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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 2022, Winter 2023, Summer 2023
Instructors: B茅langer-Rioux, Rosalie; Mazakian, Hovsep; Gerbelli-Gauthier, Mathilde; Alfieri, Antonio (Fall) Duchesne, Gabriel William (Winter) Leroux-Lapierre, Alexis (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.
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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 2022, Winter 2023, Summer 2023
Instructors: Trudeau, Sidney; Huang, Peiyuan; Mellick, Sam (Fall) Collins-Woodfin, Elizabeth (Winter) Lybbert, Reginald (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
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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 2022, Winter 2023, Summer 2023
Instructors: Macdonald, Jeremy; Xu, Peter (Fall) Trudeau, Sidney; Barill, Gavin; Mazakian, Hovsep (Winter) Abi Younes, Elio; Hassan, Hazem (Summer)
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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 2022, Winter 2023, Summer 2023
Instructors: Paquette, Elliot; Wrobel, Konrad (Fall) Trudeau, Sidney (Winter) Barill, Gavin (Summer)
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; group actions on sets.
Terms: Fall 2022
Instructors: Wise, Daniel (Fall)
Fall
3 hours lecture; 1 hour tutorial
Prerequisite: MATH 133 or equivalent
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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 2023
Instructors: Pichot, Mikael (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, H脙露lder 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 2023
Instructors: Choksi, Rustum (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 2022
Instructors: Hundemer, Axel W (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 2022
Instructors: Tserunyan, Anush (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 ve