Graphs, subgraphs, isomorphism, trees, connectivity, Euler and Hamiltonian properties, matchings, vertex and edge colourings, planarity, network flows and strongly regular graphs; applications to such problems as timetabling, personnel assignment, tank form scheduling, traveling salesmen, tournament scheduling, experimental design and finite geometries.

Theory of functions of one complex variable, analytic and meromorphic functions. Cauchy's theorem, residue calculus, conformal mappings, introduction to analytic continuation and harmonic functions.

Topics in measure theory:  the Lebesgue integral, Riemann-Stieltjes integral, Lp spaces, Hilbert and Banach spaces, Fourier series.

Basic counting principles, generating functions, permutations with restrictions. Fundamentals of graph theory with algorithms; applications (including network flows). Combinatorial structures including block designs and finite geometries.

Sturm-Liouville problems, Green's functions, special functions (Bessel, Legendre), partial differential equations of second order, separation of variables, integral equations, Fourier transform, stationary phase method.

Mathematical analysis of problems associated with biology, including models of population growth, cell biology, molecular evolution, infectious diseases, and other biological and medical disciplines. A review of mathematical topics: linear algebra (matrices, eigenvalues and eigenvectors), properties of ordinary differential equations and difference equations.

Curves and surfaces in Euclidean 3-space. Serret-Frenet frames and the associated equations, the first and second fundamental forms and their integrability conditions, intrinsic geometry and parallelism, the Gauss-Bonnet theorem.

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 proofs, the applications of Mathematics, and its connection to other subjects.

Mathematical problems which have arisen repeatedly in different cultures, e.g. solution of quadratic equations, Pythagorean theorem; transmission of mathematics between civilizations; high points of ancient mathematics, e.g. study of incommensurability in Greece, Pell's equation in India.

Abstract group theory: Sylow theorems, groups of small order, simple groups, classification of finite abelian groups. Fields and Galois theory: polynomials over a field, field extensions, constructibility; Galois groups of polynomials, in particular cubics; insolvability of quintics by radicals.

An introduction to geometry with a selection of topics from the following: symmetry and symmetry groups, finite geometries and applications, non-Euclidean geometry.

This course is an introduction to axiomatic set theory and its methods. Set theory is a foundation for practically every other area of mathematics and is a deep, rich subject in its own right. The course will begin with the Zermelo-Fraenkel axioms and general set constructions. Then the natural numbers and their arithmetic are developed axiomatically. The central concepts of cardinality, cardinal numbers, and the Cantor-Bernstein theorem are studied, as are ordinal numbers and transfinite induction. The Axiom of Choice and its equivalents are presented along with applications.

A variety of topics from geometry, analysis, combinatorics, number theory and algebra, to be chosen by the instructor.

A variety of topics from geometry, analysis, combinatorics, number theory and algebra, to be chosen by the instructor.

A variety of topics from geometry, analysis, combinatorics, number theory and algebra, to be chosen by the instructor.

The main problems of coding theory and cryptography are defined. Classic linear and non-linear codes. Error correcting and decoding properties. Cryptanalysis of classical ciphers from substitution to DES and various public key systems [e.g. RSA] and discrete logarithm based systems. Needed mathematical results from number theory, finite fields, and complexity theory are stated.

An intuitive and conceptual introduction to general relativity with emphasis on a rigorous treatment of relevant topics in geometric analysis. The course aims at presenting rigorous theorems giving insights into fundamental natural phenomena. Contents: Riemannian and Lorentzian geometry (parallelism, geodesics, curvature tensors, minimal surfaces), Hyperbolic differential equations (domain of dependence, global hyperbolicity). Relativity (causality, light cones, inertial observes, trapped surfaces, Penrose incompleteness theorem, black holes, gravitational waves).

Applications of complex analysis to geometry, physics and number theory. Fractional linear transformations and the Lorentz group. Solution to the Dirichlet problem by conformal mapping and the Poisson kernel. The Riemann mapping theorem. The prime number theorem.

This course provides an introduction and exposure to dynamical systems, with particular emphasis on low-dimensional systems such as interval maps and maps of the plane. Through these simple models, students will become acquainted with the mathematical theory of chaos and will explore strange attractors, fractal geometry and the different notions of entropy. The course will focus mainly on examples rather than proofs; students will be encouraged to explore dynamical systems by programming their simulations in Mathematica.

This course will focus on combinatorics. Topics will be selected by the instructor and will vary from year to year.

This course provides an introduction to partial differential equations as they arise in physics, engineering, finance, optimization and geometry. It requires only a basic background in multivariable calculus and ODEs, and is therefore designed to be accessible to most students. It is also meant to introduce beautiful ideas and techniques which are part of most analysts' bag of tools.

This course introduces students to combinatorial games, two-player (matrix) games, Nash equilibrium, cooperative games, and multi-player games. Possible additional topics include: repeated (stochastic) games, auctions, voting schemes and Arrow's paradox. Numerous examples will be analyzed in depth, to offer insight into the mathematical theory and its relation to real-life situations.

Manifolds, vector fields, tangent spaces, vector bundles, differential forms, integration on manifolds.

A significant project in any area of mathematics. The project may be undertaken individually or in small groups. This course is offered by arrangement with a mathematics faculty member. This course may be taken in any session and the project must be completed by the last day of classes in the session in which it is taken.

A significant project in any area of mathematics. The project may be undertaken individually or in small groups. This course is offered by arrangement with a mathematics faculty member. This course may be taken in any session and the project must be completed by the last day of classes in the session in which it is taken.

Independent study under direction of a faculty member.

Independent study under direction of a faculty member.

In this course students explore a variety of topics relating to songwriting. Advanced techniques relating to melody, lyric, and chord writing will be discussed and applied creatively to original songs. This course is taught at Centennial College.

This course will introduce students to live and studio sound by giving them hands-on experience on equipment in a professional recording studio. This course is taught at Centennial College.

Students will develop a foundational knowledge of the music industry that will serve as a base for all other music business-related courses. Students will be introduced to the terminology, history, infrastructure, and careers of the music industry. Students will be introduced to fundamental areas of business management. Legal issues and the future of the music industry will also be discussed. All material will be taught from a uniquely Canadian perspective.