Program Requirements
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 advisor. 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.
Required Courses (42 credits)
* COMP 250 may be preceded by COMP 202.

COMP 250 Introduction to Computer Science (3 credits) *
Overview
Computer Science (Sci) : An introduction to the design of computer algorithms, including basic data structures, analysis of algorithms, and establishing correctness of programs. Overview of topics in computer science.
Terms: Fall 2010, Winter 2011
Instructors: Doina Precup (Fall) Michael Langer (Winter)
 3 hours
 Prerequisites: Familiarity with a high level programming language and CEGEP level Math.
 Restrictions: COMP 203 and COMP 250 are considered to be equivalent from a prerequisite point of view, and cannot both be taken for credit.

COMP 252 Algorithms and Data Structures (3 credits)
Overview
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 2011
Instructors: Luc P Devroye (Winter)
 3 hours
 Prerequisite: COMP 250 and MATH 240
 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.

MATH 235 Algebra 1 (3 credits)
Overview
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 2010
Instructors: Heekyoung Hahn (Fall)
 Fall
 3 hours lecture; 1 hour tutorial
 Prerequisite: MATH 133 or equivalent

MATH 242 Analysis 1 (3 credits)
Overview
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 2010
Instructors: Reem Adel Yassawi (Fall)
 Fall
 Prerequisite: MATH 141

MATH 248 Honours Advanced Calculus (3 credits)
Overview
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 2010
Instructors: Pengfei Guan (Fall)
 Fall and Winter and Summer
 Prerequisites: MATH 133 and MATH 222 or consent of Department.
 Restriction: Intended for Honours Mathematics, Physics and Engineering students
 Restriction: Not open to students who have taken or are taking MATH 314

MATH 251 Honours Algebra 2 (3 credits)
Overview
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 selfadjoint operators.
Terms: Winter 2011
Instructors: James G Loveys (Winter)
 Winter
 Prerequisites: MATH 235 or permission of the Department
 Restriction: Not open to students who are taking or have taken MATH 247

MATH 255 Honours Analysis 2 (3 credits)
Overview
Mathematics & Statistics (Sci) : Series of functions including power series. Riemann integration in one variable. Elementary functions.
Terms: Winter 2011
Instructors: Vojkan Jaksic (Winter)
 Winter
 Prerequisites: MATH 242 or permission of the Department

MATH 325 Honours Ordinary Differential Equations (3 credits)
Overview
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: Fall 2010, Winter 2011
Instructors: Antony Raymond Humphries (Fall) Ivo Klemes (Winter)
 Fall and Winter
 (306)
 Prerequisite: MATH 222.
 Restriction: Intended for Honours Mathematics, Physics and Engineering programs.
 Restriction: Not open to students who have taken MATH 263 (formerly MATH 261), MATH 315

MATH 350 Graph Theory and Combinatorics (3 credits)
Overview
Mathematics & Statistics (Sci) : Graph models. Graph connectivity, planarity and colouring. Extremal graph theory. Matroids. Enumerative combinatorics and listing.
Terms: Winter 2011
Instructors: Bruce Alan Reed (Winter)
 Prerequisites: MATH 235 or MATH 240 and MATH 251 or MATH 223.
 Restrictions: Not open to students who have taken or are taking MATH 343 or MATH 340.
 Intended for students in mathematics or computer science honours programs.

MATH 356 Honours Probability (3 credits)
Overview
Mathematics & Statistics (Sci) : Basic combinatorial probability. Introductory distribution theory of univariate and multivariate distributions with special reference to the Binomial, Poisson, Gamma and Normal distributions. Characteristic functions. Weak law of large numbers. Central limit theorem.
Terms: Fall 2010
Instructors: Johanna Neslehova (Fall)
 Fall
 Prerequisite: MATH 255 or MATH 243
 Restriction: Not open to students who have taken or are taking MATH 323

MATH 357 Honours Statistics (3 credits)
Overview
Mathematics & Statistics (Sci) : Data analysis. Estimation and hypothesis testing. Power of tests. Likelihood ratio criterion. The chisquared goodness of fit test. Introduction to regression analysis and analysis of variance.
Terms: Winter 2011
Instructors: Masoud AsgharianDastenaei (Winter)
 Winter
 Prerequisite: MATH 356 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 324

MATH 375 Honours Partial Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First order partial differential equations, geometric theory, classification of second order linear equations, SturmLiouville 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 2010
Instructors: Charles Roth (Fall)
 Fall
 Prerequisites: MATH 247 or MATH 251 or equivalent, MATH 248 or equivalent, MATH 325

MATH 376 Honours Nonlinear Dynamics (3 credits)
Overview
Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 326, but will be assessed at the honours level.
Terms: Fall 2010
Instructors: Antony Raymond Humphries (Fall)
 Fall
 Prerequisites: MATH 222, MATH 223
 Restrictions: Intended primarily for Honours students. Not open to students who have taken or are taking MATH 326.
 Note: Additionally, a special project or projects may be assigned.

