MATH 113 114 117 205 211 213 249 251 253 271 273 281 283 311 313 321 331 335 349 353 355 381 401 403 411 423 445 447 501 521 545 601 621

Instruction offered by members of the Department of Mathematics and Statistics in the Faculty of Science.
Department Head  M. Lamoureux
Note: For listings of related courses, see Actuarial Science, Applied Mathematics, Pure Mathematics, and Statistics.

Mathematics
113

Eigenvalues and Eigenvectors


A review of these particular topics for students who have completed Mathematics 211 or equivalent.
Course Hours:
E(8 hours)
Antirequisite(s):
Credit for both Mathematics 113 and 013 will not be allowed.
Notes:
Open to students with credit in Mathematics 211 or equivalent.
NOT INCLUDED IN GPA

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Mathematics
114

Multivariate Topics from Applied Mathematics 219


Multiple Integration and applications.
Course Hours:
E(16 hours)
Prerequisite(s):
Mathematics 253 or 283 or consent of the Department.
Antirequisite(s):
Credit for both Mathematics 114 and 014 will not be allowed.
Notes:
Designed to rectify a deficiency for those students whose Calculus I and II courses did not cover the multivariate topics from Applied Mathematics 219.
NOT INCLUDED IN GPA

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Mathematics
117

Topics from Applied Mathematics 217


Inverse functions and inverse trigonometric functions. Hyperbolic and inverse hyperbolic functions. Indeterminate forms. Applications of integration.
Course Hours:
E(8 hours)
Prerequisite(s):
Mathematics 249 or 251 or 281 or consent of the Department.
Antirequisite(s):
Credit for both Mathematics 117 and 017 will not be allowed.
Notes:
Designed to rectify a deficiency for those students whose first Calculus course did not cover some of the topics from Applied Mathematics 217.
NOT INCLUDED IN GPA

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Junior Courses
Note: Students who have not studied mathematics for some time are strongly advised to review high school material thoroughly prior to registering in any junior level mathematics course.

Mathematics
205

Mathematical Explorations


A mathematics appreciation course. Topics selected by the instructor to provide a contemporary mathematical perspective and experiences in mathematical thinking. May include historical material on the development of classical mathematical ideas as well as the evolution of recent mathematics.
Course Hours:
H(31)
Prerequisite(s):
Pure Mathematics 30 or Mathematics II (offered by Continuing Education).
Notes:
For students whose major interests lie outside the sciences. Highly recommended for students pursuing an Elementary School Education degree. It is not a prerequisite for any other course offered by the Department of Mathematics and Statistics, and cannot be used for credit towards any Major or Minor program in the Faculty of Science except for a major in General Mathematics.

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Mathematics
211

Linear Methods I


Systems of equations and matrices, vectors, matrix representations and determinants. Complex numbers, polar form, eigenvalues, eigenvectors. Applications.
Course Hours:
H(31T1)
Prerequisite(s):
A grade of 70 per cent or higher in Pure Mathematics 30. (Alternatives are presented in C.1 Mathematics Diagnostic Test in the Academic Regulations section of this Calendar).
Antirequisite(s):
Credit for Mathematics 211 and either 213 or 221 will not be allowed.

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Mathematics
213

Honours Linear Algebra I


Systems of equations and matrices, vectors, linear transformations, determinants, eigenvalues and eigenvectors.
Course Hours:
H(31T1)
Prerequisite(s):
A grade of 70 per cent or higher in Pure Mathematics 30.
Antirequisite(s):
Credit for Mathematics 213 and either 211 or 221 will not be allowed.

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Mathematics
249

Introductory Calculus


Algebraic operations. Functions and graphs. Limits, derivatives, and integrals of exponential, logarithmic and trigonometric functions. Fundamental theorem of calculus. Applications.
Course Hours:
H(41T1)
Prerequisite(s):
A grade of 70 per cent or higher in Pure Mathematics 30. (Alternatives are presented in C.1 Mathematics Diagnostic Test in the Academic Regulations section of this Calendar).
Antirequisite(s):
Not open to students with 60% or higher in Mathematics 31, except with special departmental permission. Credit for more than one of Mathematics 249, 251, 281, or Applied Mathematics 217 will not be allowed.

