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Academic Calendar 2024-2025

Table of Contents

Mathematics

Mathematics is a discipline which has been said to be the Queen of the Sciences, and is the foundation of most modern quantitative and qualitative studies. The permanence and universality of mathematics throughout the ages is a consequence of its very nature. Mathematics is cumulative, developing from the earliest use of numbers by prehistoric civilizations to the highly deductive nature of geometry as developed by the Greeks, from the practical applications of calculus developed in the seventeenth century to the modern use of number theory in computer cryptography. Mathematics has many faces, from practical uses of its statistical tools to theoretical studies of abstract relationships. Our goal is to introduce students to all facets of the discipline, and to give them an appreciation of the historical, theoretical and applied nature of the discipline, as well as a full understanding of the beauty of the subject.

The Department offers a broad variety of courses and programs in Mathematics. Beginning courses may introduce students to the applications to which Calculus may be applied or the practical uses of statistics; more advanced courses deal with topics ranging from geometry to game theory. All courses in the Mathematics curriculum offer a blend of theory and practical applications. Many of the courses offered include a substantial computational component, and students are encouraged to use the mathematical software tools available. Courses are designed to address the needs of a wide variety of users, from the casual to the professional. Some students may enrol in a course to familiarize themselves with university level mathematics, while others will take a series of courses related directly to their chosen study area. Those choosing to pursue a minor or major in mathematics will be exposed to more advanced courses which blend Mathematical theory and practice.

91看片 has been very successful in placing many of its students in graduate programs in Mathematics, while many others have found employment after graduation in one of many fields for which mathematical understanding is an asset. Teaching, actuarial work, law and medicine are all areas requiring the ability to think and reason logically and for which a mathematical background can prove beneficial.

Disciplinary B.A. and B.Sc. Programs

B.A. or B.Sc. MINOR in Mathematics is 24 credits earned as follows:

3from MATH 1111, 1151
3from MATH 1121
12from MATH 1311, 2111, 2121, 2211, 2221, 2321.
6from Mathematics at the 3/4000 level.

B.A. MAJOR in Mathematics is 60 credits earned as follows:

3from MATH 1111, 1151
12from MATH 1121, 2111, 2211, 2221
3from MATH 1311, 2121
3from MATH 3111, 3141, 3161
3from MATH 3211, 3221, 3231, 4011
3from MATH 3151, 3311, 3411
15from Mathematics at the 3/4000 level
6from COMP 1631, 1731
12credits from complementary disciplines chosen in consultation with the Program Advisor

B.A. HONOURS in Mathematics is 72 credits earned as follows:

3from MATH 1111, 1151
15from MATH 1121, 2111, 2121, 2211, 2221
6from COMP 1631, 1731
6from MATH 3111, 3211
3from MATH 3311, 3411
6from MATH 4011, 4111, 4121, 4221, 4311, 4951, 4991
15from MATH at the 3/4000 level
6from MATH 4901 and 4911, or 6 from MATH at the 3/4000 level
6from Mathematics or Computer Science at the 3/4000 levels
6from Computer Science, Economics, or Mathematics at the 2000 level or above, or from COMM 3411, LING 2001, 3001, PHIL 2611, PHIL 3631

B.A. or B.Sc. HONOURS in Computer Science and Mathematics is 75 or 87 credits earned as follows:

18from COMP 1631, 1731, 2211, 2611, 2711, 2931
3from MATH 1111, 1151
12from MATH 1121, 2111, 2121, 2221
9from MATH 3111, 3211, 3311
3from MATH 3221, 3231, 3251, 4011, 4221
3from Mathematics at the 3/4000 levels
3from COMP 3361, 3971
12from COMP 3411, 3611, 3911, 4721
12from Computer Science or Mathematics at the 3/4000 level, which may include 6 credits from either COMP 4990 or MATH 4901 and 4911
9from CHEM 1001, 1021; PHYS 1051, 1551 (only for B.Sc.)
3from BIOL 1001, BIOL 1501, BIOC 1001, GENS 1401, PSYC 1001 or PSYC 1011 (only for B. Sc.)

