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.
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MATH 133 Linear Algebra and Geometry (3 credits)
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 2024, Winter 2025
Instructors: Macdonald, Jeremy; Ayala, Miguel; Branchereau, Romain; Giard, Antoine (Fall)
3 hours lecture, 1 hour tutorial
Prerequisite: a course in functions
Restriction(s): 1) Not open to students who have taken CEGEP objective 00UQ or equivalent. 2) Not open to students who have taken or are taking MATH 123, except by permission of the Department of Mathematics and Statistics.
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MATH 140 Calculus 1 (3 credits)
Overview
Mathematics & Statistics (Sci) : Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
Terms: Fall 2024, Winter 2025
Instructors: Sabok, Marcin; Trudeau, Sidney; Kalmykov, Artem (Fall)
3 hours lecture, 1 hour tutorial
Prerequisite: High School Calculus
Restriction(s): 1) Not open to students who have taken MATH139 or MATH 150 or CEGEP objective 00UN or equivalent. 2) 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
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MATH 141 Calculus 2 (4 credits)
Overview
Mathematics & Statistics (Sci) : The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Terms: Fall 2024, Winter 2025
Instructors: Hassan, Hazem; Trudeau, Sidney; Zlotchevski, Andrei (Fall) Trudeau, Sidney (Winter)
Restriction(s): Not open to students who have taken CEGEP objective 00UP or equivalent.
Restriction(s): 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
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MATH 222 Calculus 3 (3 credits)
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 2024, Winter 2025
Instructors: Pym, Brent; Tageddine, Damien (Fall)
Required Courses (9 credits)
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MATH 235 Algebra 1 (3 credits)
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; homomorphisms and quotient groups.
Terms: Fall 2024
Instructors: Sabbagh, Magid (Fall)
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MATH 251 Honours Algebra 2 (3 credits)
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 2025
Instructors: Przytycki, Piotr (Winter)
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MATH 255 Honours Analysis 2 (3 credits)
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 2025
Instructors: Vetois, Jerome (Winter)
Complementary Courses (27 credits)
3 credits selected from:
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MATH 242 Analysis 1 (3 credits)
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 2024
Instructors: Jakobson, Dmitry (Fall)
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MATH 254 Honours Analysis 1 (3 credits) *
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 2024
Instructors: Hundemer, Axel W (Fall)
* It is strongly recommended that students take MATH 254.
3 credits selected from:
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MATH 248 Honours Vector Calculus (3 credits)
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 2024
Instructors: Mutanguha, Jean Pierre (Fall)
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MATH 358 Honours Advanced Calculus (3 credits)
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 2025
Instructors: Toth, John A (Winter)
** 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.
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MATH 325 Honours Ordinary Differential Equations (3 credits)
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 2025
Instructors: Lessard, Jean-Philippe (Winter)
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MATH 356 Honours Probability (3 credits)
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 2024
Instructors: Asgharian, Masoud (Fall)
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MATH 357 Honours Statistics (3 credits)
Overview
Mathematics & Statistics (Sci) : Sampling distributions. Point estimation. Minimum variance unbiased estimators, sufficiency, and completeness. Confidence intervals. Hypothesis tests, Neyman-Pearson Lemma, uniformly most powerful tests. Likelihood ratio tests for normal samples. Asymptotic sampling distributions and inference.
Terms: Winter 2025
Instructors: Khalili, Abbas (Winter)
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MATH 454 Honours Analysis 3 (3 credits) *
Overview
Mathematics & Statistics (Sci) : Measure theory: sigma-algebras, Lebesgue measure in R^n and integration, L^1 functions, Fatou's lemma, monotone and dominated convergence theorem, Egorov’s theorem, Lusin's theorem, Fubini-Tonelli theorem, differentiation of the integral, differentiability of functions of bounded variation, absolutely continuous functions, fundamental theorem of calculus.
Terms: Fall 2024
Instructors: Chen, Linan (Fall)
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MATH 455 Honours Analysis 4 (3 credits) **
Overview
Mathematics & Statistics (Sci) : Review of point-set topology: topological spaces, dense sets, completeness, compactness, connectedness and path-connectedness, separability, Baire category theorem, Arzela-Ascoli theorem, Stone-Weierstrass theorem..Functional analysis: L^p spaces, linear functionals and dual spaces, Hilbert spaces, Riesz representation theorems. Fourier series and transform, Riemann-Lebesgue Lemma,Fourier inversion formula, Plancherel theorem, Parseval’s identity, Poisson summation formula.
Terms: Winter 2025
Instructors: Lin, Jessica (Winter)
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MATH 456 Honours Algebra 3 (3 credits) ***
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 2024
Instructors: Darmon, Henri (Fall)
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MATH 457 Honours Algebra 4 (3 credits) +
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 2025
Instructors: Darmon, Henri (Winter)
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MATH 458 Honours Differential Geometry (3 credits) ++
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 2025
Instructors: Mutanguha, Jean Pierre (Winter)
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MATH 466 Honours Complex Analysis (3 credits)
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 2024
Instructors: Hurtubise, Jacques Claude (Fall)