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Mathematics
251

Calculus I


Functions and graphs, transcendental functions. Limits, derivatives, and integrals of exponential, logarithmic and trigonometric functions. Fundamental theorem of calculus. Applications.
Course Hours:
H(31T1)
Prerequisite(s):
A grade of 70 per cent or higher in Pure Mathematics 30 and a grade of 50 per cent or higher in Mathematics 31. (Alternatives to Pure Mathematics 30 are presented in C.1 Mathematics Diagnostic Test in the Academic Regulations section of this Calendar).
Antirequisite(s):
Credit for more than one of Mathematics 249, 251, 281, or Applied Mathematics 217 will not be allowed.
Notes:
This course provides the basic techniques of differential calculus as motivated by various applications. Students performing sufficiently well in a placement test may be advised to transfer directly to Mathematics 253.

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Mathematics
253

Calculus II


Inverses of trigonometric functions. Methods of integration, improper integrals. Separable differential equations, first and second order linear differential equations, applications.
Course Hours:
H(31T1)
Prerequisite(s):
Mathematics 249 or 251 or 281 or Applied Mathematics 217.
Antirequisite(s):
Credit for more than one of Mathematics 253, 263, 283, or Applied Mathematics 219 will not be allowed.
Notes:
Mathematics 253 or 283 is a prerequisite for many 300level courses in Pure Mathematics, Applied Mathematics, Statistics and Actuarial Science. Students in programs offered by the Department of Mathematics and Statistics are strongly recommended to take Mathematics 283.

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Mathematics
271

Discrete Mathematics


Proof techniques. Sets and relations. Induction. Counting and probability. Graphs and trees.
Course Hours:
H(31T1)
Prerequisite(s):
Pure Mathematics 30.
Antirequisite(s):
Credit for both Mathematics 271 and 273 will not be allowed.
Notes:
Philosophy 279 or 377 is highly recommended to complement this course.

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Mathematics
273

Honours Mathematics: Numbers and Proofs


Introduction to proofs. Functions, sets and relations. The integers: Euclidean division algorithm and prime factorization; induction and recursion; integers mod n. Real numbers: sequences of real numbers; completeness of the real numbers; open and closed sets. Complex numbers.
Course Hours:
H(31T1)
Prerequisite(s):
A grade of 80 per cent or higher in Pure Mathematics 30. (Alternatives are presented in C.1 Mathematics Diagnostic Test in the Academic Regulations section of this Calendar).
Antirequisite(s):
Credit for both Mathematics 273 and 271 will not be allowed.

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Mathematics
281

Honours Calculus I


Limits and continuity; Differentiation of functions of one real variable; the Mean Value Theorem and its consequences; Riemann integration; fundamental theorem of calculus; applications.
Course Hours:
H(31T1)
Prerequisite(s):
A grade of 80 per cent or higher in Pure Mathematics 30 and a grade of 50 per cent or higher in Mathematics 31. (Alternatives to Pure Mathematics 30 are presented in C.1 Mathematics Diagnostic Test in the Academic Regulations section of this Calendar).
Antirequisite(s):
Credit for more than one of Mathematics 249 or 251 or 281 or Applied Mathematics 217 will not be allowed.

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Mathematics
311

Linear Methods II


Vector spaces and subspaces. Linear independence. Matrix representations of linear transformations. GramSchmidt orthogonalization. Students will complete a project using a computer algebra system.
Course Hours:
H(31T)
Prerequisite(s):
One of Mathematics 211 or 213.
Antirequisite(s):
Credit for both Mathematics 311 and 313 will not be allowed.

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Mathematics
313

Honours Linear Algebra II


Diagonalization. Canonical forms. Inner products, orthogonalization. Spectral theory. Students will be required to complete a project using a computer algebra system.
Course Hours:
H(31T)
Prerequisite(s):
Mathematics 213 or a grade of "B+" or better in Mathematics 211.
Antirequisite(s):
Credit for both Mathematics 311 and 313 will not be allowed.

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Mathematics
321

Mathematical Probability


Sample spaces. Discrete probability. Discrete and continuous random variables. Standard distributions. Mathematical expectation and variance. Moments and moment generating functions. Central limit theorem. Functions of random variables. Introduction to statistical inference.
Course Hours:
H(31T)
Prerequisite(s):
Mathematics 253 or 283 or Applied Mathematics 219.