B.Sc. MAJOR in Mathematics is 60 credits earned as follows:

3from MATH 1111, 1151
15from MATH 1121, 2111, 2121, 2211, 2221
3from MATH 3111, 3141, 3161
3from MATH 3211, 3221, 3231, 4011
3from MATH 3151, 3311, 3411
15from Mathematics at the 3/4000 level
6from COMP 1631, 1731
9from CHEM 1001, 1021; PHYS 1051, 1551
3from BIOL 1001, BIOL 1501, BIOC 1001, GENS 1401, PSYC 1001 or PSYC 1011

B.Sc. HONOURS in Mathematics is 78 credits earned as follows:

3from MATH 1111, 1151
15from MATH 1121, 2111, 2121, 2211, 2221
6from COMP 1631, 1731
6from MATH 3111, 3211
3from MATH 3311, 3411
6from MATH 4011, 4111, 4121, 4221, 4311, 4951, 4991
15from MATH at the 3/4000 level
6from MATH 4901 and 4911, or 6 from MATH at the 3/4000 level
6from Mathematics or Computer Science at the 3/4000 level
9from CHEM 1001, 1021; PHYS 1051, 1551
3from BIOL 1001, BIOL 1501, BIOC 1001, GENS 1401, PSYC 1001 or PSYC 1011

Interdisciplinary B.A. Program

B.A. HONOURS in Economics and Mathematics is 81 credits earned as follows:

21from ECON 1001, 1011, 2001, 2011, 2101, 2111, 2701
3from MATH 1111, 1151
15from MATH 1121, 2111, 2121, 2211, 2221
3from ECON 1701, MATH 1311, 2311
3from COMP 1631
6from MATH 3111, 3211
12from ECON 4711, 4721, 4801, 4811, 4821
6from ECON at the 3/4000 levels which may include ECON 4990
12from MATH at the 3/4000 level

Interdisciplinary B.Sc. Program

B.Sc. HONOURS in Mathematics and Physics is 90 credits earned as follows:

3from BIOL 1001, BIOL 1501, BIOC 1001, GENS 1401, PSYC 1001 or PSYC 1011
3from MATH 1111 or 1151
15from MATH 1121, 2111, 2121, 2211, 2221
3from COMP 1631
6from CHEM 1001, 1021
12from PHYS 1051, 1551, 2251, 2801
3from PHYS 3451
9from MATH 3111, 3211, 3311
6from MATH 3141, 3161
6from MATH 3131, 3221, 3151, 3231, 3411, 3531, 4111, 4121, 4311, PHYS 4101, 4201, 4311, 4831, 4851, 4911; only 3 credits may be selected from the listed Physics courses
18from PHYS 2811, 3101, 3201, 3701, 3821, 4411
6from PHYS 4990

狈辞迟别:�Students pursuing Honours in Mathematics and Physics may be allowed to substitute PHYS 1041 for PHYS 1051 with permission of the Department

PLACEMENT IN MATHEMATICS

Students wishing to take the introductory calculus course (Mathematics 1111 or Mathematics 1151) are required to write a Mathematics Assessment Test to determine their level of mathematical preparation.

MATHEMATICS COURSES

狈辞迟别:� The listing of a course in the Calendar is not a guarantee that the course is offered every year.

狈辞迟别:� Students must obtain a grade of at least C- in all courses used to fulfill prerequisite requirements. Otherwise, written permission of the appropriate Department Head or Program Coordinator must be obtained.

