Course Descriptions

ACSC 041 - Actuarial Science Internship Term 1

First four month term of Actuarial Science Internship Program.

ACSC 042 - Actuarial Science Internship Term 2

Second Term of Actuarial Science Internship Program.
*** Prerequisite: ACSC 041 ***

ACSC 043 - Actuarial Science Internship Term 3

Third term of Actuarial Science Internship Program.
*** Prerequisite: ACSC 042 ***

ACSC 044 - Actuarial Science Internship Term 4

Fourth term of Actuarial Science Internship Program.
*** Prerequisite: ACSC 043 ***

ACSC 116 - Mathematics of Finance I

This course provides a basis of financial mathematics. Topics include measurement of interest, basic and general annuities, yield rates, amortization schedules, and sinking funds.
***Prerequisite: MATH 103 or 110***
*Note: Students can receive credit for only one of MATH 116 and ACSC 116*

ACSC 216 - Mathematics of Finance II

This course is a continuation of Mathematics of Finance I and covers more advanced topics ranging from the theory of interest to principles of corporate finance. Specific topics include bonds, securities, analysis of risk and basic principles of pricing theory.
***Prerequisite: ACSC 116 or MATH 116***
*Note: Students can receive credit for only one of MATH 216 and ACSC 216*

ACSC 217 - Introduction to Actuarial Mathematics

Topics include: economics of insurance, applications of probability to problems of life insurance, life annuities, and life tables.
***Prerequisite: ACSC 116 or MATH 116, and STAT 251.***
*Note: Students may receive credit for only one of ACSC 217 or STAT 217.*

ACSC 300 - Statistical Learning and Predictive Modeling

Selected topics and techniques in statistical learning and predictive modeling, including linear models, logistic regression models, regression trees, classification models and statistical software.
***Prerequisite: MATH 122, STAT 252, and CS 110***
*Note: Students can receive credit for only one of ACSC 300 and STAT 300*

ACSC 316 - Mathematics of Finance III

This course covers the theory and pricing of financial derivatives such as Puts and Calls, with particular emphasis on the Black-Scholes model.
***Prerequisite: ACSC 216 or MATH 216, and STAT 251***
*Note: Students can receive credit for only one of MATH 316, STAT 316, and ACSC 316.*

ACSC 317 - Actuarial Models I

Probabilistic and deterministic contingency mathematics in life insurance and pensions. Topics include: benefit premiums, benefit reserves, multiple life functions, and multiple decrement models.
***Prerequisite: ACSC 217 or STAT 217***
*Note: Students may receive credit for only one of ACSC 317 or STAT 317*

ACSC 318 - Actuarial Models II

This course introduces collective risk models over an extended period. Stochastic processes are introduced, followed by definition and application of Markov chains. Introductory loss model material is also presented.
***Prerequisite: ACSC 317 or STAT 317***
*Note: Students may receive credit for only one of ACSC 318 or STAT 318*

ACSC 390AA - Canadian Pension Plan Review

A review of Canadian Pension Plans with an emphasis on actuarial mathematics.

ACSC 390AB - Intro. Stoch. Actuarial Models

An introduction to the use of Stochastic Models to solving actuarial problems.
*** Prerequisite: ACSC 317 and STAT 351 ***

ACSC 390AC - Mathematics of Finance III - Derivative Pricing

Covers the pricing of European and American style options on investment vehicles including stocks, currencies, commodities and indices. Methods used include the Black-Scholes and binomial tree and other models. Interest rate models will also be covered.
***Prerequisite: ACSC 216 and STAT 251***
**Corequisite: ACSC 318**

ACSC 390AD - Topics in Property & Casualty Insurance

This class is intended to give students an introduction to Property and Casualty insurance and actuarial applications with respect to P&C insurers in Canada. Topics will be selected from the following: Products and Marketplace, Regulatory and Legal Environments, Underwriting, Actuarial Pricing models, Actuarial Valuation models, and Financial Reporting.
***Prerequisite: ACSC 217***

ACSC 416 - Introduction to Financial Enterprise Risk Management

This course aims to provide students with an introduction to financial enterprise risk management. Topics include risk classification, quantitative risk analysis, scenario generation, risk aggregation, risk measures and economic capital, and capital allocation.
***Prerequisite: ACSC 316.***

ACSC 417 - Introduction to Casualty Insurance and Credibility

An introduction to property/casualty loss reserving techniques. Topics include: reserves in casualty insurance, ratemaking process, credibility and ruin theory.
***Prerequisite: ACSC 317.***

