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Note: This is the 2017–2018 eCalendar. Update the year in your browser's URL bar for the most recent version of this page, or .
Note: This is the 2017–2018 eCalendar. Update the year in your browser's URL bar for the most recent version of this page, or .
Applied Mathematics is a very broad field and students are encouraged to choose a coherent program of complementary courses. Most students specialize in "continuous" or "discrete" applied mathematics, but there are many sensible combinations of courses, and the following informal guidelines should be discussed with the student's adviser. Also, aside from seeking to develop a sound basis in Applied Mathematics, one of the objectives of the program is to kindle the students' interest in possible areas of application. To develop an appreciation of the diversity of Applied Mathematics, students are advised to develop some depth (e.g., by completing a minor) in a field related to Applied Mathematics such as Atmospheric and Oceanic Sciences, Biology, Biochemistry, Chemistry, Computer Science, Earth and Planetary Sciences, Economics, Engineering, Management, Physics, Physiology, and Psychology.
* COMP 250 may be preceded by COMP 202.
** Students select either MATH 251 or MATH 247, but not both.
Computer Science (Sci) : Mathematical tools (binary numbers, induction, recurrence relations, asymptotic complexity, establishing correctness of programs), Data structures (arrays, stacks, queues, linked lists, trees, binary trees, binary search trees, heaps, hash tables), Recursive and non-recursive algorithms (searching and sorting, tree and graph traversal). Abstract data types, inheritance. Selected topics.
Terms: Fall 2017, Winter 2018
Instructors: Langer, Michael (Fall) Gonzalez Oliver, Carlos; Waldispuhl, Jérôme (Winter)
Computer Science (Sci) : The design and analysis of data structures and algorithms. The description of various computational problems and the algorithms that can be used to solve them, along with their associated data structures. Proving the correctness of algorithms and determining their computational complexity.
Terms: Winter 2018
Instructors: Devroye, Luc P (Winter)
3 hours
Restrictions: Open only to students registered in following programs: Honours in Computer Science, Joint Honours in Mathematics and Computer Science, Honours in Applied Mathematics, Honours in Mathematics. Not open to students who have taken or are taking COMP 251.
Note: COMP 252 can be used instead of COMP 251 to satisfy prerequisites.
Mathematics & Statistics (Sci) : Sets, functions and relations. Methods of proof. Complex numbers. Divisibility theory for integers and modular arithmetic. Divisibility theory for polynomials. Rings, ideals and quotient rings. Fields and construction of fields from polynomial rings. Groups, subgroups and cosets; group actions on sets.
Terms: Fall 2017
Instructors: Wise, Daniel (Fall)
Fall
3 hours lecture; 1 hour tutorial
Prerequisite: MATH 133 or equivalent
Mathematics & Statistics (Sci) : Matrix algebra, determinants, systems of linear equations. Abstract vector spaces, inner product spaces, Fourier series. Linear transformations and their matrix representations. Eigenvalues and eigenvectors, diagonalizable and defective matrices, positive definite and semidefinite matrices. Quadratic and Hermitian forms, generalized eigenvalue problems, simultaneous reduction of quadratic forms. Applications.
Terms: Winter 2018
Instructors: Hundemer, Axel W (Winter)
Mathematics & Statistics (Sci) : Partial derivatives; implicit functions; Jacobians; maxima and minima; Lagrange multipliers. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line integrals; Green's theorem; the divergence theorem. Stokes' theorem; irrotational and solenoidal fields; applications.
Terms: Fall 2017
Instructors: Guan, Pengfei (Fall)
Mathematics & Statistics (Sci) : Linear equations over a field. Introduction to vector spaces. Linear maps and their matrix representation. Determinants. Canonical forms. Duality. Bilinear and quadratic forms. Real and complex inner product spaces. Diagonalization of self-adjoint operators.
Terms: Winter 2018
Instructors: Vonk, Jan (Winter)
Mathematics & Statistics (Sci) : Basic point-set topology, metric spaces: open and closed sets, normed and Banach spaces, Hölder and Minkowski inequalities, sequential compactness, Heine-Borel, Banach Fixed Point theorem. Riemann-(Stieltjes) integral, Fundamental Theorem of Calculus, Taylor's theorem. Uniform convergence. Infinite series, convergence tests, power series. Elementary functions.
