Liberal Program - Core Science Component Mathematics (45 credits)

Offered by: Mathematics and Statistics     Degree: Bachelor of Science

Program Requirements

Program Prerequisites

Students entering the Core Science Component in Mathematics 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 45 credits required for the program.

• 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 2018, Winter 2019, Summer 2019

Instructors: Jerome Fortier, Liangming Shen, Yann Batiste Pequignot, Damian Osajda (Fall) Jerome Fortier (Winter) Rebecca Patrias (Summer)

• 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 2018, Winter 2019, Summer 2019

Instructors: Sidney Trudeau, Jerome Fortier, Rebecca Patrias (Fall) Alexander Garver (Winter) Peter Zenz (Summer)

• 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 2018, Winter 2019, Summer 2019

Instructors: Corentin Perret-Gentil-dit-Maillard, Jonah Gaster (Fall) Sidney Trudeau, Jerome Fortier, Thomas F Fox (Winter) Bogdan Nica (Summer)

• 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

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)

* 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 2018, Winter 2019, Summer 2019

Instructors: Jeremy Macdonald, Dmitry Faifman (Fall) Lars Sektnan (Winter) Yann Batiste Pequignot (Summer)

• 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 2018

Instructors: Daniel Wise (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 2019

Instructors: Bogdan Nica (Winter)

• 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 2018

Instructors: Jerome Vetois (Fall)

• Fall

• Prerequisite: MATH 141

• Restriction(s): Not open to students who are taking or who have taken MATH 254.

• MATH 243 Analysis 2 (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

Overview

Mathematics & Statistics (Sci) : Definition and properties of Riemann integral, Fundamental Theorem of Calculus, Taylor's theorem. Infinite series: alternating, telescoping series, rearrangements, conditional and absolute convergence, convergence tests. Power series and Taylor series. Elementary functions. Introduction to metric spaces.

Terms: Winter 2019

Instructors: Axel W Hundemer (Winter)

• 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 2019

Instructors: Charles Roth (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 2018, Winter 2019

Instructors: Charles Roth (Fall) Stephen W Drury (Winter)

• 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 2018, Winter 2019, Summer 2019

Instructors: Jean-Christophe Nave (Fall) Antony Raymond Humphries (Winter) Charles Roth (Summer)

• 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 2018

Instructors: Bogdan Nica (Fall)

• 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 2018, Winter 2019, Summer 2019

Instructors: David Stephens (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 (18 credits)

18 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 2018

Instructors: Peter Bartello (Fall)

• 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 2018, Winter 2019

Instructors: Abbas Khalili Mahmoudabadi (Fall) Masoud Asgharian-Dastenaei (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 2018-2019 academic year.

Instructors: There are no professors associated with this course for the 2018-2019 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 2019

Instructors: Jerome Fortier (Winter)

the remainder of the 18 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 2019

Instructors: Christian Genest (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 logic: truth-tables, formal proof systems, completeness and compactness theorems, Boolean algebras; first-order logic: formal proofs, Gödel's completeness theorem; axiomatic theories; set theory; Cantor's theorem, axiom of choice and Zorn's lemma, Peano arithmetic; Gödel's incompleteness theorem.

Terms: Fall 2018

Instructors: Marcin Sabok (Fall)

• 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 2019

Instructors: Jessica Lin (Winter)

• 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 2018-2019 academic year.

Instructors: There are no professors associated with this course for the 2018-2019 academic year.

• 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 2018

Instructors: Jean-Philippe Lessard (Fall)

• 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 2019

Instructors: Ivo Panayotov (Winter)

• 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 2019

Instructors: Djivede Kelome (Winter)

• 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 2018

Instructors: Thomas F Fox (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 2019

Instructors: Michael Lipnowski (Winter)

• Winter

• Prerequisite: MATH 235 or consent of instructor

• Restriction: Not open to students who have taken or are taking MATH 377.

• MATH 348 Euclidean Geometry (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

Overview

Mathematics & Statistics (Sci) : Points and lines in a triangle. Quadrilaterals. Angles in a circle. Circumscribed and inscribed circles. Congruent and similar triangles. Area. Power of a point with respect to a circle. Ceva’s theorem. Isometries. Homothety. Inversion.

Terms: Fall 2018

Instructors: Piotr Przytycki (Fall)

• Prerequisite: MATH 133 or equivalent or permission of instructor.

• Restriction: Not open to students who have taken MATH 398.

• 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 2018

Instructors: Jacques Claude Hurtubise (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 2018-2019 academic year.

Instructors: There are no professors associated with this course for the 2018-2019 academic year.

• MATH 410 Majors Project (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

Overview

Mathematics & Statistics (Sci) : A supervised project.

Terms: Fall 2018, Winter 2019, Summer 2019

Instructors: Djivede Kelome, Johanna Neslehova, Jean-Philippe Lessard, David Stephens, Russell Steele, Gantumur Tsogtgerel (Fall) Djivede Kelome, David Stephens, Dmitry Jakobson, Christian Genest, Russell Steele, Gantumur Tsogtgerel, Masoud Asgharian-Dastenaei, Niky Kamran (Winter) Djivede Kelome, Russell Steele (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 Linear Optimization (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

Overview

Mathematics & Statistics (Sci) : An introduction to linear optimization and its applications: Duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interior-point methods, quadratic optimization, applications in game theory.

Terms: Fall 2018

Instructors: Van Quang Nguyen (Fall)

• 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 2018

Instructors: Yi Yang (Fall)

• 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 2019

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 2019

Instructors: Russell Steele (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. Contingency tables: logistic regression, log-linear models. Censored data. Applications to current problems in medicine, biological and physical sciences. R software.

Terms: Winter 2019

Instructors: Johanna Neslehova (Winter)

• Winter

• Prerequisite: MATH 423

• Restriction: Not open to students who have taken MATH 426

• MATH 524 Nonparametric Statistics (4 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

Overview

Mathematics & Statistics (Sci) : Distribution free procedures for 2-sample problem: Wilcoxon rank sum, Siegel-Tukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: Kruskal-Wallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chi-square, likelihood ratio, Kolmogorov-Smirnov tests. Statistical software packages used.

Terms: Fall 2018

Instructors: Christian Genest (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)

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: Winter 2019

Instructors: Russell Steele (Winter)

• 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 2018

Instructors: Russell Steele (Fall)

Faculty of Science—2018-2019 (last updated Aug. 22, 2018) (disclaimer)