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Mathematics
331

Multivariate Calculus


Systems of ordinary differential equations. Calculus of functions of several variables. Introduction to vector analysis, theorems of Green, Gauss and Stokes.
Course Hours:
H(31T)
Prerequisite(s):
Mathematics 253 or 283 or Applied Mathematics 219 and Mathematics 211 or 213.
Antirequisite(s):
Credit for both Mathematics 331 and either 353 or 381 or Applied Mathematics 309 will not be allowed.
Notes:
This course is not a member of the list of courses constituting the fields of Actuarial Science, Applied Mathematics, Pure Mathematics, or Statistics and cannot normally be substituted for Mathematics 353 or 381 in degree programs in any of those fields.

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Mathematics
335

Analysis I


The real numbers, sequences, series, functions, continuity and uniform continuity, differentiation, intermediate and mean value theorems, the Riemann integral, integrability of continuous functions on closed intervals.
Course Hours:
H(31T)
Prerequisite(s):
Mathematics 253 or 263 or 283 or Applied Mathematics 219, or consent of the Department.
Antirequisite(s):
Credit for more than one of Mathematics 335, 355, Pure Mathematics 435 and 455 will not be allowed.

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Mathematics
349

Calculus III


Infinite sequences and series. Polar coordinates, parametric equations, arc length. Vector geometry, differentiation of vectorvalued functions. Partial differentiation. Students will complete a project using a computer algebra system.
Course Hours:
H(31T)
Prerequisite(s):
Mathematics 253 or 283 or Applied Mathematics 219 and Mathematics 211 or 213.
Antirequisite(s):
Credit for both Mathematics 349 and 381 will not be allowed.

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Mathematics
355

Honours Analysis I


The real numbers, sequences, series, functions, continuity and uniform continuity, differentiation, intermediate and mean value theorems, the Riemann integral, integrability of continuous functions on closed intervals.
Course Hours:
H(31T)
Prerequisite(s):
Mathematics 283 or 263; or a grade of "B+" or better in Mathematics 253 or Applied Mathematics 219.
Antirequisite(s):
Credit for more than one of Mathematics 335, 355, Pure Mathematics 435 and 455 will not be allowed.

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Mathematics
401

Special Topics


Higher level topics which can be repeated for credit.
Course Hours:
H(30)
Prerequisite(s):
Consent of the Department.
Notes:
This course is designed to add flexibility to completion of an undergraduate pure mathematics or general mathematics program.
MAY BE REPEATED FOR CREDIT

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Mathematics
403

Topics in Mathematics for Economics


Techniques of integration. Multiple integrals. Analysis of functions. Continuity. Compact sets. Convex sets. Separating hyperplanes. Lower and upper hemicontinuous correspondences. Fixed point theorems, Optimal control.
Course Hours:
H(30)
Prerequisite(s):
Mathematics 211 or 213 and Mathematics 253 or 283 or Applied Mathematics 219; or both Economics 387 and 389.

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Mathematics
411

Linear Spaces with Applications


Canonical forms. Inner product spaces, invariant subspaces and spectral theory. Quadratic forms.
Course Hours:
H(31T)
Prerequisite(s):
Mathematics 311 and one of 331, 353, 381, or Applied Mathematics 309.
Antirequisite(s):
Credit for Mathematics 411 and 313 or Applied Mathematics 441 will not be allowed.
Notes:
May not be offered every year. Consult the Department for listings.

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Mathematics
421

Complex Analysis I


Basic complex analysis – complex numbers and functions, differentiation, CauchyRiemann equations, line integration, Cauchy’s theorem and Cauchy’s integral formula, Taylor’s theorem, the residue theorem, applications to computation of definite integrals.
Course Hours:
H(31T)
Prerequisite(s):
Both Mathematics 349 and 353; or both Mathematics 283 and 381.
Antirequisite(s):
Credit for more than one of Mathematics 421, 423, Pure Mathematics 421 or 521 will not be allowed.