Terms: Winter 2018
Instructors: Choksi, Rustum (Winter)
Mathematics & Statistics (Sci) : First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications.
Terms: Winter 2018
Instructors: Humphries, Antony Raymond (Winter)
Mathematics & Statistics (Sci) : Graph models. Graph connectivity, planarity and colouring. Extremal graph theory. Matroids. Enumerative combinatorics and listing.
Terms: Fall 2017
Instructors: Volec, Jan (Fall)
Mathematics & Statistics (Sci) : Sample space, probability axioms, combinatorial probability. Conditional probability, Bayes' Theorem. Distribution theory with special reference to the Binomial, Poisson, and Normal distributions. Expectations, moments, moment generating functions, uni-variate transformations. Random vectors, independence, correlation, multivariate transformations. Conditional distributions, conditional expectation.Modes of stochastic convergence, laws of large numbers, Central Limit Theorem.
Terms: Fall 2017
Instructors: Chen, Linan (Fall)
Mathematics & Statistics (Sci) : Data analysis. Estimation and hypothesis testing. Power of tests. Likelihood ratio criterion. The chi-squared goodness of fit test. Introduction to regression analysis and analysis of variance.
Terms: Winter 2018
Instructors: Wolfson, David B (Winter)
Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 326, but will be assessed at the honours level.
Terms: Fall 2017
Instructors: Humphries, Antony Raymond (Fall)
Mathematics & Statistics (Sci) : The project will contain a significant research component that requires substantial independent work consisting of a written report and oral examination or presentation.
Terms: Fall 2017, Winter 2018, Summer 2018
Instructors: Kelome, Djivede; Tsogtgerel, Gantumur; Vetois, Jerome; Hoheisel, Tim; Toth, John A; Kamran, Niky; Addario-Berry, Dana Louis; Yang, Yi; Wise, Daniel; Goren, Eyal Z (Fall) Kelome, Djivede; Khadra, Anmar; Chen, Linan; Yang, Yi; Jakobson, Dmitry; Goren, Eyal Z; Toth, John A; Choksi, Rustum; Przytycki, Piotr (Winter) Kelome, Djivede; Vetois, Jerome; Chen, Linan (Summer)
Fall and Winter and Summer
Requires Departmental Approval
Students are advised to start contacting potential project supervisors early during their U2 year.
Prerequisite: appropriate honours courses with approval of the project supervisor
Mathematics & Statistics (Sci) : First order partial differential equations, geometric theory, classification of second order linear equations, Sturm-Liouville problems, orthogonal functions and Fourier series, eigenfunction expansions, separation of variables for heat, wave and Laplace equations, Green's function methods, uniqueness theorems.
Terms: Fall 2017
Instructors: Choksi, Rustum (Fall)
Restriction(s): Not open to students who have taken MATH 375.
3 credits selected from:
Mathematics & Statistics (Sci) : A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.
Terms: Fall 2017
Instructors: Vetois, Jerome (Fall)
Mathematics & Statistics (Sci) : Properties of R. Cauchy and monotone sequences, Bolzano- Weierstrass theorem. Limits, limsup, liminf of functions. Pointwise, uniform continuity: Intermediate Value theorem. Inverse and monotone functions. Differentiation: Mean Value theorem, L'Hospital's rule, Taylor's Theorem.
Terms: Fall 2017
Instructors: Hundemer, Axel W (Fall)
*** It is strongly recommended that students take MATH 254.
Advising Notes:
Students interested in continuous applied mathematics are urged to choose these as part of their Complementary Courses: MATH 454 and MATH 455, and are advised to choose additional courses from MATH 387, MATH 397, MATH 555, MATH 560, MATH 574, MATH 578, MATH 579, MATH 580, MATH 581.
Students interested in discrete applied mathematics are advised to choose from these as part of their Complementary Courses: COMP 362, COMP 490, MATH 456, MATH 457, MATH 407, MATH 547, MATH 487, MATH 550, MATH 552, MATH 560.
