Instruction offered by members of the Department of Mathematics and Statistics in the Faculty of Science.
Department Head  T. Bisztriczky
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)
Notes:
Open to students with credit in Mathematics 211 or 221 or equivalent.
Also known as:
(formerly Mathematics 013)
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 263 or 283 or consent of the Department.
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.
Also known as:
(formerly Mathematics 014)
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.
Notes:
Designed to rectify a deficiency for those students whose first Calculus course did not cover some of the topics from Applied Mathematics 217.
Also known as:
(formerly Mathematics 017)
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 the paragraph titled Mathematics Diagnostic Test in the Program section of this Calendar.)
Antirequisite(s):
Note: Credit for both Mathematics 211 or 221 and 213 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):
Note: Credit for both Mathematics 211 or 221 and 213 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 the paragraph titled Mathematics Diagnostic Test in the Program section of this Calendar.)
Antirequisite(s):
Note: Not open to students with 60% or higher in Mathematics 31, except with special departmental permission. Note: 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 the paragraph titled Mathematics Diagnostic Test in the Program section of this Calendar.)
Antirequisite(s):
Note: 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
271

Discrete Mathematics


Proof techniques. Sets and relations. Induction. Counting and probability. Graphs and trees.
Course Hours:
H(31T1)
Prerequisite(s):
Mathematics 211 or 221 or 213.
Antirequisite(s):
Note: 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 70 per cent or higher in Pure Mathematics 30. (Alternatives are presented in the paragraph titled Mathematics Diagnostic Test in the Program section of this Calendar.)
Antirequisite(s):
Note: Credit for both Mathematics 271 and 273 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 the paragraph titled Mathematics Diagnostic Test in the Program section of this Calendar.)
Antirequisite(s):
Note: 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):
Mathematics 211 or 221 or 213.
Antirequisite(s):
Note: Credit will not be given for Mathematics 311 and Mathematics 313

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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 or 221
Antirequisite(s):
Note: 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 263 or 283 or Applied Mathematics 219.

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Mathematics
323

Introduction to Mathematical Statistics


Bivariate distributions. Sampling distributions. Chisquared, F and t distributions. Estimation. Hypothesis tests (proportions, means, variance, chisquare). Method of moments. Maximum likelihood estimators. NeymanPearson lemma. Likelihood ratio tests. Elementary regression and correlation.
Course Hours:
H(31T)
Prerequisite(s):
Mathematics 321.
Notes:
Prior or concurrent completion of Mathematics 353 or 381 is strongly recommended.

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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 263 or 283 or Applied Mathematics 219 and either Mathematics 221 or 211.
Antirequisite(s):
Note: 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
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 263 or 283 or Applied Mathematics 219; and Mathematics 211 or 221.
Antirequisite(s):
Note: Credit for both Mathematics 349 and 381 will not be allowed.

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Mathematics
381

Honours Calculus III


Functions of several variables; differentiability, extrema. Implicit and inverse function theorems. Integration of functions of several variables; line integrals; surface integrals. Students will complete a project using a computer algebra system.
Course Hours:
H(31T)
Prerequisite(s):
Mathematics 283 or a grade of B+ or better in Mathematics 253 or Applied Mathematics 219; and Mathematics 211 or 221.
Antirequisite(s):
Note: Credit for more than one of Mathematics 331, 353, 381, and Applied Mathematics will not be allowed. Note: Credit for both Mathematics 349 and 381 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.
Antirequisite(s):
Note: 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 221 and 253 or 263 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(3)
Prerequisite(s):
Mathematics 311 and one of 331, 353, or Applied Mathematics 309.
Antirequisite(s):
Note: Mathematics 411 is not open to students with credit in Mathematics 313.
Notes:
May not be offered every year. Consult the Department for listings.
Also known as:
(formerly Applied Mathematics 441)

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