# Major Mathematics (54 credits)

Offered by: Mathematics and Statistics     Degree: Bachelor of Science

### Program Requirements

Revision, June 2012. Start of revision.

#### Program Prerequisites

Students entering the Major program are normally expected to have completed the courses below or their equivalents. Otherwise, they will be required to make up any deficiencies in these courses over and above the 54 credits of required courses.

• MATH 133 Linear Algebra and Geometry (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Systems of linear equations, matrices, inverses, determinants; geometric vectors in three dimensions, dot product, cross product, lines and planes; introduction to vector spaces, linear dependence and independence, bases; quadratic loci in two and three dimensions.

Terms: Fall 2012, Winter 2013, Summer 2013

Instructors: Djivede Kelome, William J Anderson, Eric Cormier, Michael Bailey (Fall) William J Anderson, Alexey Eremin (Winter)

• 3 hours lecture, 1 hour tutorial
• Prerequisite: a course in functions
• Restriction A: Not open to students who have taken MATH 221 or CEGEP objective 00UQ or equivalent.
• Restriction B: Not open to students who have taken or are taking MATH 123, MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.
• Restriction C: Not open to students who are taking or have taken MATH 134.
• MATH 140 Calculus 1 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.

Terms: Fall 2012, Winter 2013, Summer 2013

Instructors: Sidney Trudeau, Stephen W Drury, William G Brown, Thomas F Fox (Fall)

• 3 hours lecture, 1 hour tutorial
• Prerequisite: High School Calculus
• Restriction: Not open to students who have taken MATH 120, MATH 139 or CEGEP objective 00UN or equivalent
• Restriction: Not open to students who have taken or are taking MATH 122 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics
• Each Tutorial section is enrolment limited
• MATH 141 Calculus 2 (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.

Terms: Fall 2012, Winter 2013, Summer 2013

Instructors: Antonio Lei (Fall) Sidney Trudeau, Stephen W Drury, Thomas F Fox (Winter)

• Prerequisites: MATH 139 or MATH 140 or MATH 150.
• Restriction: Not open to students who have taken MATH 121 or CEGEP objective 00UP or equivalent
• Restriction Note B: Not open to students who have taken or are taking MATH 122 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.
• Each Tutorial section is enrolment limited

#### Guidelines for Selection of Courses in the Major Program

The following informal guidelines should be discussed with the student's adviser. Where appropriate, Honours courses may be substituted for equivalent Major courses. Students planning to pursue graduate studies are encouraged to make such substitutions.

Students interested in computer science are advised to choose courses from the following: MATH 317, MATH 318, MATH 327, MATH 328, MATH 335, MATH 340, MATH 407, MATH 417 and to complete the Computer Science Minor.

Students interested in probability and statistics are advised to take MATH 204, MATH 324, MATH 407, MATH 423, MATH 447, MATH 523, MATH 525.

Students interested in applied mathematics should take MATH 317, MATH 319, MATH 324, MATH 326, MATH 327, MATH 407, MATH 417.

Students considering a career in secondary school teaching are advised to take MATH 318, MATH 328, MATH 338, MATH 339, MATH 346, MATH 348.

Students interested in careers in business, industry or government are advised to select courses from the following list:
MATH 317, MATH 319, MATH 327, MATH 329, MATH 407, MATH 417, MATH 423, MATH 430, MATH 447, MATH 523, MATH 525.

#### Required Courses (27 credits)

Note: Students who have done well in MATH 235 and MATH 242 should consider entering the Honours stream by registering in MATH 251 and MATH 255 instead of MATH 236 and MATH 243.

* Students may select either MATH 249 or MATH 316 but not both.
** Students who have successfully completed a course equivalent to MATH 222 with a grade of C or better may omit MATH 222, but must replace it with 3 credits of elective courses.

• MATH 222 Calculus 3 (3 credits) **

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.

Terms: Fall 2012, Winter 2013, Summer 2013

Instructors: Wilbur Jonsson, Mathew Donald Rogers (Fall) Wilbur Jonsson (Winter) Eric Cormier (Summer)

• Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133
• Restriction: Not open to students who have taken CEGEP course 201-303 or MATH 150, MATH 151 or MATH 227
• MATH 235 Algebra 1 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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 2012

Instructors: Henri Darmon (Fall)

• Fall
• 3 hours lecture; 1 hour tutorial
• Prerequisite: MATH 133 or equivalent
• MATH 236 Algebra 2 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Linear equations over a field. Introduction to vector spaces. Linear mappings. Matrix representation of linear mappings. Determinants. Eigenvectors and eigenvalues. Diagonalizable operators. Cayley-Hamilton theorem. Bilinear and quadratic forms. Inner product spaces, orthogonal diagonalization of symmetric matrices. Canonical forms.

Terms: Winter 2013

Instructors: There are no professors associated with this course for the 2012-2013 academic year.