ACSC 418 - Time Series Analysis and Forecasting

This course aims to introduce various statistical models for time series and cover the main methods for analysis and forecasting. Topics include: Deterministic time series: Trends and Seasonality; Random walk models; Stationary time series: White noise processes, Autoregressive (AR), Moving Average (MA), Autoregressive Moving Average (ARMA) models; Estimation, Diagnosis and Forecasting with various time series models; computer programming for Time Series Analysis.
***Prerequisite: STAT 354***
*Note: Students may receive credit for only one of ACSC 418 or STAT 418*

ACSC 419 - Estimation and Selection of Actuarial Models

This course continues topics relating to loss models covered in ACSC 318, and includes estimating the parameters for severity, frequency, and aggregate distributions using Maximum Likelihood Estimation as well as Bayesian estimation. The topic of model selection is also considered.
***Prerequisite: ACSC 318 and STAT 351***

ACSC 456 - Applied Stochastic Processes

An introduction to stochastic processes; Markov chains; Poisson processes; renewal processes; Brownian motion; simulation.
***Prerequisite: STAT 351.***
*Note: Credit can be earned for only one of ACSC 456, STAT 456, or STAT 856.*

MATH 051 - Mathematics Co-op Work Term

Four-month co-op work term approved by the department and arranged by the co-op coordinator.

MATH 052 - Mathematics Co-op Work Term

Four-month co-op work term #2 approved by the department and arranged by the co-op coordinator.
*** Prerequisite: MATH 051 ***

MATH 053 - Mathematics Co-op Work Term

Four month co-op work term #3 approved by the department and arranged by the co-op coordinator.
*** Prerequisite: MATH 052 ***

MATH 054 - Mathematics Co-op Work Term

Four month co-op work term #4 approved by the department and arranged by the coop coordinator.
*** Prerequisite: MATH 053 ***

MATH 101 - Introductory Finite Mathematics I

This is an introductory course intended to familiarize the students with the basic concepts of arithmetic, number theory, set theory, symbolic logic, and finite mathematics. Topics include logic, sets, numeration systems, arithmetic in non-decimal systems, system of integers, elementary number theory and modular arithmetic. There will be a strong emphasis on critical thinking, problem solving, understanding concepts and their applications.
***Prerequisite: University Admission.***
*Note: Students who have received credit for any mathematics or statistics course (other than MATH 108) cannot take this class for credit, unless it is explicitly required in their program or they have received consent from the Head of the Department of Mathematics and Statistics.*

MATH 102 - Mathematical Modelling and Precalculus

A course in problem solving through the use of mathematical models involving algebraic, exponential, logarithmic, and trigonometric functions and their graphs. The purpose of this course is to enhance students’ abilities to express, visualize, and model real-world problems through an understanding of common functions and their graphs.
***Prerequisite: Any one of the following: Foundations of Mathematics 30, Precalculus 20, Math B30, Math C30, or AMTH 092***
*Note: Students who have received credit in Math 103 or 110 cannot take Math 102 for credit*

MATH 103 - Applied Calculus I

Differentiation of algebraic, exponential, and logarithmic functions. Optimization, curve sketching, and integration by substitution.
***Prerequisite: Precalculus 30 or Mathematics B30 with a grade of at least 65%, or PMTH 092 with a grade of at least 70%, or Math102***
*Note: Although Math 103 leads to Math 112, students who require three or more calculus-based courses should take Math 110 instead of Math 103. Students will only receive credit for one of MATH 103 or 110*

MATH 108 - Mathematical Problems, Ideas and Personalities

This course explores some of the most significant and enduring ideas in mathematics: the great theorems, discoveries of beauty and insight that stand today as monuments to the human intellect.
*** Prerequisite: Precalculus 20 or Foundations of Math 20 or Math A30 or AMTH 092***
* Note: This course is designed mainly for students in arts or education who wish some exposure to mathematical ideas. It satisfies the critical thinking requirement in the Faculty of Arts.

MATH 110 - Calculus I

An introductory class in the theory and techniques of differentiation and integration of algebraic and trigonometric functions. Topics include limits, optimization, curve sketching, and areas.
***Prerequisite: Precalculus 30 with at least 75%, or Calculus 30 or Mathematics B30 and C30 with a grade of at least 65% in each or Math 102***
*Note: Students can receive credit for only one of MATH 103 or 110*

MATH 111 - Calculus II

Differentiation and integration of exponential and logarithmic functions; methods of integration and applications; indeterminate forms, L'Hospital's rule and improper integrals; sequences, series, power series and Taylor series.
***Prerequisite: MATH 110, or MATH 103 with a grade of at least 80%***