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Mathematics
423

Honours Complex Analysis


Basic complex analysis – complex numbers and functions, differentiation, CauchyRiemann equations, line integration, Cauchy’s theorem and Cauchy’s integral formula, Taylor’s theorem, the residue theorem, applications to computation of definite integrals.
Course Hours:
H(31T)
Prerequisite(s):
Both Mathematics 349 and 353; or both Mathematics 283 and 381.
Antirequisite(s):
Credit for more than one of Mathematics 421, 423, Pure Mathematics 421 or 521 will not be allowed.
Notes:
Open only to Honours Applied Mathematics and Honours Pure Mathematics students.

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Mathematics
445

Analysis II


Basic topology of Euclidean space, Fubini’s theorem, the total derivative, change of variable in multiple integrals, inverse and implicit function theorems, submanifolds of Euclidean spaces, differential forms, Stokes’ theorem in arbitrary dimension.
Course Hours:
H(30)
Prerequisite(s):
Mathematics 353 or 381; and Mathematics 311; and Mathematics 335 or 355 or Pure Mathematics 435 or 455, or consent of the Department.
Antirequisite(s):
Credit for more than one of Mathematics 445, 447 or Pure Mathematics 545 will not be allowed.

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Mathematics
447

Honours Analysis II


Basic topology of Euclidean space, Fubini’s theorem, the total derivative, change of variable in multiple integrals, inverse and implicit function theorems, submanifolds of Euclidean spaces, differential forms, Stokes’ theorem in arbitrary dimension.
Course Hours:
H(30)
Prerequisite(s):
Mathematics 353 or 381; and Mathematics 311; and Mathematics 335 or 355 or Pure Mathematics 435 or 455, or consent of the Department.
Antirequisite(s):
Credit for more than one of Mathematics 445, 447 or Pure Mathematics 545 will not be allowed.

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Mathematics
501

Measure and Integration


Abstract measure theory, basic integration theorems, Fubini's theorem, RadonNikodym theorem, Lp Spaces, Riesz representation theorems.
Course Hours:
H(30)
Prerequisite(s):
Mathematics 545 or Pure Mathematics 545 or consent of the Division.
Antirequisite(s):
Credit for more than one of Mathematics 501, 601, Pure Mathematics 501 or 601 will not be allowed.

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Mathematics
521

Complex Analysis II


Analytic functions as mappings, local properties of analytic functions, Schwarz lemma, CasoratiWeierstrass and Picard theorems, analytic continuation, harmonic and subharmonic functions, approximation theorems, conformal mappings, Riemann surfaces.
Course Hours:
H(30)
Prerequisite(s):
Mathematics 335 or 355 or Pure Mathematics 435 or 455; and Mathematics 421 or 423 or Pure Mathematics 421; or consent of the Department.
Antirequisite(s):
Not open to students with credit in Pure Mathematics 521.

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Mathematics
545

Analysis III


Sequences and series of functions; Lebesgue integration on the line, Fourier series and the Fourier transform, pointwise convergence theorems, distributions and generalized functions.
Course Hours:
H(30)
Prerequisite(s):
Mathematics 447 or a grade of "B+" or better in Pure Mathematics 445 or Mathematics 445.
Antirequisite(s):
Not open to students with credit in Pure Mathematics 545.

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Graduate Courses
Note: In addition to the prerequisites listed below, consent of the Applied Mathematics Division or the Pure Mathematics Division is a prerequisite for these graduate courses.

Mathematics
601

Measure and Integration


Abstract measure theory, basic integration theorems, Fubini's theorem, RadonNikodym theorem, Lp spaces, Riesz representation theorem.
Course Hours:
H(30)
Prerequisite(s):
Mathematics 545 or Pure Mathematics 545 or consent of the Division.
Antirequisite(s):
Credit for more than one of 501, 601, Pure Mathematics 501 or 601 will not be allowed.

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Mathematics
621

Complex Analysis


Analytic functions as mappings, local properties of analytic functions, Schwarz lemma, CasoratiWeierstrass and Picard theorems, analytic continuation, harmonic and subharmonic functions, approximation theorems, conformal mappings, Riemann surfaces.
Course Hours:
H(30)
Prerequisite(s):
Mathematics 335 or 355 or Pure Mathematics 435 or 455 or consent of the Department.

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