Fall 2026
MAT386H5F • Topics in Applied Mathematics
Fall 2026 topic title: Introduction to Mathematical Finance
Instructor: Q. Wang
Topic description: This course provides a mathematical formulation of pricing methods and trading strategy of basic financial products, as well as their numerical simulations. Topics include forward, futures and option contracts, discrete and continuous models of asset prices, binomial pricing methods, Itô’s Lemma and the Black–Scholes model, no arbitrage principle, finite difference and Monte Carlo simulations.
Prerequisites: MAT264H5 and (MAT232H5 or MAT257Y5)
Enrollment Limits: Priority is given to students enrolled in the Mathematical Sciences - Major: Applied Mathematics program
MAT387H5F • Topics in Mathematics
Fall 2026 topic title: Introduction to Mathematical Acoustics
Instructor: Janelle Resch
Topic Description: This course introduces the mathematics of acoustics and wave phenomena, focusing on how calculus and differential equations are used to model sound in physical systems. Beginning with sound and mechanical oscillators, students develop models for vibrating strings and propagating waves, leading to the wave equation and concepts such as damping, energy transport, dispersion, dissipation, and phase and group velocity. The course then extends these ideas to acoustic waves in fluids and gases, including sound propagation in air and water, impedance, reflection, and high-intensity sound. Emphasis is placed on conceptual understanding, physical interpretation, and simplified mathematical models supported by demonstrations and visualizations. The course is suitable for students from a range of disciplines.
Prerequisites: (MAT223H5 or MAT240H5) and (MAT232H5 or MAT233H5) and MAT244H5, or with instructor's permission
Exclusions: MAT387H5 (Fall 2025), MAT322H5
Enrollment Limits: This course is Restricted at all times to students enrolled in the Mathematical Sciences Minor program.
MAT478H5F • Topics in Mathematics
Fall 2026 topic title: Introduction to Hilbert Spaces
Instructor: S. Fuchs
Topic Description: The course will focus on the geometry of infinite-dimensional inner-product spaces and how they differ from finite dimensional spaces. Some applications will be covered as well, with the main one being the theory of Fourier series.
Topics include: Inner product and normed spaces, Hilbert and Banach spaces, the closest point property, orthogonality and complete orthonormal systems, classical Fourier series and Weierstrass' approximation theorem, dual spaces and the Riesz-Frechet theorem, introduction to linear operators on normed spaces.
Prerequisites: (MAT157Y5 or MAT159H5 or MAT257H5 or MAT337H5) and (MAT224H5 or MAT247H5).
Recommended preparation: MAT405H5.
Enrollment Limits: Priority is given to students enrolled in the Mathematical Sciences or Applied Statistics Specialist or Major programs
Winter 2027
MAT388H5S • Topics in Advanced Mathematics
Winter 2027 topic title: Representation Theory of the Symmetric Group
Instructor: V. Tewari
Topic Description: The symmetric group of permutations -- the group of all ways to shuffle a finite set -- is one of the most familiar objects in mathematics. Its representation theory opens onto a landscape where combinatorics, linear algebra, and algebra become one story.
We begin with the combinatorial structures at the heart of the subject: partitions, Young diagrams, tableaux, and the elegant rules that govern them. These pictures of boxes turn out to predict the dimensions and behavior of abstract vector spaces. We then build the representation theory itself—irreducibles, characters, and the beautiful fact that the irreducibles are indexed by partitions—developing it through the modern Okounkov–Vershik approach, which assembles the whole theory from the inside out in a conceptually clean and hands-on manner.
The course suits a broad audience. No prior familiarity with representation theory is assumed.
Prerequisites: (MAT224H5 or MAT247H5), MAT301H5, MAT344H5
Enrollment Limits: Priority is given to students enrolled in the Mathematical Sciences and Applied Statistics Specialist or Major programs.
MAT488H5S • Topics in Advanced Mathematics
Winter 2027 topic title: Modules and Representations
Instructor: E. Hossain
Topic Description: An introduction to the theory of modules over a general ring, with a focus on semisimplicity and representations of a finite group. Topics will selected from: exact sequences, tensor products, chain conditions, projective and injective modules, prime and primitive ideals, Artin--Wedderburn Theorem, group algebras.
Prerequisite: MAT301H5
Enrolment Limits: Priority is given to students enrolled in the Mathematical Sciences or Applied Statistics Specialist or Major programs