MATH 112 - Applied Calculus II

An introduction to calculus in two and three variables, first-order differential equations, infinite series, and calculus of trigonometric functions.
***Prerequisites: MATH 103 and Precalculus 30, or MATH 110***
*Note: MATH 112 is a terminal course and is not intended for students who require further calculus courses. Students will receive credit for only one of MATH 111 and 112*

MATH 116 - Mathematics of Finance I

his course provides a basis of financial mathematics. Topics include measurement of interest, basic and general annuities, yield rates, amortization schedules, and sinking funds.
***Prerequisite: MATH 103 or 110.***
*Note: Students can receive credit for only one of MATH 116 and ACSC 116*

MATH 122 - Linear Algebra I

A course intended to introduce students to elementary linear algebra, particularly at a computational and applied level. Topics include matrices and systems of equations, inversion, determinants, vectors, inner products, eigenvectors and eigenvalues.
***Prerequisite: Precalculus 30, Mathematics B30 and C30, or Math 102.***

MATH 124 - The Art and Science of Secret Writing

The course examines methods of message encryption and cryptoanalysis. Attention will be given to the history of cryptology and the public-policy questions raised by its use in conjunction with the Internet. However, the focus will be on the mathematical tools needed to develop and analyze encryption algorithms.
*** Prerequisites: Foundations of Math 30 or Precalculus 20 or Math B30 or AMTH 092 ***

MATH 127 - Introductory Finite Mathematics II

Elementary linear programming, counting methods involving permutations and combinations, probability, statistics, regression, and consumer mathematics including interest calculations, annuities and amortizations.
***Prerequisite: Foundations of Math 20 or Precalculus 20 or Math B30 or AMTH 092 or MATH 101***
*Note: Mathematics 127 is not algebra, nor pre-calculus, nor calculus. It satisfies the critical thinking requirement in the Faculty of Arts.*
*Note: Students outside of the Faculty of Education cannot take this course for credit if they have received credit for a MATH, STAT, or ACSC course above 200.*

MATH 184 - Problem Solving Techniques

A course providing hands-on training in mathematical problem solving, with a view towards preparing for the Putnam Competition. However, participation in the Putnam is not a requirement. The course covers strategies to tackle problems, as well as selected topics from algebra, combinatorics, number theory, geometry, and analysis.
***Prerequisite: Precalculus 30 with at least a 75%; or Calculus 30; or Mathematics B30 and C30 with a grade of at least 65% in each; or MATH 102.***
*Note: This course carries only one credit hour.*

MATH 213 - Vector Calculus

A study of vector functions and functions of several variables and their derivatives; Applied maximum and minimum problems, Lagrange multipliers, multiple integration, integration in polar, cylindrical and spherical coordinates; Green's, Stokes' and the Divergence Theorem.
***Prerequisite: MATH 111 and 122***

MATH 216 - Mathematics of Finance II

This course is a continuation of Mathematics of Finance I and covers more advanced topics ranging from the theory of interest to principles of corporate finance. Specific topics include bonds, securities, analysis of risk and basic principles of pricing theory.
***Prerequisite: MATH 116 or ACSC 116***
*Note: Students can receive credit for only one of Math 216 and ACSC 216*

MATH 217 - Differential Equations I

Ordinary differential equations, modelling with differential equations, Laplace transforms.
***Prerequisite: MATH 111 and MATH 122***

MATH 221 - Introduction to Proofs and Problem Solving

An introductory course intended to familiarize students with mathematical reasoning and proof techniques, including direct reasoning, indirect reasoning, and mathematical induction. Topics include elementary number theory, logic, sets, functions, and relations.
***Prerequisite: Two university math courses beyond MATH 102.***

MATH 222 - Linear Algebra II

A second course in linear algebra. There will be some emphasis on proofs. Topics include matrices, abstract vector spaces, subspaces, bases, inner product spaces, linear transformations, matrix factorizations, symmetric matrices, quadratic forms, and applications of linear algebra.
***Prerequisite: MATH 122, and one of MATH 103 or 110.***

MATH 223 - Introduction to Abstract Algebra

An introductory course in abstract algebra. Topics include number systems and an introduction to groups, and some other mathematical structures.
***Prerequisite: MATH 221.***

MATH 231 - Euclidean Geometry

This course is intended to familiarize the student with Euclidean geometry. Topics include the postulates and theorems of both classical and modern Euclidean geometry.
***Prerequisite: MATH 221***
*Note: This course is designed for students without a strong background in Euclidean geometry. Students with a mark of at least 70% in either Mathematics C30 or Precalculus 30 should register in MATH 331*

MATH 251 - Introduction to Probability

Basic notions of probability; discrete and continuous random variables; expectation; moment generating functions; joint discrete random variables.
***Prerequisites: MATH 111 or MATH 112 and one of STAT 160 or STAT 200***
*Note: Students can receive credit for only one of Math 251 and Stat 251*