MATH 470 Honours Research Project (3 credits)
Overview
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 2010, Winter 2011
Instructors: Djivede Kelome (Fall) Djivede Kelome (Winter)
 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
Complementary Courses (18 credits)
Advising Notes:
Students interested in continuous applied mathematics are urged to choose these as part of their Complementary Courses: MATH 354 and MATH 355 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 370, MATH 371, MATH 407, MATH 447, MATH 487, MATH 550, MATH 552, MATH 560.
3 credits selected from:

MATH 249 Honours Complex Variables (3 credits)
Overview
Mathematics & Statistics (Sci) : Functions of a complex variable; CauchyRiemann 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; SchwarzChristoffel transformation; Poisson's integral formulas; applications.
Terms: Winter 2011
Instructors: Robert Seiringer (Winter)
 Winter
 Prerequisite: MATH 248.
 Restriction: Intended for Honours Physics and Engineering students
 Restriction: Not open to students who have taken or are taking MATH 316

MATH 366 Honours Complex Analysis (3 credits)
Overview
Mathematics & Statistics (Sci) : Functions of a complex variable, CauchyRiemann 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: This course is not scheduled for the 20102011 academic year.
Instructors: There are no professors associated with this course for the 20102011 academic year.
 Prerequisite: MATH 248.
 Corequisite: MATH 354.
 Restriction: Not open to students who have taken or are taking MATH 466, MATH 249, MATH 316, MATH 381.
at least 3 credits selected from:

MATH 387 Honours Numerical Analysis (3 credits)
Overview
Mathematics & Statistics (Sci) : Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Terms: This course is not scheduled for the 20102011 academic year.
Instructors: There are no professors associated with this course for the 20102011 academic year.
 Taught in alternate years
 Winter (even years)
 Prerequisites: MATH 325 or MATH 315, COMP 202 or permission of instructor.
 Corequisites: MATH 255 or MATH 243.
 Restriction: Intended primarily for Honours students.

MATH 397 Honours Matrix Numerical Analysis (3 credits)
Overview
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: Winter 2011
Instructors: Antony Raymond Humphries (Winter)
 Winter
 Prerequisites: MATH 251 or MATH 247, COMP 202 or permission of the instructor.
and the remainder of credits selected from:

COMP 362 Honours Algorithm Design (3 credits)
Overview
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: Fall 2010
Instructors: Mohit Singh (Fall)
 3 hours
 Prerequisite: COMP 252
 Restriction: Not open to students who have taken or are taking COMP 360.
 Note: COMP 362 can be used instead of COMP 360 to satisfy prerequisites.

COMP 490 Introduction to Probabilistic Analysis of Algorithms (3 credits)
Overview
Computer Science (Sci) : Fundamental tools from probability are used to analyze algorithms. Notions covered included independence, generating functions, probability inequalities, random walks and Markov chains. Analysis of probabilistic recurrences, Las Vegas algorithms, randomized approximation algorithms, random sampling methods, Monte Carlo techniques and algorithms for combinatorial search and graph theoretic problems.
Terms: This course is not scheduled for the 20102011 academic year.
Instructors: There are no professors associated with this course for the 20102011 academic year.
 3 hours
 Prerequisites: COMP 251 and MATH 323

MATH 352 Problem Seminar (1 credit)
Overview
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 2010
Instructors: James G Loveys (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.

MATH 354 Honours Analysis 3 (3 credits)
Overview
Mathematics & Statistics (Sci) : Introduction to metric spaces. Multivariable differential calculus, implicit and inverse function theorems.
Terms: Fall 2010
Instructors: Dmitry Jakobson (Fall)
 Fall
 Prerequisite: MATH 255 or equivalent

MATH 355 Honours Analysis 4 (3 credits)
Overview
Mathematics & Statistics (Sci) : Lebesque measure, integration and Fubini's theorem. Abstract measure and integration. Convergence theorems. Introduction to Hilbert spaces, L_2 spaces, Fourier series. Fourier integrals (if time allows).
Terms: Winter 2011
Instructors: Dmitry Jakobson (Winter)
 Winter
 Prerequisite: MATH 354 or equivalent.

MATH 370 Honours Algebra 3 (3 credits)
Overview
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 2010
Instructors: Jayce Getz (Fall)
 Fall
 Prerequisite: MATH 251

MATH 371 Honours Algebra 4 (3 credits)
Overview
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 2011
Instructors: Jayce Getz (Winter)
 Winter
 Prerequisite: MATH 370

MATH 377 Honours Number Theory (3 credits)
Overview
Mathematics & Statistics (Sci) : This course consists of the lectures of MATH 346, but will be assessed at the honours level.
Terms: Winter 2011
Instructors: Henri Darmon (Winter)
 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.

