º£ÍâÖ±²¥bÕ¾

Program Requirements

Students who wish to study at the Honours level in two Arts disciplines may apply to combine Joint Honours program components from two Arts disciplines. For a list of available Joint Honours programs, see "Overview of Programs Offered" and "Joint Honours Programs".

To remain in the Joint Honours program and receive the Joint Honours degree, a student must maintain the standards set by each discipline, as well as by the Faculty. In the Mathematics courses of the program a GPA of 3.00 and a CGPA of 3.00 must be maintained. Students who have difficulty in maintaining the required level should change to another program before entering their final year.

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. Linear transformations. Eigenvalues and diagonalization.

  Terms: Fall 2023, Winter 2024, Summer 2024

  Instructors: Trudeau, Sidney; Collins-Woodfin, Elizabeth; Branchereau, Romain (Fall) Gerbelli-Gauthier, Mathilde (Winter) Bellemare, Hugues (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, 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 2023, Winter 2024, Summer 2024

  Instructors: Fortier, Jérôme; Cant, Dylan; Fu, Hao (Fall) Fortier, Jérôme (Winter) Sajjad, Alia (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, 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 2023, Winter 2024, Summer 2024

  Instructors: Sroka, Marcin; Cairns, Hannah (Fall) Trudeau, Sidney; Macdonald, Jeremy; Mazakian, Hovsep (Winter) Mazakian, Hovsep; Abi Younes, Elio (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, except by permission of the Department of Mathematics and Statistics.

  • Each Tutorial section is enrolment limited

• 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 2023, Winter 2024, Summer 2024

  Instructors: Sabok, Marcin; Allen, Patrick (Fall) Trudeau, Sidney (Winter) Bibby, Sean (Summer)

  • Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133

  • Restriction: Not open to students who have taken MATH 150, MATH 151 or MATH 262.

Required Courses (9 credits)

• 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 2023

  Instructors: Macdonald, Jeremy; Goren, Eyal Z (Fall)

  • Fall

  • 3 hours lecture; 1 hour tutorial

  • Prerequisite: MATH 133 or equivalent

• MATH 251 Honours 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 maps and their matrix representation. Determinants. Canonical forms. Duality. Bilinear and quadratic forms. Real and complex inner product spaces. Diagonalization of self-adjoint operators.

  Terms: Winter 2024

  Instructors: Tserunyan, Anush (Winter)

  • Winter

  • Prerequisites: MATH 235 or permission of the Department

  • Restriction: Not open to students who are taking or have taken MATH 247

• MATH 255 Honours Analysis 2 (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Basic point-set topology, metric spaces: open and closed sets, normed and Banach spaces, Hölder and Minkowski inequalities, sequential compactness, Heine-Borel, Banach Fixed Point theorem. Riemann-(Stieltjes) integral, Fundamental Theorem of Calculus, Taylor's theorem. Uniform convergence. Infinite series, convergence tests, power series. Elementary functions.

  Terms: Winter 2024

  Instructors: Jakobson, Dmitry (Winter)

  • Winter

  • Prerequisites: MATH 242 or MATH 254 or permission of the Department

Complementary Courses (27 credits)

3 credits selected from:

• 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 2023

  Instructors: Hundemer, Axel (Fall)

  • Fall

  • Prerequisite: MATH 141

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

• MATH 254 Honours Analysis 1 (3 credits) *

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Properties of R. Cauchy and monotone sequences, Bolzano- Weierstrass theorem. Limits, limsup, liminf of functions. Pointwise, uniform continuity: Intermediate Value theorem. Inverse and monotone functions. Differentiation: Mean Value theorem, L'Hospital's rule, Taylor's Theorem.

  Terms: Fall 2023

  Instructors: Jaksic, Vojkan (Fall)

  • Prerequisite(s): MATH 141

  • Restriction(s): Not open to students who are taking or who have taken MATH 242.

* It is strongly recommended that students take MATH 254.

3 credits selected from:

• MATH 248 Honours Vector Calculus (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Partial derivatives and differentiation of functions in several variables; Jacobians; maxima and minima; implicit functions. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line and surface integrals; irrotational and solenoidal fields; Green's theorem; the divergence theorem. Stokes' theorem; and applications.

  Terms: Fall 2023

  Instructors: Kamran, Niky (Fall)

  • Fall and Winter and Summer

  • Prerequisites: MATH 133 and MATH 222 or consent of Department.

  • Restriction: Intended for Honours Physics, Computer Science, Physiology and Engineering students.

  • Restriction: Not open to students who have taken or are taking MATH 314 or MATH 358.

• MATH 358 Honours Advanced Calculus (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Point-set topology in Euclidean space; continuity and differentiability of functions in several variables. Implicit and inverse function theorems. Vector fields, divergent and curl operations. Rigorous treatment of multiple integrals: volume and surface area; and Fubini’s theorem. Line and surface integrals, conservative vector fields. Green's theorem, Stokes’ theorem and the divergence theorem.

  Terms: Winter 2024

  Instructors: Toth, John A (Winter)

  • Prerequisites: MATH 222, MATH 247 or MATH 251, MATH 255 or permission of the Department.

  • Restrictions: Intended for students in Honours Mathematics programs, Not open to students who have taken or are taking MATH 314 or MATH 248

** It is strongly recommended that students take MATH 358.

15 credits selected from the list below. The remaining credits are to be chosen from the full list of available Honours courses in Mathematics and Statistics.