MATH 261 - Methods of Numerical Analysis

Topics will include number systems and errors, solutions of polynomial and other nonlinear equations, interpolation, numerical differentiation and integration, and the cubic spline.
***Prerequisite: MATH 111, MATH 122, and CS 110.***
*Note: Students will receive credit for only one of CS 261, CS 345 or MATH 261.*

MATH 284 - Problem Solving Techniques

A course providing hands-on training in mathematical problem solving, with a view towards preparing for the Putnam Competition. However, participation in the Putnam is not a requirement. The course covers strategies to tackle problems, as well as selected topics from algebra, combinatorics, number theory, geometry, and analysis.
***Prerequisite: MATH 184 or permission of the instructor.***
*Note: This course carries only one credit hour.*

MATH 300 - Introduction to Set Theory

Sets, relations, and operations on them. Natural numbers. Finite and infinite sets, ordinals and cardinals. Recursion theorems. Arithmetic of cardinals and ordinals. A brief introduction to set-theoretic topology. Construction of the real numbers and basic properties.
***Prerequisite: MATH 221.***

MATH 301 - Introduction to Mathematical Logic

Propositional and first-order predicate logic from a mathematical viewpoint. Axiomatically built theories and their models. Detailed study of one or more simple mathematical theories. Recursive functions. Basic ideas of automated theorem proving.
***Prerequisite: MATH 221.***

MATH 305 - Introductory Mathematical Analysis

Cardinality, real numbers and their topology, sequences, limits, continuity, and differentiation for functions of one real variable.
***Prerequisite: MATH 221 and 111.***
*Note: This course is designed for students interested in majoring in Mathematics. Students considering a degree in Mathematics with Honours are encouraged to complete this course by the end of their second year.*

MATH 308 - Topics in the History of Mathematics

A survey of the history of mathematics, focusing on mathematics developed before 1850. Topics may include mathematics of ancient cultures, cultural aspects of mathematics, how mathematics developed around the world, famous mathematicians and classical mathematics texts. This course is designed for majors in mathematics or mathematics education with a solid background in mathematics. It will be offered in the winter semester, alternating with MATH 309.
***Prerequisite: MATH 111, 122, and 221.***

MATH 309 - Topics in Modern Mathematics

A survey of modern mathematics, examining the objectives of mathematical advancement, important modern results in mathematics, mathematicians of the modern era, and the influences of modern mathematics on contemporary science. The focus of this course will be on mathematics after Gauss (post 1850). The emphasis will be on general modern approaches to mathematical problems and the philosophy of mathematics, rather than specific results. Topics will include (but are not limited to): the nature of mathematical knowledge, origins of modern mathematics, biographies of mathematicians and the influence of mathematics on contemporary science.
***Prerequisite: MATH 111, 122 and 221.***
*Note: This course is designed for majors in mathematics or mathematics education with a solid background in mathematics. It will be offered in the winter semester, alternating with MATH 308.*

MATH 312 - Complex Analysis I

Complex numbers, analytic functions, contour integration, Cauchy's theorem, infinite series, calculus of residues, basic theory of conformal mappings.
***Prerequisite: MATH 213.***

MATH 313 - Mathematical Analysis II

The Riemann integral for functions of one variable, sequences and series of functions, differentiation and integration for functions of several variables.
***Prerequisites: MATH 213 and MATH 305.***

MATH 316 - Mathematics of Finance III

This course covers the theory and pricing of financial derivatives such as Puts and Calls, with particular emphasis on the Black-Scholes model.
***Prerequisite: ACSC 216 or MATH 216, and STAT 251***
*Note: Students can receive credit for only one of MATH 316, STAT 316, and ACSC 316.*

MATH 317 - Real Analysis

Construction of the real numbers, structure of metric spaces, continuous functions on metric spaces, convergence of series, differential equations.
***Prerequisite: MATH 217 and 313.***

MATH 321 - Number Theory I

This is an introductory course in number theory. Topics include divisibility, primes, congruences, number theoretic functions, and diophantine equations.
***Prerequisite: MATH 221***

MATH 322 - Matrix Theory

Topics include: positive definiteness, Jordan canonical form, nonnegative matrices, and applications in matrix analysis.
***Prerequisite: MATH 222.***

MATH 323 - Modern Algebra I

A course in abstract algebra dealing with groups, rings, unique factorization domains and fields.
***Prerequisite: MATH 223.***

MATH 327 - Introductory Combinatorics

A first course in Combinatorics. Topics include counting, permutations and combinations, inclusion and exclusion, binomial theorem and identities with binomial coefficients, generating functions and recurrence relations, and a brief introduction to design theory.
***Prerequisite: MATH 221 and 111.***

