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
MAT386H5S • Topics in Applied Mathematics
Winter 2027 topic title: TBA
MAT387H5F • Topics in Mathematics
Fall 2026 topic title: TBA
MAT387H5S • Topics in Mathematics
Winter 2027 topic title: TBA
MAT388H5F • Topics in Advanced Mathematics
Fall 2026 topic title: TBA
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.
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
MAT486H5S • Topics in Applied Mathematics
Winter 2027 topic title: TBA
MAT488H5S • Topics in Advanced Mathematics
Winter 2027 topic title: Commutative Algebra
Instructor: E. Hossain
Topic Description: An introduction to the theory of commutative rings and their modules, illustrating connections to number theory and algebraic geometry. Topics will be selected from: exact sequences, tensor products, chain conditions, projective and injective modules, localisation, Krull dimension, primary decomposition.
Prerequisite: MAT301H5
Enrolment Limits: Priority is given to students enrolled in the Mathematical Sciences or Applied Statistics Specialist or Major programs