This course is an introduction to the theory of matrix groups with a particular emphasis on applications and examples. This course will cover orthogonal transformations in two and three dimensions, quaternions, isometries of Euclidean space, Lie algebras and matrix exponentials.

This course is an introduction to the theory of curves and surfaces with a particular emphasis on applications and computational techniques. This course will cover curves in R2 and R3, curvature, torsion, differential of maps, First Fundamental Form, Parallel transport, Bishop Frames, Geodesics, Gauss-Bonnet Theorem, and Gaussian curvature.

The relationships among axioms, proofs, consistency and truth in mathematics. Soundness and Completeness. Introductions to model theory, set theory, and computability; arithmetic as a central example. Gödel's incompleteness theorems; outlines of their proofs. This course emphasizes rigour.

Partial differential equations of applied mathematics, mathematical models of physical phenomena, basic methodology.

Elementary topics in number theory such as: prime numbers; arithmetic with residues; Gaussian integers, quadratic reciprocity law, representation of numbers as sums of squares. (This course emphasizes rigour).

The course will serve as an introduction to mathematical modelling of biological processes. It will cover a selection of the following topics: Difference equations and applications. Linear differential equations and systems; phase plane analysis; nonlinear systems of differential equations and linearization; Poincaré-Bendixson Theorem. Applications of differential equations to biology, including a logistic population with harvesting; predator-prey model; competing species; epidemic models. Examples of partial differential equations; reaction-diffusion equation; pattern formation.

Stability in nonlinear systems of differential equations, bifurcation theory, chaos, strange attractors, iteration of nonlinear mappings and fractals. This course will be geared towards students with interest in sciences.

Theory of functions of one complex variable: analytic and meromorphic functions; Cauchy's theorem, residue calculus. Topics from: conformal mappings, analytic continuation, harmonic functions.

The real numbers; Sequences and series; Functional limits; Topology in R^n; Differentiation and Integration; Power Series; Metric Spaces; Integrability and sets of measure zero. The course emphasizes rigour and theory.

Basic counting principles, generating functions, permutations with restrictions. Fundamentals of graph theory with algorithms; applications (including network flows).

Complex numbers, the complex plane and Riemann sphere, Möbius transformations, elementary functions and their mapping properties, conformal mapping, holomorphic functions, Cauchy's theorem and integral formula. Taylor and Laurent series, maximum modulus principle, Schwarz' lemma, residue theorem and residue calculus.

The course discusses the Mathematics curriculum (K-12) from the following aspects: the strands of the curriculum and their place in the world of Mathematics, the nature of the proofs, applications of Mathematics, and the connection of Mathematics to other subjects. Restricted to students in the MAT major and specialist programs.

Introduction to a topic of current interest in applied mathematics. Content will vary from year to year. The contact hours for this course may vary in terms of contact type (L, T) from year to year, but will be between 36-48 contact hours in total. See the UTM Timetable.

Introduction to a topic of current interest in mathematics. Content will vary from year to year. The contact hours for this course may vary in terms of contact type (L, T) from year to year, but will be between 36-60 contact hours in total. See the UTM Timetable.

Introduction to a topic of current interest in mathematics. Content will vary from year to year. This course may include a tutorial and/or practical section in some years. The contact hours for this course may vary in terms of contact type (L, T) from year to year, but will be between 36-60 contact hours in total. See the UTM Timetable.

This is a one-term course to give students extensive practice in the writing of mathematics. The format will be to study excellent expositions of important ideas of mathematics and then to assign short writing assignments based on them.

Students explore a topic in mathematics under the supervision of a faculty member. 

Students explore a topic in mathematics under the supervision of a faculty member.

This course provides a richly rewarding opportunity for students in their third or fourth year to work in the research project of a professor in return for 399H course credit. Students enrolled have an opportunity to become involved in original research, learn research methods and share in the excitement and discovery of acquiring new knowledge. Participating faculty members post their project descriptions for the following summer and fall/winter sessions in early February and students are invited to apply in early March. See Research Opportunity Program (ROP) for more details.

This course provides a richly rewarding opportunity for students in their third or fourth year to work in the research project of a professor in return for 399Y course credit. Students enrolled have an opportunity to become involved in original research, learn research methods and share in the excitement and discovery of acquiring new knowledge. Participating faculty members post their project descriptions for the following summer and fall/winter sessions in early February and students are invited to apply in early March. See Research Opportunity Program (ROP) for more details.

Commutative rings; quotient rings. Construction of the rationals. Polynomial algebra. Fields and Galois theory: Field extentions, adjunction of roots of a polynomial. Constructibiliy, trisection of angles, construction of regular polygons. Galois groups of polynomials, in particular cubics, quartics. Insolvability of quintics by radicals.

Euclidean and non-Euclidean plane and space geometries. Real and complex projective space. Models of the hyperbolic plane. Connections with the geometry of surfaces.

Sets and functions; Topology in R^n; Topological spaces; Open and closed sets; Closure and interior; Continuous functions; Quotient spaces; Connectedness and compactness; Separation axioms and related theorems.

Combinatorial games: Nim and other impartial games; Sprague-Grundy value; existence of a winning strategy in partisan games. Two-player (matrix) games: zero-sum games and Von-Neuman's minimax theorem; general sum-matrix games, prisoner's dilemma, Nash equilibrium, cooperative games, asymmetric information. Multi-player games: coalitions and the Shapley value. Possible additional topics: repeated (stochastic) games; auctions; voting schemes and Arrow's paradox. Mathematical tools that may be introduced include hyperplane separation of convex sets and Brouwer's fixed point theorem. Numerous examples will be analyzed in depth, to offer insight to the mathematical theory and its relation with real life situations.

Introduction to a topic of current interest in mathematics. Content will vary from year to year. This course may include a tutorial and/or practical section in some years. The contact hours for this course may vary in terms of contact type (L, T) from year to year, but will be between 36-60 contact hours in total. See the UTM Timetable.

Introduction to a topic of current interest in applied mathematics. Content will vary from year to year. The contact hours for this course may vary in terms of contact type (L, T) from year to year, but will be between 36-48 contact hours in total. See the UTM Timetable.

Introduction to a topic of current interest in mathematics. Content will vary from year to year. This course may include a tutorial and/or practical section in some years. The contact hours for this course may vary in terms of contact type (L, T) from year to year, but will be between 36-60 contact hours in total. See the UTM Timetable.

An exposition on a topic in mathematics written under the supervision of a faculty member. Open to students in Mathematical Sciences Specialist program.

Students explore a topic in mathematics under the supervision of a faculty member. 

Students explore a topic in mathematics under the supervision of a faculty member.