MATH 328 - Introduction to Graph Theory

A first course in Graph Theory. Topics include isomorphism, Graph Algorithms, Trees, Digraphs and Networks, Planar graphs, Connectivity, Independence number, cliques and graph colouring.
***Prerequisite: MATH 221 and 111.***

MATH 329 - Linear and Discrete Optimization

A course in the theory and techniques of linear programming; convexity and extreme points of polyhedral sets, the simplex method, duality and selected applications will be covered.
***Prerequisite: CS 110, MATH 122 and MATH 221 or permission of Department Head.***

MATH 331 - Non-Euclidean Geometry

This course gives an explaination of the nature and foundations of geometry and uses for this purpose the systems of non-Euclidean geometry. It outlines the concept of mathematical models and the historical and logical significance of the parallel postulate.
***Prerequisite: MATH 110, and one of MATH 122 or MATH 231.***
*Note: Students may receive credit for only one of Math 232 and Math 331.*

MATH 335 - Introduction to Differential Geometry

Differential invariants of curves and surfaces in Euclidean three-space.
***Prerequisite: MATH 217.***

MATH 361 - Numerical Analysis I

Least squares and other approximations. Difference equations. Solutions of algebraic systems. Symbol manipulators.
***Prerequisite: MATH 213 and either MATH 261 or CS 261.***

MATH 381 - Differential Equations II

Series solutions of linear equations, systems of linear first-order equations, Fourier series, boundary-value problems, integral transforms, and numerical methods.
***Prerequisite: MATH 217.***

MATH 382 - Ordinary Differential Equations

Existence and uniqueness of solutions, linear systems, non-linear equations, stability, Liapunov's method, applications.
***Prerequisite: MATH 217.***

MATH 384 - Problem Solving Techniques

A course providing hands-on training in mathematical problem solving, with a view towards preparing for the Putnam Competition. However, participation in the Putnam is not a requirement. The course covers strategies to tackle problems, as well as selected topics from algebra, combinatorics, number theory, geometry, and analysis.
***Prerequisite: MATH 284 or permission of the instructor.***
*Note: This course carries only one credit hour.*

MATH 395AB - Directed Readings in Probability Theory

Selected advanced topics concerning multivariate random variables and distributions, and stochastic processes.
***Permission of the Department Head is required to register***

MATH 401 - Matrix Groups

An introduction to Lie group theory through study of the classical groups.
*** Prerequisite: MATH 305 and 323 ***

MATH 411 - Measure and Integration

Measurable functions, Lebesgue integrals, Lp spaces, modes of convergence, signed measures, Radon-Nikodym Theorem.
***Prerequisite: MATH 313.***

MATH 412 - Complex Analysis II

This is a continuation of MATH 312. Topics include conformal mappings, argument principle, Rouche's theorem, harmonic functions, Riemann Mapping Theorem, infinite products, asymptotic expansions.
***Prerequisite: MATH 312.***

MATH 416 - Introduction to Quantum Information Theory

A first course in the mathematics of quantum information theory. Topics include information measures, quantum states and observables, qubits, entanglement, quantum channels, entropy, and measurements.
***Prerequisite: MATH 305 or MATH 312 or MATH 322, or permission of the Department Head***

MATH 418 - Introduction to Lie Algebras and Representation Theory

This course is an introduction to the structure of finite dimensional complex semisimple Lie algebras, via root systems, as well as their finite dimensional irreducible representations, through highest weight modules.
***Prerequisites: MATH 222 and 323***
*Note: Students can only receive credit for one of MATH 418, 495AD, and MATH 818.*

MATH 420 - Introduction To Commutative Algebra

A first course in commutative algebra. Topics include prime and maximal ideal, radicals, Nakayama's Lemma, exact sequences, tensor products, localization, Noetherian and Artinian rings. Additional topics may vary. This class is designed for advanced students in disciplines such as Mathematics and Computer Science who want to learn some commutative algebra.
***Prerequisite: MATH 222 and MATH 323***

MATH 421 - Number Theory II

This course is a second course in number theory. Topics include quadratic reciprocity, arithmetic functions, distribution of primes, and the prime number theorem.
***Prerequisite: MATH 321, 305, and 312.***

MATH 422 - Abstract Linear Algebra

A course which presents linear algebra in a theoretical setting. Topics include vector spaces, dual spaces, linear transformations, Jordan canonical form, the spectral theorem, and selected topics.
***Prerequisite: MATH 222 and MATH 323. ***

