# Minor Concentration Mathematics (18 credits)

Offered by: Mathematics and Statistics     Degree: Bachelor of Arts and Science

### Program Requirements

The Minor Concentration Mathematics is offered in two versions: an expandable version, for students who wish to leave open the option of expanding the program into a Major Concentration Mathematics, and a non-expandable version for students who know on entry into the Minor that they do not wish to expand it into a major concentration.

The Minor Concentration Mathematics may be taken in conjunction with a major concentration in some other discipline under option A of the Multi-track System. Students planning on taking the Major Concentration Mathematics and the Minor Concentration Mathematics as part of Multi-track option C should select the Supplementary Minor Concentration in Mathematics in place of this Minor concentration.

Under option C, it is not possible to combine the Minor Concentration Mathematics and the Minor Concentration Statistics. Students wishing to do this should instead take the Major Concentration Mathematics under option B (two major concentrations) and select a large number of statistics complementaries.

No overlap is permitted with other programs.

#### Program Prerequisites

Students who have not completed the program prerequisite courses listed below or their equivalents will be required to make up any deficiencies in these courses over and above the 18 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, Peter Xu (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

#### Expandable Version: Required Courses (12 credits)

* Note: Credit cannot be received for both MATH 236 and MATH 223 (listed as a required course in the non-expandable version of this Minor concentration).

• 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 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.

#### Expandable Version: Complementary Courses (6 credits)

Students selecting the expandable version of this program complete 6 credits of complementary courses from the Complementary Course List.

It is strongly recommended that students take MATH 323 as a complementary course.

#### Non-Expandable Version: Required Courses (9 credits)

* Note: Credit cannot be received for both MATH 223 and MATH 236 (listed as a required course in the expandable version of this Minor concentration).

• 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 223 Linear Algebra (3 credits) *

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Review of matrix algebra, determinants and systems of linear equations. Vector spaces, linear operators and their matrix representations, orthogonality. Eigenvalues and eigenvectors, diagonalization of Hermitian matrices. Applications.

Terms: Fall 2018, Winter 2019

Instructors: Djivede Kelome (Fall) Jeremy Macdonald (Winter)

• Fall and Winter

• Prerequisite: MATH 133 or equivalent

• Restriction: Not open to students in Mathematics programs nor to students who have taken or are taking MATH 236, MATH 247 or MATH 251. It is open to students in Faculty Programs

• 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.

#### Non-Expandable Version: Complementary Courses (9 credits)

Students selecting the non-expandable version of this program complete 9 credits of complementary courses from the Complementary Course List.

It is strongly recommended that students take MATH 323 as a complementary course.

#### Complementary Course List

* Note: Either MATH 249 or MATH 316 may be taken but not both.

• 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 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 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 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 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

• 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 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 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)

• 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 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 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)

Bachelor of Arts & Science—2018-2019 (last updated Aug. 22, 2018) (disclaimer)