Program Requirements
This Minor concentration is open only to students registered in the Major Concentration Mathematics. Taken together, these two concentrations constitute a program equivalent to the Major in Mathematics offered by the Faculty of Science.
No course overlap between the Major Concentration Mathematics and the Supplementary Minor Concentration in Mathematics is permitted.
Note that according to the Faculty of Arts Multitrack System degree requirements, option C, students registered in the Supplementary Minor Concentration in Mathematics must also complete another minor concentration in a discipline other than Mathematics.
For more information about the Multitrack System options please refer to the Faculty of Arts regulations under "Faculty Degree Requirements", "About Program Requirements", and "Departmental Programs".
Required Course (3 credits)
* Note: If Math 315 has already been taken as part of the Major Concentration Mathematics, an additional 3credit complementary course must be taken to replace it.

MATH 315 Ordinary Differential Equations (3 credits) *
Overview
Mathematics & Statistics (Sci) : First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Terms: Fall 2012, Winter 2013, Summer 2013
Instructors: JianJun Xu (Fall) Alexey Eremin (Winter)
 Prerequisite: MATH 222.
 Corequisite: MATH 133.
 Restriction: Not open to students who have taken or are taking MATH 325.
Complementary Courses (15 credits)
15 credits selected as follows:
3 credits from:
* Note: If either of MATH 249 or MATH 316 has been taken as part of the Major Concentration Mathematics, another 3credit complementary course must be taken.

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 2013
Instructors: Johannes Walcher (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 316 Complex Variables (3 credits) *
Overview
Mathematics & Statistics (Sci) : Algebra of complex numbers, CauchyRiemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.
Terms: Fall 2012
Instructors: John A Toth (Fall)
 Fall
 Prerequisites: MATH 314 and MATH 243
 Restriction: Not open to students who have taken or are taking MATH 249, MATH 366, MATH 381 or MATH 466.
12 credits from:

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 2013
Instructors: David Stephens (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.

MATH 317 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: Fall 2012
Instructors: Peter Bartello (Fall)
 Fall
 Prerequisites: MATH 315 or MATH 325 or MATH 263, and COMP 202 or permission of instructor.

MATH 318 Mathematical Logic (3 credits)
Overview
Mathematics & Statistics (Sci) : Propositional calculus, truthtables, switching circuits, natural deduction, first order predicate calculus, axiomatic theories, set theory.
Terms: Fall 2012
Instructors: Diana Dubrovsky (Fall)
 Fall
 Restriction: Not open to students who are taking or have taken PHIL 210

MATH 319 Introduction to Partial Differential Equations (3 credits)
Overview
Mathematics & Statistics (Sci) : First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, SturmLiouville theory, Fourier series, boundary and initial value problems.
Terms: Winter 2013
Instructors: There are no professors associated with this course for the 20122013 academic year.
 Winter
 Prerequisites: MATH 223 or MATH 236, MATH 314, MATH 315

MATH 320 Differential Geometry (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of Euclidean geometry. Local theory of plane and space curves: the Frenet formulas. Local theory of surfaces: the first and second fundamental forms, the shape operator, the mean and Gaussian curvatures, surfaces of revolution with prescribed curvature, ruled and developable surfaces. Geodesic curves on surfaces of revolution. The GaussCodazzi equations, rigidity.
Terms: This course is not scheduled for the 20122013 academic year.
Instructors: There are no professors associated with this course for the 20122013 academic year.
 Fall
 Prerequisites: MATH 236 or MATH 223 or MATH 247, and MATH 314 or MATH 248

MATH 324 Statistics (3 credits)
Overview
Mathematics & Statistics (Sci) : Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Terms: Fall 2012, Winter 2013
Instructors: William J Anderson (Fall) David B Wolfson (Winter)
 Fall and Winter
 Prerequisite: MATH 323 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 357
 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 326 Nonlinear Dynamics and Chaos (3 credits)
Overview
Mathematics & Statistics (Sci) : Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, PoincareBendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.
Terms: Fall 2012
Instructors: JeanChristophe Nave (Fall)
 Fall
 Prerequisites: MATH 222, MATH 223
 Restriction: Not open to students who have taken or are taking MATH 376

MATH 327 Matrix Numerical Analysis (3 credits)
Overview
Mathematics & Statistics (Sci) : An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems.
Terms: Winter 2013
Instructors: Antony Raymond Humphries (Winter)
 Winter
 Prerequisites: MATH 223 or MATH 236 or MATH 247 or MATH 251, COMP 202 or consent of instructor.

MATH 329 Theory of Interest (3 credits)
Overview
Mathematics & Statistics (Sci) : Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Terms: Winter 2013
Instructors: Neville G F Sancho (Winter)
 Winter
 Prerequisite: MATH 141

MATH 335 Computational Algebra (3 credits)
Overview
Mathematics & Statistics (Sci) : Computational aspects of modern algebra. Computing in groups: algorithms, algorithmic problems in groups, finitely generated abelian groups, free groups and automata, finitely presented groups. Computing in rings: elementary notions of ring theory, ideals of polynomial rings in several variables, Groebner bases, elements of field theory.
Terms: This course is not scheduled for the 20122013 academic year.
Instructors: There are no professors associated with this course for the 20122013 academic year.
 Prerequisites: MATH 235 and MATH 236.
 Note: This course is intended primarily for students in the Major Program in Mathematics and the Joint Major Program in Mathematics and Computer Science.