MATH 423 - Modern Algebra II

Continuation of Modern Algebra I with further study of rings, groups and fields.
***Prerequisite: MATH 323.***

MATH 424 - Applied Algebra

This is a course in applications of algebra to a selection of topics concerning enumeration, coding, finite state machines and cryptography.
***Prerequisite: MATH 223.***

MATH 425 - Matrix Analysis

A survey of some of the important topics from Matrix Theory with emphasis on matrix canonical forms, norms, spectral theory, perturbation theory of matrices, and special classes of matrices
***Prerequisite: MATH 305, MATH 322, and MATH 323.***

MATH 426 - Combinatorial Matrix Theory

A survey of some of the topics from combinatorial matrix theory including: spectral graph theory and algebraic graph theory.
***Prerequisite MATH 222 and 328.***

MATH 427 - Graph Theory

This course is a survey of topics in graph theory. Topics may include the following: matchings and factorizations, connectivity, colouring, isomorphisms, homomorphisms, automorphism groups and transitive graphs, extremal problems, adjacency matrices, spectral graph theory, strongly regular graphs, Cayley graphs, Ramsey theory and random graphs
***Prerequisite: MATH 223 and 328.***

MATH 431 - Differential Geometry I

Differentiable manifolds, the tangent bundle, differential forms, and the general Stokes' theorem.
***Prerequisite: MATH 313 or MATH 335.***

MATH 438 - Associative Algebras, Groups, and Representation Theory

An introductory course on the fundamental results concerning associative algebras, groups, and the representation theory of groups and algebras.
***Prerequisite: MATH 222 and MATH 323***

MATH 441 - General Topology

An introduction to point set topology including separation axioms, compactness, connectedness, continuous functions and metric spaces.
***Prerequisite: MATH 305.***

MATH 442 - Algebraic Topology

A first course in algebraic topology. Topics include, homotopy type, more detailed information on the fundamental group, and the homology and cohomology of topological spaces.
***Prerequisite MATH 441, or approval of the department chair.***

MATH 443 - Homological Algebra

A first course in homological algebra. Topics include modules over rings, chain complexes, homology, projective and injective resolutions, derived
functors, abelian categories, derived categories, and selected additional topics
***Prerequisite: MATH 222 and MATH 323.***
*Note: Students may receive credit for one of MATH 443 or MATH 843.*

MATH 461 - Numerical Analysis II

Numerical solutions of ordinary differential equations; numerical solutions of partial differential equations; linear and non-linear problems.
***Prerequisite: MATH 361 or CS 361.***

MATH 481 - Partial Differential Equations

Classification and basic properties of equations, separation of variables, Fourier series, Sturm-Liouville theory, Fourier and Laplace transforms.
***Prerequisite: MATH 381.***

MATH 482 - Laplace Transforms

Properties of the Laplace Transform. Convolutions. The inversion integral. Applications to solutions of differential equations.
*** Prerequisite: MATH 217 and 312.***

MATH 485 - Introduction to Functional Analysis

Metric, normed linear and inner-product spaces, linear operators and fixed point theorems. Spectral decompositions the Stone-Weierstrass theorem, applications.
***Prerequisite: MATH 312 and 313.***

MATH 495AB - Topology II

Topology II consists of Tietze extension theorem, Urysohn metrization theorem, tychonoff theorem, compact metric spaces.

MATH 495AC - Introduction to Continuum Mechanics

his course is an introduction to the physical concepts and mathematical methods of continuum mechanics with the aim of preparing the student for further studies and research in fluid dynamics.

***Prerequisite: MATH 381***

MATH 495AE - Introduction to von Neumann algebras

In this course we introduce von Neumann algebras and we emphasize connections with ergodic&group theory. We present constructions of von Neumann algebras from groups&actions; explain how group theoretical aspects (e.g. amenability) and orbit equivalence are connected to von Neumann algebras. We assume no background except basic knowledge of real analysis.

MATH 497 - Honours Seminar I

This is the first of two honours seminars. This course must be taken by all honours students in their fourth year. Students are required to attend the seminars and to work in consultation with an assigned supervisor on an independent research project. To receive credit for MATH 497, students must present a seminar on their preliminary work.
*Note: This seminar is restricted to honours standing students in mathematics.*

MATH 498 - Honours Seminar II

This is the second of two honours seminars. This course must be taken by all honours students in their fourth year. Students are required to attend the seminars and to work in consultation with an assigned supervisor on an independent research project. To receive credit for MATH 498, students must present their project in both written form and as a seminar.
*Note: This seminar is restricted to honours standing students in mathematics.*

STAT 051 - Statistics Co-op Work Term #1

Four-month co-op work term #1 approved by the department and arranged by the co-op coordinator.