• Winter
• Prerequisite: MATH 235
• MATH 242 Analysis 1 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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 2012

Instructors: Suresh Eswarathasan, Ivo Klemes (Fall)

• Fall
• Prerequisite: MATH 141
• MATH 243 Analysis 2 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Infinite series; series of functions; power series. The Riemann integral in one variable. A rigorous development of the elementary functions.

Terms: Winter 2013

Instructors: Ivo Klemes (Winter)

• Winter
• Prerequisite: MATH 242
• MATH 249 Honours Complex Variables (3 credits) *

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

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 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 314 Advanced Calculus (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss. Fourier series with applications.

Terms: Fall 2012, Winter 2013, Summer 2013

Instructors: Jian-Jun Xu (Fall) Wilbur Jonsson (Winter) Charles Roth (Summer)

• Prerequisites: MATH 133, MATH 222
• Restriction: Not open to students who have taken or are taking MATH 248
• MATH 315 Ordinary Differential Equations (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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: Jian-Jun Xu (Fall) Alexey Eremin (Winter)

• Prerequisite: MATH 222.
• Corequisite: MATH 133.
• Restriction: Not open to students who have taken or are taking MATH 325.
• MATH 316 Complex Variables (3 credits) *

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Algebra of complex numbers, Cauchy-Riemann 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.
• MATH 323 Probability (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem.

Terms: Fall 2012, Winter 2013, Summer 2013

Instructors: Masoud Asgharian-Dastenaei (Fall) David B Wolfson (Winter) Djivede Kelome (Summer)

• Prerequisites: MATH 141 or equivalent.
• Restriction: Intended for students in Science, Engineering and related disciplines, who have had differential and integral calculus
• Restriction: Not open to students who have taken or are taking MATH 356

#### Complementary Courses (27 credits)

27 credits selected as follows:

21 credits selected from the following list, with at least 6 credits selected from:

• MATH 317 Numerical Analysis (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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 324 Statistics (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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 335 Computational Algebra (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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 2012-2013 academic year.

Instructors: There are no professors associated with this course for the 2012-2013 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 340 Discrete Structures 2 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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.

the remainder of the 21 credits to be selected from:

• MATH 204 Principles of Statistics 2 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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 318 Mathematical Logic (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Propositional calculus, truth-tables, 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)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : First order equations, geometric theory; second order equations, classification; Laplace, wave and heat equations, Sturm-Liouville theory, Fourier series, boundary and initial value problems.

Terms: Winter 2013

Instructors: There are no professors associated with this course for the 2012-2013 academic year.

• Winter
• Prerequisites: MATH 223 or MATH 236, MATH 314, MATH 315
• MATH 320 Differential Geometry (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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 Gauss-Codazzi equations, rigidity.

Terms: This course is not scheduled for the 2012-2013 academic year.

Instructors: There are no professors associated with this course for the 2012-2013 academic year.

• Fall
• Prerequisites: MATH 236 or MATH 223 or MATH 247, and MATH 314 or MATH 248
• MATH 326 Nonlinear Dynamics and Chaos (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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, Poincare-Bendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.

Terms: Fall 2012

Instructors: Jean-Christophe 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)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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 338 History and Philosophy of Mathematics (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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)

• Fall
• MATH 346 Number Theory (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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, non-Euclidean geometry and problems in discrete geometry.

Terms: Summer 2013

Instructors: There are no professors associated with this course for the 2012-2013 academic year.

• Prerequisite: MATH 133 or equivalent or permission of instructor.
• MATH 352 Problem Seminar (1 credit)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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 2012-2013 academic year.

Instructors: There are no professors associated with this course for the 2012-2013 academic year.

• Winter
• Prerequisites: COMP 202; MATH 223 or MATH 236, MATH 314, MATH 315 and MATH 323
• MATH 410 Majors Project (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : An introductory course in optimization by linear algebra, and calculus methods. Linear programming (convex polyhedra, simplex method, duality, multi-criteria 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)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Least-squares estimators and their properties. Analysis of variance. Linear models with general covariance. Multivariate normal and chi-squared distributions; quadratic forms. General linear hypothesis: F-test and t-test. Prediction and confidence intervals. Transformations and residual plot. Balanced designs.

Terms: Fall 2012

• 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)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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. Quasi-likelihood. Sliced inverse regression. Contingency tables: logistic regression, log-linear 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 525 Sampling Theory and Applications (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### 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
• MATH 545 Introduction to Time Series Analysis (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Stationary processes; estimation and forecasting of ARMA models; non-stationary and seasonal models; state-space models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models.

Terms: Fall 2012

Instructors: David Stephens (Fall)

• Prerequisite: MATH 324 or MATH 357 or equivalent

6 additional credits in Mathematics or related disciplines selected in consultation with the Adviser.

Revision, June 2012. End of revision.
Faculty of Science—2012-2013 (last updated Dec. 20, 2012) (disclaimer)