Functions

This course focuses on the real number system, inequalities, plane analytic geometry (lines and conics), functions, inverse functions, polynomials, rational functions, trigonometric functions, and exponential and logarithmic functions. It emphasizes fundamental methods of graphing functions, using non-calculus based techniques. [Note 1: This course is primarily intended for non-science students or as a prerequisite for MATH 1111 or 1151 for those students who have not passed the Mathematics Placement Test. Science students who have passed the Mathematics Placement Test require the permission of the Department of Mathematics and Computer Science to enrol in this course. Credit will not be given for this course if credit has already been granted for MATH 1111 or 1151.] (Format: Lecture 3 Hours, Laboratory 1.5 Hours) (Exclusion: Any version of MATH 1011 previously offered with a different title)

Calculus I

This course introduces differential calculus. Topics include derivatives of algebraic, trigonometric, and exponential functions and applications such as curve sketching, related rates, and optimization problems. [Note 1: This course has a Challenge for Credit option; see Calendar Section 3.11] (Format: Lecture 3 Hours, Laboratory 1.5 Hours)(Exclusion: MATH 1151; any version of MATH 1111 previously offered with a different title)

Calculus II

Prereq: 3 credits from MATH 1111, 1151; or permission of the Department
This course continues the introduction to calculus begun in MATH 1111. Topics include techniques of integration; applications of the integral such as finding volumes and solving elementary differential equations; and sequences and series. (Format: Lecture 3 Hours, Laboratory 1.5 Hours) (Exclusion: Any version of MATH 1121 previously offered with a different title)

Applied Calculus

This course introduces differential calculus with an emphasis on applications. Topics include modeling with functions, interpretation of the derivative and partial derivatives, optimization in one and two dimensions, and some computational methods. (Format: Lecture 3 Hours, Laboratory 1.5 Hours) (Exclusion: MATH 1111)

Finite Mathematics

This course introduces common applications of finite mathematics. Topics include Markov chains, linear programming and game theory. [Note 1: This course is restricted to non-mathematics majors and is intended in particular for students in behavioural sciences, commerce, and social sciences. Mathematics majors require the instructor's permission to enrol.] (Format: Lecture 3 Hours)

Introduction to Data Science

This course emphasizes practical techniques for working with large-scale data and introduces tools and techniques for managing, visualizing, and making sense of data through the use of statistical software. Topics include: descriptive statistics, confidence intervals, regression, and machine learning. (Format: Lecture 3 hours, Laboratory 1.5 hours)

Special Topic in Mathematics

This course either focuses on topics not covered by the current course offerings in a department or program or offers the opportunity to pilot a course that is being considered for inclusion in the regular program. [Note 1: Prerequisite set by Department/Program when the topic and level are announced. Note 2: When a Department or Program intends to offer a course under this designation, it must submit course information, normally at least three months in advance, to the Dean. Note 3: Students may register for MATH 1991 more than once, provided the subject matter differs.] (Format: Variable)

Multivariable Calculus

Prereq: MATH 1121; or permission of the Department
This course introduces the calculus of functions of several variables, including conic sections, quadric surfaces, polar co-ordinates in the plane, cylindrical and spherical co-ordinates in three space, continuity, partial derivatives, tangent planes, chain rule, maximum and minimum values, Lagrange multipliers, and double and triple integrals.(Format: Lecture 3 Hours)

Differential Equations I

Prereq: MATH 1121; or permission of the Department
This course introduces first and second order differential equations. Topics include techniques for solving simple differential equations and the qualitative analysis of linear and non-linear equations. Applications include growth and decay, heating and cooling, and mixing and chemical reactions. (Format: Lecture 3 Hours) (Exclusion: Any version of MATH 2121 previously offered with a different title)

Discrete Structures

Prereq: 3 credits from MATH 1111, 1151; or permission of the Department
This course introduces the terminology and concepts of discrete mathematics. Topics may include: logical arguments, proofs and algorithm verification, sets, relations, functions and cardinality of sets, induction and recursion, enumeration, and algorithms and complexity. [Note 1: This course is cross-listed with COMP 2211 and may therefore count as three credits in either discipline.] (Format: Lecture 3 Hours)

Linear Algebra

Prereq: 3 credits from MATH 1111, 1151; or permission of the Department
This course introduces linear algebra and its applications. Topics may include: linear equations, matrices, determinants, vector spaces, linear transformations, inner products, eigenvalues, and eigenvectors. Whenever possible, the course provides geometric interpretation in two- and three-dimensional space. (Format: Lecture 3 Hours)