* Not open to students who have taken MATH 354.

** Not open to students who have taken MATH 355.

*** Not open to students who have taken MATH 370.

+ Not open to students who have taken MATH 371.

++ Not open to students who have taken MATH 380.

• MATH 325 Honours Ordinary Differential Equations (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : First and second order equations, linear equations, series solutions, Frobenius method, introduction to numerical methods and to linear systems, Laplace transforms, applications.

  Terms: Winter 2024

  Instructors: Humphries, Tony (Winter)

  • Fall and Winter

  • (3-0-6)

  • Prerequisite: MATH 222.

  • Restriction: Intended for Honours Mathematics, Physics and Engineering programs.

  • Restriction: Not open to students who have taken MATH 263 (formerly MATH 261), MATH 315

• MATH 356 Honours Probability (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Sample space, probability axioms, combinatorial probability. Conditional probability, Bayes' Theorem. Distribution theory with special reference to the Binomial, Poisson, and Normal distributions. Expectations, moments, moment generating functions, uni-variate transformations. Random vectors, independence, correlation, multivariate transformations. Conditional distributions, conditional expectation.Modes of stochastic convergence, laws of large numbers, Central Limit Theorem.

  Terms: Fall 2023

  Instructors: Addario-Berry, Louigi (Fall)

  • Fall

  • Prerequisite(s): MATH 243 or MATH 255, and MATH 222 or permission of the Department.

  • Restriction: Not open to students who have taken or are taking MATH 323

• MATH 357 Honours Statistics (3 credits)

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Data analysis. Estimation and hypothesis testing. Power of tests. Likelihood ratio criterion. The chi-squared goodness of fit test. Introduction to regression analysis and analysis of variance.

  Terms: Winter 2024

  Instructors: Asgharian, Masoud (Winter)

  • Winter

  • Prerequisite: MATH 356 or equivalent

  • Restriction: Not open to students who have taken or are taking MATH 324

• MATH 454 Honours Analysis 3 (3 credits) *

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Review of point-set topology: topological space, dense sets, completeness, compactness, connectedness and path-connectedness, separability. Arzela-Ascoli, Stone-Weierstrass, Baire category theorems. Measure theory: sigma algebras, Lebesgue measure and integration, L^1 functions. Fatou's lemma, monotone and dominated convergence theorem. Egorov, Lusin's theorems. Fubini-Tonelli theorem.

  Terms: Fall 2023

  Instructors: Vetois, Jerome (Fall)

  • Prerequisite: MATH 255 or equivalent.

  • Restriction: Not open to students who have taken MATH 354.

• MATH 455 Honours Analysis 4 (3 credits) **

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Continuation of measure theory. Functional analysis: L^p spaces, linear functionals and dual spaces, Hahn-Banach theorem, Riesz representation theorem. Hilbert spaces, weak convergence. Spectral theory of compact operator. Introduction to Fourier analysis, Fourier transforms.

  Terms: Winter 2024

  Instructors: Jakobson, Dmitry (Winter)

  • Prerequisite: MATH 454 or equivalent.

  • Restriction(s): Not open to students who have taken MATH 355.

• MATH 456 Honours Algebra 3 (3 credits) ***

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Introduction to monoids, groups, permutation groups; the isomorphism theorems for groups; the theorems of Cayley, Lagrange and Sylow; structure of groups of low order. Introduction to ring theory; integral domains, fields, quotient field of an integral domain; polynomial rings; unique factorization domains.

  Terms: Fall 2023

  Instructors: Darmon, Henri (Fall)

  • Prerequisites: MATH 235 and either (MATH 247 or MATH 251).

  • Restriction: Not open to students who have taken MATH 370.

• MATH 457 Honours Algebra 4 (3 credits) +

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : Introduction to modules and algebras; finitely generated modules over a principal ideal domain. Field extensions; finite fields; Galois groups; the fundamental theorem of Galois theory; application to the classical problem of solvability by radicals.

  Terms: Winter 2024

  Instructors: Darmon, Henri (Winter)

  • Prerequisite: MATH 456 or equivalent

  • Restriction(s): Not open to students who have taken MATH 371.

• MATH 458 Honours Differential Geometry (3 credits) ++

  Offered by: Mathematics and Statistics (Faculty of Science)

  Overview

  Mathematics & Statistics (Sci) : In addition to the topics of MATH 320, topics in the global theory of plane and space curves, and in the global theory of surfaces are presented. These include: total curvature and the Fary-Milnor theorem on knotted curves, abstract surfaces as 2-d manifolds, the Euler characteristic, the Gauss-Bonnet theorem for surfaces.

  Terms: Winter 2024

  Instructors: Kamran, Niky (Winter)

  • Prerequisites: MATH 251 or MATH 247, and MATH 248 or MATH 314 or MATH 358

  • Restriction: Not open to students who have taken MATH 380.

• MATH 466 Honours Complex Analysis (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 its consequences. Uniform convergence on compacta. Taylor and Laurent series, open mapping theorem, Rouché's theorem and the argument principle. Calculus of residues. Fractional linear transformations and conformal mappings.

  Terms: Fall 2023

  Instructors: Hurtubise, Jacques Claude (Fall)

  • Prerequisite: MATH 255.

  • Restriction: Not open to students who have taken or are taking MATH 366, MATH 249, MATH 316 and MATH 381.