STAT 052 - Statistics Co-op Work Term #2

Four-month co-op work term #2 approved by the department and arranged by the co-op coordinator.
*** Prerequisite: STAT 051 ***

STAT 053 - Statistics Co-op Work Term #3

Four-month co-op work term #3 approved by the department and arranged by the co-op coordinator.
*** Prerequisite: STAT 052 ***

STAT 054 - Statistics Co-op Work Term #4

Four-month co-op work term #4 approved by the department and arranged by the co-op coordinator.
*** Prerequisite: STAT 053 ***

STAT 100 - Elementary Statistics for Applications

An introduction to statistical methods; descriptive statistics; the normal distribution; basic techniques of statistical inference; confidence intervals and hypothesis tests for population means and proportions; simple linear regression; and one-way analysis of variance.
***Prerequisite: Foundations of Math 20 or Precalculus 20 or Apprenticeship & Workplace Math 30 or MATH A30 or AMTH 091 or MATH 101***
*Note: STAT 100 and STAT 200 are designed to provide a year-long introduction to statistical methodology with a view towards applications and are not intended for majors in statistics, actuarial science, or any other program requiring a detailed knowledge of statistics. Students who receive credit for STAT 100 may not receive credit for STAT 160*

STAT 160 - Introductory Statistics

A comprehensive introduction to probability, probability distributions, sampling distributions, basic techniques of statistical inference, analysis of variance, linear regression, inference for categorical variables, and nonparametric statistics. ***Prerequisite: Precalculus 30, or MATH B30 and MATH C30, or MATH 127***
*Note: STAT 160 is designed to provide a comprehensive single semester introduction to statistical techniques and is intended for students majoring in statistics, actuarial science, or any other program requiring a detailed knowledge of statistics. Students who receive credit for STAT 160 may not receive credit for STAT 100 or STAT 200*

STAT 165 - Introduction to Programming with Python

An introduction to problem-solving techniques using Python. This course will introduce fundamental programming principles and topics: data types, expressions, control structures, elementary data structures, functions, files, and the mechanics of running, testing and debugging. These concepts will be applied to problem solving and applications in data analysis.
***Prerequisite: Foundations of Mathematics 30, Precalculus 20, Math B30, Math C30, or PMTH 092.***
*Note: Students may receive credit for one of CS 165 or STAT 165.*

STAT 200 - Intermediate Statistics for Applications

A continuation of STAT 100; inference for two categorical variables; basic multiple linear regression; two-way analysis of variance; introduction to nonparametric methods; statistical process control; introduction to survey design.
***Prerequisite: STAT 100***
*Note: STAT 100 and STAT 200 are designed to provide a year-long introduction to statistical methodology with a view towards applications and are not intended for majors in statistics, actuarial science, or any other program requiring a detailed knowledge of statistics. Students who receive credit for STAT 200 may not receive credit for STAT 160*

STAT 217 - Introduction to Actuarial Mathematics

Topics include: economics of insurance, applications of probability to problems of life insurance, life annuities, and life tables.
***Prerequiste: ACSC 116 or MATH 116, and STAT 251***
*Note: Students may receive credit for only one of ACSC 217 or STAT 217*

STAT 251 - Introduction to Probability

Basic notions of probability; discrete and continuous random variables; expectation; moment generating functions; joint discrete random variables.
***Prerequisites: MATH 111 or MATH 112 and one of STAT 160 or STAT 200***
*Note: Students can receive credit for only one of Math 251 and Stat 251*

STAT 252 - Introduction to Statistical Inference

Sampling distribution theory and the Central Limit Theorem; large sample theory; methods of estimation and hypothesis testing including maximum likelihood estimation, likelihood ratio testing, and confidence interval construction. ***Prerequisite: STAT 251.***

STAT 289 - Statistics for Engineers

Topics include probability, discrete and continuous distributions, the central limit theorem, confidence intervals and hypothesis tests for one and two samples, linear regression and correlation.
***Prerequisite: MATH 111***
*Note: Designed for engineering students. Students who received credit for STAT 289 may not receive credit for STAT 100, 160, or 200.

