# Major Concentration Mathematics (36 credits)

Offered by: Mathematics and Statistics     Degree: Bachelor of Arts

### Program Requirements

Students who have done well in MATH 242 and MATH 235 at the end of their first term should consider, in consultation with their adviser and the instructors of the courses involved, the possibility of entering into an Honours program in Mathematics, in Applied Mathematics, in Probability and Statistics, or a Joint Honours program in Mathematics and another discipline.

#### 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 36 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 2015, Winter 2016

Instructors: Djivede Kelome, William J Anderson (Fall) Djivede Kelome (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 2015, Winter 2016

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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 2015, Winter 2016

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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 Course Selection

Where appropriate, Honours-level courses may be substituted for their Majors-level counterparts. Students planning to undertake graduate studies in mathematics are urged to make such substitutions.

Students interested in computer science should consider the courses MATH 317, MATH 318, MATH 327, MATH 328, MATH 340, MATH 407, MATH 417, and take the Minor Concentration Computer Science.

Students interested in probability and statistics should consider either taking the Minor Concentration Statistics under option C, or else including some or all of the courses MATH 423, MATH 447, MATH 523, MATH 524, and MATH 525.

Students interested in applied mathematics should consider the courses MATH 317, MATH 319, MATH 324, MATH 326, MATH 327, MATH 407 and MATH 417.

Students interested in careers in business, industry or government should consider the courses MATH 317, MATH 319, MATH 327, MATH 407, MATH 417, MATH 423, MATH 447, MATH 523, and MATH 525.

#### Required Courses (21 credits)

• 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 2015, Winter 2016

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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 2015

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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 2016

Instructors: There are no professors associated with this course for the 2015-2016 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 2015

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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 2016

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• Winter
• Prerequisite: MATH 242 or MATH 254.
• 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 2015, Winter 2016

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• Prerequisites: MATH 133, MATH 222
• Restriction: Not open to students who have taken or are taking MATH 248
• 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 2015, Winter 2016

Instructors: William J Anderson (Fall)

• 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 (15 credits)

15 credits selected as follows:

At least 9 credits from:

* 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 2016

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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 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 2015, Winter 2016

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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 2015

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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 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 2015

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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 2015, Winter 2016

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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 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 2016

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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 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 2015

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• Fall
• Prerequisites: MATH 324, and MATH 223 or MATH 236
• Restriction: Not open to students who have taken or are taking MATH 533.

Remaining credits 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 2016

Instructors: There are no professors associated with this course for the 2015-2016 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 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 2015

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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 2016

Instructors: There are no professors associated with this course for the 2015-2016 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 2015-2016 academic year.

Instructors: There are no professors associated with this course for the 2015-2016 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 2015

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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: This course is not scheduled for the 2015-2016 academic year.

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• Winter
• Prerequisites: MATH 223 or MATH 236 or MATH 247 or MATH 251, COMP 202 or consent of instructor.
• 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: This course is not scheduled for the 2015-2016 academic year.

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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: This course is not scheduled for the 2015-2016 academic year.

Instructors: There are no professors associated with this course for the 2015-2016 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 2015

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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 2015-2016 academic year.

Instructors: There are no professors associated with this course for the 2015-2016 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 2015, Winter 2016

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

• 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 2015

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 427 Statistical Quality Control (3 credits)

Offered by: Mathematics and Statistics (Faculty of Science)

### Overview

Mathematics & Statistics (Sci) : Introduction to quality management; variability and productivity. Quality measurement: capability analysis, gauge capability studies. Process control: control charts for variables and attributes. Process improvement: factorial designs, fractional replications, response surface methodology, Taguchi methods. Acceptance sampling: operating characteristic curves; single, multiple and sequential acceptance sampling plans for variables and attributes.

Terms: Fall 2015

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• Prerequisites: MATH 323 + MATH 324
• 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 2016

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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 2016

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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: This course is not scheduled for the 2015-2016 academic year.

Instructors: There are no professors associated with this course for the 2015-2016 academic year.

• 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: Fall 2015

Instructors: Russell Steele (Fall)

• Prerequisite: MATH 324 or equivalent
• Restriction: Not open to students who have taken MATH 425
Faculty of Arts—2015-2016 (last updated Jul. 28, 2015) (disclaimer)