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 2012
Instructors: Niky Kamran (Fall)

MATH 340 Discrete Structures 2 (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of mathematical writing, proof techniques, graph theory and counting. Mathematical logic. Graph connectivity, planar graphs and colouring. Probability and graphs. Introductory group theory, isomorphisms and automorphisms of graphs. Enumeration and listing.
Terms: Winter 2013
Instructors: Frederick Shepherd (Winter)
 Winter
 Prerequisites: MATH 235 or MATH 240 or MATH 242.
 Corequisites: MATH 223 or MATH 236.
 Restriction: Not open to students who have taken or are taking MATH 343 or MATH 350.

MATH 346 Number Theory (3 credits)
Overview
Mathematics & Statistics (Sci) : Divisibility. Congruences. Quadratic reciprocity. Diophantine equations. Arithmetical functions.
Terms: Winter 2013
Instructors: Henri Darmon (Winter)
 Winter
 Prerequisite: MATH 235 or consent of instructor
 Restriction: Not open to students who have taken or are taking MATH 377.

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 2013
Instructors: There are no professors associated with this course for the 20122013 academic year.
 Prerequisite: MATH 133 or equivalent or permission of instructor.

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 2012
Instructors: Sergey Norin (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 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 20122013 academic year.
Instructors: There are no professors associated with this course for the 20122013 academic year.
 Winter
 Prerequisites: COMP 202; MATH 223 or MATH 236, MATH 314, MATH 315 and MATH 323

MATH 410 Majors Project (3 credits)
Overview
Mathematics & Statistics (Sci) : A supervised project.
Terms: Fall 2012, Winter 2013, Summer 2013
Instructors: Djivede Kelome (Fall) Djivede Kelome, David Stephens (Winter) Djivede Kelome, David Stephens (Summer)
 Prerequisite: Students must have 21 completed credits of the required mathematics courses in their program, including all required 200 level mathematics courses.
 Requires departmental approval.

MATH 417 Mathematical Programming (3 credits)
Overview
Mathematics & Statistics (Sci) : An introductory course in optimization by linear algebra, and calculus methods. Linear programming (convex polyhedra, simplex method, duality, multicriteria problems), integer programming, and some topics in nonlinear programming (convex functions, optimality conditions, numerical methods). Representative applications to various disciplines.
Terms: Fall 2012
Instructors: Frederick Shepherd (Fall)
 Prerequisites: COMP 202, and MATH 223 or MATH 236, and MATH 314 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 487.

MATH 423 Regression and Analysis of Variance (3 credits)
Overview
Mathematics & Statistics (Sci) : Leastsquares estimators and their properties. Analysis of variance. Linear models with general covariance. Multivariate normal and chisquared distributions; quadratic forms. General linear hypothesis: Ftest and ttest. Prediction and confidence intervals. Transformations and residual plot. Balanced designs.
Terms: Fall 2012
Instructors: Abbas Khalili Mahmoudabadi (Fall)
 Fall
 Prerequisites: MATH 324, and MATH 223 or MATH 236
 Restriction: Not open to students who have taken or are taking MATH 533.

MATH 430 Mathematical Finance (3 credits)
Overview
Mathematics & Statistics (Sci) : Introduction to concepts of price and hedge derivative securities. The following concepts will be studied in both concrete and continuous time: filtrations, martingales, the change of measure technique, hedging, pricing, absence of arbitrage opportunities and the Fundamental Theorem of Asset Pricing.
Terms: Winter 2013
Instructors: Djivede Kelome (Winter)
 Restrictions: Not open to students who have taken MATH 330. Not open to students who have taken or are taking MATH 490.

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 2013
Instructors: William J Anderson (Winter)
 Winter
 Prerequisite: MATH 323
 Restriction: Not open to students who have taken or are taking MATH 547.

MATH 523 Generalized Linear Models (4 credits)
Overview
Mathematics & Statistics (Sci) : Modern discrete data analysis. Exponential families, orthogonality, link functions. Inference and model selection using analysis of deviance. Shrinkage (Bayesian, frequentist viewpoints). Smoothing. Residuals. Quasilikelihood. Sliced inverse regression. Contingency tables: logistic regression, loglinear models. Censored data. Applications to current problems in medicine, biological and physical sciences. GLIM, S, software.
Terms: Winter 2013
Instructors: David Stephens (Winter)
 Winter
 Prerequisite: MATH 423 or EPIB 697
 Restriction: Not open to students who have taken MATH 426

MATH 524 Nonparametric Statistics (4 credits)
Overview
Mathematics & Statistics (Sci) : Distribution free procedures for 2sample problem: Wilcoxon rank sum, SiegelTukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: KruskalWallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chisquare, likelihood ratio, KolmogorovSmirnov tests. Statistical software packages used.
Terms: Fall 2012
Instructors: Johanna Neslehova (Fall)
 Fall
 Prerequisite: MATH 324 or equivalent
 Restriction: Not open to students who have taken MATH 424

MATH 525 Sampling Theory and Applications (4 credits)
Overview
Mathematics & Statistics (Sci) : Simple random sampling, domains, ratio and regression estimators, superpopulation models, stratified sampling, optimal stratification, cluster sampling, sampling with unequal probabilities, multistage sampling, complex surveys, nonresponse.
Terms: Fall 2012
Instructors: Russell Steele (Fall)
 Prerequisite: MATH 324 or equivalent
 Restriction: Not open to students who have taken MATH 425