Statistics I

This course introduces some of the concepts and techniques of probability and statistics. Topics include descriptive statistics, elementary probability, probability distributions, statistical estimation, hypothesis testing, and the use of a statistical software package in analyzing data. Examples come from a wide variety of disciplines. (Format: Lecture 3 Hours)

Statistical Methods for Data Science

Prereq: MATH 1151; 3 credits from MATH 1311, 2311; or permission of the Department
This is a second course in the concepts and techniques of probability, statistics, and data science. It further emphasizes practical computational techniques for modelling, understanding, and making predictions with large-scale data, as well as the mathematical basis of those techniques. Topics covered may include: basic combinatorics, independence and conditional probability, Bayesian methods, linear and nonlinear regression, correlation estimation and prediction, goodness-of-fit tests, and machine learning. (Format: Lecture 3 Hours, Laboratory 1 Hour) (Exclusion: Any version of MATH 2321 previously offered with a different title)

Special Topic in Mathematics

This course either focuses on topics not covered by the current course offerings in a department or program or offers the opportunity to pilot a course that is being considered for inclusion in the regular program. [Note 1: Prerequisite set by Department/Program when the topic and level are announced. Note 2: When a Department or Program intends to offer a course under this designation, it must submit course information, normally at least three months in advance, to the Dean. Note 3: Students may register for MATH 2991 more than once, provided the subject matter differs.] (Format: Variable)

History of Mathematics

Prereq: 6 credits from MATH 2111, 2121, 2211, 2221; or permission of the Department
This course surveys the history of mathematics. Topics include: the achievements of early civilizations, the developments in Europe leading to the calculus and its consequences, the growth of rigor in the eighteenth and nineteenth centuries, and the axiomatic method in the twentieth century. (Format: Lecture 3 Hours)

Real Analysis I

Prereq: MATH 1121; MATH 2211; or permission of the Department
This course provides a systematic and rigorous study of the real numbers and functions of a real variable, emphasizing limits and continuity. (Format: Lecture 3 Hours)

Differential Equations II

Prereq: MATH 2121; MATH 2111; MATH 2221; or permission of the Department
This course focuses on ordinary and partial differential equations. Topics for ordinary differential equations include existence and uniqueness of solutions, systems of differential equations, power series solutions, Laplace and Fourier transforms, and Fourier series. Topics for partial differential equations include separation of variables, generalized Fourier series, Sturm-Liouville theory, Legendre polynomials, Bessel functions, Green's functions, and the calculus of variations. (Format: Lecture 3 Hours) (Exclusion: Any version of MATH 3131 previously offered with a different title)

Vector Calculus

Prereq: MATH 2111; 3 credits from MATH 2221, PHYS 3451; or permission of the Department
This course covers the calculus of vector-valued functions and curves, vector fields, line and surface integrals, vector differential operators, and the various forms of Stokes' Theorem. It may also include the differential geometry of curves and differential forms. (Format: Lecture 3 Hours)

An Introduction to Mathematical Modelling

Prereq: Third-year standing; 3 credits from Math 1111, 1151; or permission of the Department
This course introduces the nature of theoretical mathematical modelling illustrated by examples drawn from the physical sciences, population dynamics (mathematical ecology), traffic flow, sociological problems (for example voting, kinship and cultural stability) and other areas depending on the interests of the class. (Format: Lecture 3 Hours)

Complex Variables With Applications

Prereq: MATH 2111; or permission of the Department
This course covers analytic functions, Cauchy-Riemann equations, conformal mapping, complex integrals, Cauchy's integral theorem, Taylor and Laurent Series, residues,evaluation of real integrals, and inverse transforms. (Format: Lecture 3 Hours; Exclusion MATH 4131)

Modern Algebra I

Prereq: MATH 2211; MATH 2221; or permission of the Department
This course introduces the theory of groups and rings. (Format: Lecture 3 Hours)