3 credits selected from:
Mathematics & Statistics (Sci) : Functions of a complex variable; Cauchy-Riemann equations; Cauchy's theorem and consequences. Taylor and Laurent expansions. Residue calculus; evaluation of real integrals; integral representation of special functions; the complex inversion integral. Conformal mapping; Schwarz-Christoffel transformation; Poisson's integral formulas; applications.
Terms: Winter 2018
Instructors: Roth, Charles (Winter)
Mathematics & Statistics (Sci) : Functions of a complex variable, Cauchy-Riemann equations, Cauchy's theorem and its consequences. Uniform convergence on compacta. Taylor and Laurent series, open mapping theorem, Rouché's theorem and the argument principle. Calculus of residues. Fractional linear transformations and conformal mappings.
Terms: Fall 2017
Instructors: Harrison, Sarah (Fall)
at least 3 credits selected from:
Mathematics & Statistics (Sci) : Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Terms: Winter 2018
Instructors: Tsogtgerel, Gantumur (Winter)
Mathematics & Statistics (Sci) : The course consists of the lectures of MATH 327 plus additional work involving theoretical assignments and/or a project. The final examination for this course may be different from that of MATH 327.
Terms: This course is not scheduled for the 2017-2018 academic year.
Instructors: There are no professors associated with this course for the 2017-2018 academic year.
and the remainder of credits selected from:
Computer Science (Sci) : Basic algorithmic techniques, their applications and limitations. Problem complexity, how to deal with problems for which no efficient solutions are known.
Terms: Winter 2018
Instructors: Cai, Yang (Winter)
Mathematics & Statistics (Sci) : Seminar in Mathematical Problem Solving. The problems considered will be of the type that occur in the Putnam competition and in other similar mathematical competitions.
Terms: Fall 2017
Instructors: Norin, Sergey (Fall)
Prerequisite: Enrolment in a math related program or permission of the instructor. Requires departmental approval.
Prerequisite: Enrolment in a math related program or permission of the instructor.
Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 346, but will be assessed at the honours level.
Terms: This course is not scheduled for the 2017-2018 academic year.
Instructors: There are no professors associated with this course for the 2017-2018 academic year.
Winter
Prerequisite: Enrolment in Mathematics Honours program or consent of instructor
Restriction: Not open to students who have taken or are taking MATH 346.
Note: Additionally, a special project or projects may be assigned.
Mathematics & Statistics (Sci) : Review of point-set topology: topological space, dense sets, completeness, compactness, connectedness and path-connectedness, separability. Arzela-Ascoli, Stone-Weierstrass, Baire category theorems. Measure theory: sigma algebras, Lebesgue measure and integration, L^1 functions. Fatou's lemma, monotone and dominated convergence theorem. Egorov, Lusin's theorems. Fubini-Tonelli theorem.
Terms: Fall 2017
Instructors: Bruneau, Laurent (Fall)
Mathematics & Statistics (Sci) : Continuation of measure theory. Functional analysis: L^p spaces, linear functionals and dual spaces, Hahn-Banach theorem, Riesz representation theorem. Hilbert spaces, weak convergence. Spectral theory of compact operator. Introduction to Fourier analysis, Fourier transforms.
Terms: Winter 2018
Instructors: Vetois, Jerome (Winter)
Restriction(s): Not open to students who have taken MATH 355.
Mathematics & Statistics (Sci) : Introduction to monoids, groups, permutation groups; the isomorphism theorems for groups; the theorems of Cayley, Lagrange and Sylow; structure of groups of low order. Introduction to ring theory; integral domains, fields, quotient field of an integral domain; polynomial rings; unique factorization domains.
Terms: Fall 2017
Instructors: Goren, Eyal Z (Fall)
Restriction(s): Not open to students who have taken MATH 370.
Mathematics & Statistics (Sci) : Introduction to modules and algebras; finitely generated modules over a principal ideal domain. Field extensions; finite fields; Galois groups; the fundamental theorem of Galois theory; application to the classical problem of solvability by radicals.
Terms: Winter 2018
Instructors: Sabok, Marcin (Winter)
Restriction(s): Not open to students who have taken MATH 371.
