differential equations is assumed.

Alan Coley (Dalhousie University)
Viqar Husain (University of New Brunswick Fredericton)

This course provides an introduction to the mathematical and physical ideas underlying the general theory of relativity. Topics covered include review of curved manifolds, followed by physics in curved spacetime, Einstein’s equations, spherical and cosmological solutions, and gravitational radiation.

Prerequisites include familiarity with partial differential equations, special relativity, and differential geometry; or permission of the instructors.  Text: A first course in General Relativity (2nd. ed), B. Schutz.

David Pike (Memorial University)

The course will focus on concepts and proof techniques pertaining to Graph Theory. Three areas will be covered: matchings (including covers, the Konig-Egervary theorem, Hall’s theorem, Tutte’s 1-factor theorem), connectivity (including edge-connectivity, Menger’s theorem, Dirac’s fan lemma, the Chvatal-Erdos theorem), and network flows (including cuts, the Ford-Fulkerson algorithm, Menger’s theorem).

Previous exposure to basic concepts in Graph Theory, such as from an undergraduate course in the subject, is expected.

Sara Faridi (Dalhousie)

Introduction to module theory: modules, submodules, quotient modules, module homomorphisms, generators for modules, direct sums, free modules, tensor products, exact sequences, projective modules, injective modules, and flat modules. Modules over principal ideal domains. Additional topics may include homological algebra, Ext and Tor Functors, symmetric and exterior algebras.

Students should have taken introductory course(s) similar to Dalhousie’s Math 3032.  Specifically, students should be familiar with: rings, fields, integral domains, ideals, quotient rings, prime and maximal ideals, factorization of polynomials, Unique Factorization Domains, Euclidean Domains.

Jeff Picka (University of New Brunswick Fredericton)

This course will cover basic multivariate statistical methods which are used in statistical learning. Topics to be covered include multivariate visualization, the multivariate Normal distribution, exploratory and confirmatory factor analysis, predictive versus model-based inference, various types of classification methods, and unsupervised learning.

An advanced introduction to statistical inference (e.g. STAT 3093 at UNB) and some familiarity with R and with matrices will be required.

Scott MacLachlan (Memorial University)

This course will cover the development of efficient and accurate tools for numerical simulation of time-dependent ordinary and partial differential equations. Standard numerical integration techniques for ODEs will be reviewed, followed by their extension to finite-difference and finite-volume discretizations of parabolic and hyperbolic PDEs. If time permits, advanced topics including finite-element discretization will be covered.

A basic background in numerical analysis and both ODEs and PDEs is required. Completion of the Memorial course Math 6210 is normally sufficient, as would be completion of upper-level undergraduate courses in numerical analysis and differential equations. A programming background is assumed, and the course will require homework assignments to be completed in python.

Peter Selinger (Dalhousie University)

This topic of this course will be Logic and Proof Assistants. Proof assistants are software in which one can write definitions, theorems, and proofs, and the software will check the correctness of the proofs. Students will learn about a particular kind of logic called dependent type theory. This also touches upon a number of other topics, such as predicate logic and lambda calculus. I do not plan to give an overview of all existing proof assistants (there are many), but rather, we will learn to use the particular proof assistant called Agda.

This course does not have specific prerequisites. Students must be comfortable with definitions, theorems, and proofs. Some exposure to formal logic may be useful, but familiarity with informal logic will do. Since we will actually be using Agda, access to a computer is required (and is hopefully a given, considering it is an online course). Prior programming experience is not required, but students should not be afraid of using the keyboard.

Mostly synchronous with lectures being recorded for later review.