Mathematics

The syllabus for this course is similar to that of MATH 1013. As with MATH 1053, more emphasis is placed on theory, mathematical rigor and interesting applications. NOTE: Credit may not be for only one of MATH 1013 or MATH 1063.

Matrices and systems of linear equations. Linear programming concepts; graphical solution of two variable problems. Permutations and combinations. Elementary probability. Mathematics of finance. NOTE: Credit for MATH 1833 will not be given if the student has previously taken either MATH 1503 or MATH 2213.

Logic, methods of proof, mathematical induction, elementary set theory, functions and relations. NOTE: This course is designed for students desiring a good grounding in the foundations of mathematics. Theorems and proofs are an important part of the course. Credit will not be given for both MATH 2203 and CS 1303. Students majoring in Mathematics must take MATH 2203.

This course introduces the basic concepts of linear algebra, mainly in finite dimensional real vector spaces. Systems of linear equations, vector and matrix algebra, bases and dimension of subspaces, row and column spaces, linear transformations and matrix representations, inner products, determinants, eigenvectors and diagonalization. Applications as time permits. 

Functions of several variables, partial derivatives, multiple integrals, vector functions, Green's and Stokes' Theorems. 

This course is intended for students who anticipate a career as an elementary or middle school teacher. The course focuses on topics taken from the K-8 curriculum with extensions beyond classroom topics to show the 'how' and 'why' behind school mathematics. The major topics are problem solving, number concepts, number and relationship operations, patterns and relations, shape and space, as well as data management and probability. Intended for students registered in arts programs. Not available for credit to students who would have 6 ch of Level 1000 mathematics in their degree programs. 

Graphs, Euler paths, tournaments, factors, spanning trees, applications; graph colourings, planar graphs, Menger's theorem, flows in networks, flow algorithms.

Strategic games, n-person games in normal form, dominated strategies, Nash equilibrium, mixed strategies and mixed strategy equilibrium, games with perfect information, games with imperfect information, Bayesian games, extensive games. The course introduces basic non-cooperative game theory and analytical tools for decision makers (consumers, firms, politicians, governments). It is suitable for Mathematics, Economics, Computer Science, Management Science, Political Science, Social Science and Science students or any student with a minor in such disciplines, in particular those in the Mathematics/Statistics-Economics option. Note: Students cannot obtain credit for both MATH 3373 and ECON 4673 (or ECON 5673).

The course introduces the basic concepts of mathematical logic, including the Axiom of Choice and its equivalents; propositional logic; languages and structures, axioms and theories, models; elements of model theory (Completeness, Compactness, Löwenheim-Skolem theorems, nonstandard models); theory of computability (ChurchTuring Thesis, recursive functions and sets, recursively enumerable sets, decision problems, the Halting Problem); Gödel's Incompleteness Theorems.

The course provides an introduction to the physical principles (Lorentz invariance, constancy of the speed of light, equivalence of mass and energy) and the mathematical underpinnings (Minkowski spacetime, tensors) of the theory of special relativity. This course is cross listed PHYS 3912. Credit cannot be obtained for both MATH 3463 and PHYS 3912.

A course for undergraduate students who anticipate a career as teachers. Topics build around the K-12 syllabus, with extensions beyond the classroom, to show the 'how' and 'why' behind school mathematics. Mathematical language; real numbers and other mathematical structures; Euclidean geometry; functions; mathematical connections; problem solving.

Relativistic quantum mechanics. The negative energy problem. Classical field theory, symmetries and Noether's theorem. Free field theory and Fock space quantization. The interacting field: LSZ reduction formula, Wick's theorem, Green's functions, and Feynman diagrams. Introduction to Quantum electrodynamics and renormalization. Credit cannot be obtained for both MATH 4443 and PHYS 4953.

Along with quantum theory, general relativity is one of the central pillars of modern theoretical physics with wide-ranging implications for astrophysics and high energy physics. The essential idea is that gravitation is a manifestation of the curvature of spacetime rather than a force in the Newtonian sense.  This course will provide students with a basic working understanding of general relativity and an introduction to important applications such as black holes and cosmology.  Contents: review and geometric interpretation of special relativity, foundations of general relativity, linearized gravity and classical tests, black holes, cosmology. Note: Credit cannot be obtained for both MATH 4483 and PHYS 4983. 

The numerical solution of ordinary differential equations, and partial differential equations of elliptic, hyperbolic and parabolic type. The course is a basic introduction to finite difference methods, including the associated theory of stability, accuracy and convergence. Students will gain practical experience using state-of-the-art numerical solvers and visualization tools, while solving practical problems from the physical and biological sciences. Cross-listed as CS 4115. 

Overview of the field of Mathematical Biology.  Development, simulation and analysis of mathematical models describing biological systems. Equal emphasis is placed on developing simple models and case studies of successful models. The principal mathematical tools are differential and difference equations, finite mathematics, probability and statistics. This course is intended for students in their third or fourth year having an interest in biological research.