Advanced Linear Algebra

Prereq: MATH 2221; MATH 2211 recommended; or permission of the Department
This course covers selected linear algebraic topics such as: change of basis and similarity of matrices; multilinear forms and determinants; canonical forms, Primary Decomposition Theorem, Jordan form; semisimple and normal operators; spectral theory; quadratic forms; and applications to areas such as geography, electrical networks, linear programming, differential equations, and the geometry of conic sections. (Format: Lecture 3 Hour)

Number Theory

Prereq: MATH 2211; or permission of the Department
This course introduces the theory of numbers. Topics may include: the Euclidean algorithm, the Fundamental Theorem of Arithmetic, congruences, diophantine equations, Fermat and Wilson Theorems, quadratic residues, continued fractions, and the Prime Number Theorem. (Format: Lecture 3 Hours)

Graph Theory

Prereq: MATH 2211; or permission of the Department
This course introduces terminology, techniques, and applications of graph theory and examines parameters for a variety of classes of graphs. Topics include trees, planarity, colouring, matchings, and network flow problems. (Format: Lecture 3 Hours) (Exclusion: Any version of MATH 3251 previously offered with a different title.)

Introduction to Game Theory

Prereq: 6 credits from ECON 1001, 1011; or 3 credits from MATH 1111, 1151; or permission of the Department
This course introduces the basic tools and methods of Game Theory. Game Theory is a mathematically oriented approach to understanding the strategic interaction of self-interested agents. Emphasis is on non-cooperative games. Topics include backwards induction, iterative deletion of dominated strategies, Nash equilibrium, repeated games, some equilibrium refinements, evolutionary game theory, and Bayesian Nash equilibria. [Note 1: This course is cross-listed as ECON 3301 and therefore may count as 3 credits in either discipline. Note 2: Counts as a Commerce elective for students taking a Bachelor of Commerce or a Major or Minor in Commerce] (Format: Lecture 3 Hours, Laboratory 1 Hour)

Probability and Statistics

Prereq: MATH 1121; MATH 2321; or permission of the Department
This course focuses on the mathematical theory of probability. It includes topics such as: sample space, events, axioms, conditional probability, Bayes' Theorem, random variables, combinatorial probability, moment generating functions, transformations of random variables, univariate and joint distributions with reference to the binomial, hypergeometric, normal, Gamma, Poisson, and others; convergence of sequences of variables; and the Central Limit Theorem. (Format: Lecture 3 Hours) (Exclusion: Any version of MATH 3311 previously offered with a different title)

Numerical Analysis

Prereq: MATH 1121; 3 credits from MATH 2221, PHYS 3451; 3 credits from COMP or PHYS; or permission of the Department
This course introduces numerical methods for solving a variety of problems in the sciences. Topics include numerical errors and precision, root finding, model fitting, integration and solution of differential equations, solution of linear and nonlinear systems of equations, and matrix factorization. [Note 1: This course is cross-listed as COMP 3411 and PHYS 3411 and may therefore count as three credits in any of the three disciplines.] (Format: Lecture 3 Hours)

Simulation and Modelling

Prereq: 3 credits from MATH 1111, 1151; 3 credits from MATH 1311, 2311, 3311, PSYC 2001, 2011; 3 credits from COMP; or permission of the Department
This course introduces the simulation technique for studying mathematical models. Topics include: systems theory and system models, continuous system simulation, discrete system simulation, Monte Carlo methods, random number generators, and simulation languages. It emphasizes computer implementation of the methods studied. [Note 1: This course is cross listed as COMP 3531 and may therefore count as three credits in either discipline.] (Format: Lecture 3 Hours)

Special Topic in Mathematics

This course either focuses on topics not covered by the current course offerings in a department or program or offers the opportunity to pilot a course that is being considered for inclusion in the regular program. [Note 1: Prerequisite set by Department/Program when the topic and level are announced. Note 2: When a Department or Program intends to offer a course under this designation, it must submit course information, normally at least three months in advance, to the Dean. Note 3: Students may register for MATH 3991 more than once, provided the subject matter differs.] (Format: Variable)