Mathematics & Statistics (Sci) : In addition to the topics of MATH 320, topics in the global theory of plane and space curves, and in the global theory of surfaces are presented. These include: total curvature and the Fary-Milnor theorem on knotted curves, abstract surfaces as 2-d manifolds, the Euler characteristic, the Gauss-Bonnet theorem for surfaces.
Terms: Winter 2018
Instructors: Hurtubise, Jacques Claude (Winter)
Restriction(s): Not open to students who have taken MATH 380.
Mathematics & Statistics (Sci) : Reading projects permitting independent study under the guidance of a staff member specializing in a subject where no appropriate course is available. Arrangements must be made with an instructor and the Chair before registration.
Terms: Fall 2017, Winter 2018, Summer 2018
Instructors: Hundemer, Axel W; Panangaden, Prakash; Przytycki, Piotr (Fall) Hundemer, Axel W; Goren, Eyal Z; Hoheisel, Tim; Chen, Linan; Nica, Bogdan Lucian (Winter) Neslehova, Johanna; Lin, Jessica; Jakobson, Dmitry (Summer)
Fall and Winter and Summer
Please see regulations concerning Project Courses under Faculty Degree Requirements
Requires approval by the chair before registration
Mathematics & Statistics (Sci) : The course consists of the lectures of MATH 417, but will be assessed at the honours level.
Terms: Fall 2017
Instructors: Hoheisel, Tim (Fall)
Mathematics & Statistics (Sci) : Axioms of set theory. Operations on sets. Ordinal and cardinal numbers. Well-orderings, transfinite induction and recursion. Consequences of the axiom of choice. Boolean algebras. Cardinal arithmetic.
Terms: This course is not scheduled for the 2017-2018 academic year.
Instructors: There are no professors associated with this course for the 2017-2018 academic year.
Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 430, but will be assessed at the honours level.
Terms: This course is not scheduled for the 2017-2018 academic year.
Instructors: There are no professors associated with this course for the 2017-2018 academic year.
* Not open to students who have taken MATH 354.
** Not open to students who have taken MATH 355.
*** Not open to students who have taken MATH 370.
+ Not open to students who have taken MATH 371.
++ Not open to students who have taken MATH 380.
All MATH 500-level courses.
No more than 6 credits from the following courses for which no Honours equivalent exists:
Mathematics & Statistics (Sci) : The concept of degrees of freedom and the analysis of variability. Planning of experiments. Experimental designs. Polynomial and multiple regressions. Statistical computer packages (no previous computing experience is needed). General statistical procedures requiring few assumptions about the probability model.
Terms: Winter 2018
Instructors: Steele, Russell (Winter)
Winter
Prerequisite: MATH 203 or equivalent. No calculus prerequisites
Restriction: This course is intended for students in all disciplines. For extensive course restrictions covering statistics courses see Section 3.6.1 of the Arts and of the Science sections of the calendar regarding course overlaps.
You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
Mathematics & Statistics (Sci) : Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Terms: Winter 2018
Instructors: Panayotov, Ivo (Winter)
Winter
Prerequisite: MATH 141
Mathematics & Statistics (Sci) : Egyptian, Babylonian, Greek, Indian and Arab contributions to mathematics are studied together with some modern developments they give rise to, for example, the problem of trisecting the angle. European mathematics from the Renaissance to the 18th century is discussed in some detail.
Terms: Fall 2017
Instructors: Fox, Thomas F (Fall)
Fall
Mathematics & Statistics (Sci) : Selected topics - the particular selection may vary from year to year. Topics include: isometries in the plane, symmetry groups of frieze and ornamental patterns, equidecomposibility, non-Euclidean geometry and problems in discrete geometry.
Terms: Fall 2017
Instructors: Fox, Thomas F (Fall)
Prerequisite: MATH 133 or equivalent or permission of instructor.
Mathematics & Statistics (Sci) : Sequential decision problems, resource allocation, transportation problems, equipment replacement, integer programming, network analysis, inventory systems, project scheduling, queuing theory calculus of variations, markovian decision processes, stochastic path problems, reliability, discrete and continuous control processes.
Terms: This course is not scheduled for the 2017-2018 academic year.
Instructors: There are no professors associated with this course for the 2017-2018 academic year.
Other courses with the permission of the Department.