MATH 380 Honours Differential Geometry (3 credits)
Overview
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 FaryMilnor theorem on knotted curves, abstract surfaces as 2d manifolds, the Euler characteristic, the GaussBonnet theorem for surfaces.
Terms: Winter 2011
Instructors: Pengfei Guan (Winter)
 Winter
 Prerequisites: MATH 251 or MATH 247, and MATH 248 or MATH 314

MATH 480 Honours Independent Study (3 credits)
Overview
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 2010, Winter 2011
Instructors: Axel W Hundemer (Fall) Axel W Hundemer (Winter)
 Fall and Winter and Summer
 Please see regulations concerning Project Courses under Faculty Degree Requirements
 Requires approval by the chair before registration

MATH 487 Honours Mathematical Programming (3 credits)
Overview
Mathematics & Statistics (Sci) : The course consists of the lectures of MATH 417, but will be assessed at the honours level.
Terms: This course is not scheduled for the 20102011 academic year.
Instructors: There are no professors associated with this course for the 20102011 academic year.
 Prerequisites: MATH 248, MATH 251 and COMP 202 or COMP 250 or permission of instructor.
 Restriction: Intended primarily for honours students. Not open to students who have taken or are taking MATH 417.
 Note: Additionally, a special project or projects may be assigned.

MATH 488 Honours Set Theory (3 credits)
Overview
Mathematics & Statistics (Sci) : Axioms of set theory. Operations on sets. Ordinal and cardinal numbers. Wellorderings, transfinite induction and recursion. Consequences of the axiom of choice. Boolean algebras. Cardinal arithmetic.
Terms: This course is not scheduled for the 20102011 academic year.
Instructors: There are no professors associated with this course for the 20102011 academic year.
 Fall
 Prerequisites: MATH 251 or MATH 255 or permission of instructor

MATH 490 Honours Mathematics of Finance (3 credits)
Overview
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 20102011 academic year.
Instructors: There are no professors associated with this course for the 20102011 academic year.
 Prerequisites: MATH 222, MATH 323 or equivalent. (Intended primarily for honours students.)
 Restrictions: Not open to students who have taken MATH 330. Not open to students who have taken or are taking MATH 430.
 Note: Additionally, a special project or projects may be assigned.
All MATH 500level courses.
No more than 6 credits from the following courses for which no Honours equivalent exists:

MATH 204 Principles of Statistics 2 (3 credits)
Overview
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 2011
Instructors: There are no professors associated with this course for the 20102011 academic year.
 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.

MATH 329 Theory of Interest (3 credits)
Overview
Mathematics & Statistics (Sci) : Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Terms: Winter 2011
Instructors: Neville G F Sancho (Winter)
 Winter
 Prerequisite: MATH 141

MATH 338 History and Philosophy of Mathematics (3 credits)
Overview
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 2010
Instructors: Niky Kamran (Fall)
 Fall

MATH 339 Foundations of Mathematics (3 credits)
Overview
Mathematics & Statistics (Sci) : A continuation of MATH 338. Topics are chosen mainly from 19th and 20th century mathematics, with some emphasis on philosophical and foundational problems. Sample topics are: progress in number theory, construction of the number system, infinity according to Cantor, logic and foundations from Aristotle to Cohen, Gödel's incompleteness theorem, calculability and programs, formalism versus intuitionism, abstract mathematics and categories.
Terms: This course is not scheduled for the 20102011 academic year.
Instructors: There are no professors associated with this course for the 20102011 academic year.
 Winter
 Prerequisites: MATH 235, MATH 318

MATH 348 Topics in Geometry (3 credits)
Overview
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, nonEuclidean geometry and problems in discrete geometry.
Terms: Summer 2011
Instructors: There are no professors associated with this course for the 20102011 academic year.
 Prerequisite: MATH 133 or equivalent or permission of instructor.

MATH 407 Dynamic Programming (3 credits)
Overview
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 20102011 academic year.
Instructors: There are no professors associated with this course for the 20102011 academic year.
 Winter
 Prerequisites: COMP 202; MATH 223 or MATH 236, MATH 314, MATH 315 and MATH 323

MATH 437 Mathematical Methods in Biology (3 credits)
Overview
Mathematics & Statistics (Sci) : The formulation and treatment of realistic mathematical models describing biological phenomena through such qualitative and quantitative mathematical techniques as local and global stability theory, bifurcation analysis and phase plane analysis. Numerical simulation. Concrete and detailed examples will be drawn from molecular, cellular and population biology and mammalian physiology.
Terms: Fall 2010
Instructors: Michael C Mackey (Fall)
 Fall
 Prerequisites: MATH 315 or MATH 325, and MATH 323 or MATH 356, a CEGEP or higher level computer programming course

MATH 447 Introduction to Stochastic Processes (3 credits)
Overview
Mathematics & Statistics (Sci) : Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains, transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, queueing theory.
Terms: Winter 2011
Instructors: Dana Louis AddarioBerry (Winter)
 Winter
 Prerequisite: MATH 323
 Restriction: Not open to students who have taken or are taking MATH 547.
Other courses with the permission of the department.