Set Theory and Introductory Category Theory

Prereq: 3 credits from MATH 3111, 3211, 3221; or permission of the Department
This course provides an introduction to set theory via the basic ideas of category theory. Topics may include: categories, types of arrows in categories, limits and colimits, mapping sets, cardinals and ordinals, and the axiom of choice. (Format: Lecture 3 hours) (Exclusion: MATH 3011)

Topology

Prereq: MATH 2111; MATH 3111; or permission of the Department
This course introduces the essential ideas of topology. Topics include: metric and topological spaces, convergence, continuous functions, connected spaces, compact spaces, and homotopy. (Format: Lecture 3 hours)

Real Analysis II

Prereq: MATH 2111; MATH 3111; or permission of the Department
This course continues the study of analysis begun in MATH 3111 and includes a rigorous study of the Riemann and Lebesgue integrals based on formal definitions and proofs. (Format: Lecture 3 Hours; Exclusion: MATH 3121)

Modern Algebra II

Prereq: MATH 3211; or permission of the Department
This course explores the classical theory of rings and fields and their applications. (Format: Lecture 3 Hours)

Probability and Statistics II

Prereq: MATH 3311; or permission of the Department
This course focuses on mathematical statistics. It includes topics such as: estimation, unbiasedness,efficiency, Cramer-Rao lower bound, consistency, sufficiency, maximum likelihood estimators, hypothesis testing, power of tests, likelihood ratio, regression analysis and analysis of variance. (Format: Lecture 3 Hours) (Exclusion: MATH 3321)

Theory of Computation

Prereq: COMP/MATH 2211; COMP 1731; or permission of the Department
This course is an introduction to theoretical aspects of Computer Science such as formal language and automata theory and complexity theory. [Note 1: This course is cross listed as COMP 4631 and may therefore count as three credits in either discipline.] (Format: Lecture 3 Hours)

Cryptography

Prereq: COMP 1731; COMP/MATH 2211; MATH 2221; or permission of the Department
This course is an introduction to cryptographic algorithms and to the cryptanalysis of these algorithms, with an emphasis on the fundamental principles of information security. Topics include: classical cryptosystems, modern block and stream ciphers, public-key ciphers, digital signatures, hash functions, key distribution and agreement. [Note 1: This course is cross listed as COMP 4651 and may therefore count as three credits in either discipline.] (Format: Lecture 3 Hours)

Honours Thesis I

Prereq: Registered in Honors Math Program; fourth-year standing
This course comprises independent research and study under the direction of one or more supervisors approved by the Department. This first course is typically focused on background research. The student prepares a report on their progress by the end of the term. (Note: consent of supervisor(s) required). (Format: Independent Study/Thesis).

Honours Thesis II

Prereq: MATH 4901, with a grade of at least B required
This course comprises independent research and study under the direction of one or more supervisors approved by the Department. This second course is typically focused on developing, writing, and presenting the thesis itself. (Note: consent of supervisor(s) required). (Format: Independent Study/Thesis).

Independent Study in Mathematics

This course permits senior students, under the direction of faculty members, to pursue their interest in areas not covered, or not covered in depth, by other courses through a program of independent study. [Note 1: Permission of the Department/Program Advisor. Students must obtain consent of an instructor who is willing to be a supervisor and must register for the course prior to the last day for change of registration in the term during which the course is being taken. Note 2: A program on Independent Study cannot duplicate subject matter covered through regular course offerings. Note 3: Students may register for MATH 4950/51 more than once, provided the subject matter differs.] (Format: Independent Study)

Special Topic in Mathematics

This course either focuses on topics not covered by the current course offerings in a department or program or offers the opportunity to pilot a course that is being considered for inclusion in the regular program. [Note 1: Prerequisite set by Department/Program when the topic and level are announced. Note 2: When a Department or Program intends to offer a course under this designation, it must submit course information, normally at least three months in advance, to the Dean. Note 3: Students may register for MATH 4991 more than once, provided the subject matter differs.] (Format: Variable)