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Joint Honours Component Mathematics (36 credits)

Offered by: Mathematics and Statistics     Degree: Bachelor of Arts

Program Requirements

Revision, May 2014. Start of revision.

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; quadratic loci in two and three dimensions.

    Terms: Fall 2014, Winter 2015

    Instructors: Djivede Kelome, Michael Brandenbursky, Christopher Cornwell, Sidney Trudeau (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 2014, Winter 2015

    Instructors: Axel W Hundemer, Stephen W Drury, Ronan Conlon (Fall)

    • 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 2014, Winter 2015

    Instructors: Thomas F Fox (Fall) Axel W Hundemer (Winter)

    • 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
  • 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 2014, Winter 2015

    Instructors: Jian-Jun Xu, Michael Brandenbursky (Fall) Gantumur Tsogtgerel (Winter)

    • 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

Required Courses (12 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 2014

    Instructors: Payman L Kassaei (Fall)

    • Fall
    • 3 hours lecture; 1 hour tutorial
    • Prerequisite: MATH 133 or equivalent
  • MATH 248 Honours Advanced Calculus (3 credits)

    Offered by: Mathematics and Statistics (Faculty of Science)

    Overview

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

    Terms: Fall 2014

    Instructors: Pengfei Guan (Fall)

    • Fall and Winter and Summer
    • Prerequisites: MATH 133 and MATH 222 or consent of Department.
    • Restriction: Intended for Honours Mathematics, Physics and Engineering students
    • Restriction: Not open to students who have taken or are taking MATH 314
  • 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 2015

    Instructors: Piotr Przytycki (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 2015

    Instructors: Vojkan Jaksic (Winter)

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

Complementary Courses (24 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 2014

    Instructors: Axel W Hundemer (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 2014

    Instructors: Vojkan Jaksic (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.

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.

  • 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: Fall 2014, Winter 2015

    Instructors: Antony Raymond Humphries (Fall) Charles Roth (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 354 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 2014

    Instructors: Stephen W Drury (Fall)

    • Fall
    • Prerequisite: MATH 255 or equivalent
  • MATH 355 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 2015

    Instructors: Stephen W Drury (Winter)

    • Winter
    • Prerequisite: MATH 354 or equivalent.
  • 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 2014

    Instructors: Abbas Khalili Mahmoudabadi (Fall)

    • Fall
    • Prerequisite(s): MATH 133 or MATH 134, and MATH 222 or permisson of the Department.
    • Corequisite(s): MATH 242 or MATH 254
  • 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 2015

    Instructors: David B Wolfson (Winter)

    • Winter
    • Prerequisite: MATH 356 or equivalent
    • Restriction: Not open to students who have taken or are taking MATH 324
  • MATH 366 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 2014

    Instructors: Dmitry Jakobson (Fall)

    • Prerequisite: MATH 248.
    • Corequisite: MATH 354.
    • Restriction: Not open to students who have taken or are taking MATH 466, MATH 249, MATH 316, MATH 381.
  • MATH 370 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 2014

    Instructors: Payman L Kassaei (Fall)

    • Fall
    • Prerequisites: MATH 235 and either (MATH 247 or MATH 251)
  • MATH 371 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 2015

    Instructors: Henri Darmon (Winter)

    • Winter
    • Prerequisite: MATH 370
  • MATH 380 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 2015

    Instructors: Niky Kamran (Winter)

    • Winter
    • Prerequisites: MATH 251 or MATH 247, and MATH 248 or MATH 314
Revision, May 2014. End of revision.
Faculty of Arts—2014-2015 (last updated Feb. 18, 2014) (disclaimer)