STAT 300 - Statistical Learning and Predictive Modeling

Selected topics and techniques in statistical learning and predictive modeling, including linear models, logistic regression models, regression trees, classification models and statistical software.
***Prerequisite: MATH 122, STAT 252, and CS 110***
*Note: Students can receive credit for only one of ACSC 300 and STAT 300*

STAT 301 - Introduction to Statistical Computing

This course aims to provide students with an introduction to statistical computing. Topics include the basics of programing for statistics, data visualization, simulation of random variables, numerical optimization, statistical inference, and selected additional topics.
***Prerequisite: MATH 122, STAT 252, and CS 265.***

STAT 316 - Mathematics of Finance III

This course covers the theory and pricing of financial derivates such as Puts and Calls, with particular emphasis on the Black-Scholes model.
***Prerequisite: ACSC 216 or MATH 216, and STAT 251***
*Note: Students can receive credit for only one of MATH 316, STAT 316 and ACSC 316*

STAT 317 - Actuarial Models I

Probabilistic and deterministic contingency mathematics in life insurance and pensions. Topics include: benefit premiums, benefit reserves, multiple life functions, and multiple decrement models.
***Prerequisite: ACSC 217 or STAT 217***
*Note: Students may receive credit for only one of ACSC 317 or STAT 317*

STAT 318 - Actuarial Models II

This course introduces collective risk models over an extended period. Stochastic processes are introduced, followed by definition and application of Markov chains. Introductory loss model material is also presented.
***Prerequisite: ACSC 317 or STAT 317***
*Note: Students may receive credit for only one of ACSC 318 or STAT 318*

STAT 342 - Biostatistics

This course will present relevant, up-to-date coverage of research methodology using careful explanations of basic statistics and how they are used to address practical problems that arise in the medial and public health settings. Through this course, students will learn to interpret and examine data by applying common statistical tools to the biostatistical, medical, and public health fields.
***Prerequisite: STAT 160 or STAT 200.***
*Note: Students with credit in BIOL 341 cannot take STAT 342 for credit.*

STAT 351 - Intermediate Probability

Multivariate random variables; conditioning; order statistics; the multivariate normal distribution; the Poisson process.
***Prerequisite: MATH 213 and STAT 251.***

STAT 354 - Linear Statistical Methods

Simple linear regression; multiple linear regression; diagnostics and remedial measures for regression models; remedial measures and alternative regression techniques; multicollinearity diagnostics.
***Prerequisite: STAT 252 and CS 110 and MATH 122.***

STAT 357 - Sampling Theory

Simple random sampling; systematic sampling; stratified and cluster sampling; ratio and regression estimators.
***Prerequisite: STAT 252 and CS 110.***

STAT 362 - Bayesian Statistics

An introduction to Bayesian methods; Bayesian inference for discrete random variables, binomial proportions, and normal means; comparisons between Bayesian and frequentist inferences; robust Bayesian methods.
***Prerequisite: STAT 252 and CS 110.***

STAT 384 - Categorical Data Analysis

Odds ratio; two-way and higher-way contingency tables; Chi-squared tests of independence; loglinear and logit models; multinomial response models; models for matched pairs.
***Prerequisite: STAT 252 and CS 110.***
*Note: It is suggested that students register for STAT 354 concurrently if possible.*

STAT 386 - Nonparametric Statistical Methods

Nonparametric statistics for data analysis including rank-based methods, bootstrap methods, and permutation tests; one-sample and two-sample methods; paired comparisons and blocked designs; tests for trends and association; smoothing methods and robust model fitting.
***Prerequisite: STAT 252 and CS 110.***

STAT 418 - Time Series Analysis and Forecasting

This course aims to introduce various statistical models for time series and cover the main methods for analysis and forecasting. Topics include: Deterministic time series: Trends and Seasonality; Random walk models; Stationary time series: White noise processes, Autoregressive (AR), Moving Average (MA), Autoregressive Moving Average (ARMA) models; Estimation, Diagnosis and Forecasting with various time series models; computer programming for Time Series Analysis.
***Prerequisite: STAT 354***
*Note: Students may receive credit for only one of ACSC 418 or STAT 418*

STAT 426 - Survival Analysis

Life tables; survival distributions; types of censoring; estimation of and interface for basic survival quantities; proportional hazards regression model; planning and design of clinical trials.
***Prerequisite: STAT 351.***

STAT 441 - Stochastic Calculus with Applications to Finance

Processes derived from Brownian motion; the Itô integral and Itô's formula; applications of Itô's formula in financial modelling, especially within the context of the Black-Scholes option pricing model.
***Prerequisite: STAT 351.***

STAT 451 - Advanced Probability

Probability measures; distribution functions; sequences of random variables; characteristic functions; modes of convergence; convergence theorems; weak and strong laws of large numbers; Central Limit Theorem.
***Prerequisite: STAT 351.***

STAT 452 - Advanced Statstical Inference

Detailed theoretical development of statistical inference; statistical models; exponential families; sufficiency; completeness; properties of point estimation; testing hypotheses and confidence regions; asymptotic properties of estimators. ***Prerequisite: STAT 351 and STAT 252.***

STAT 454 - Applied Multivariate Analysis

Review of multivariate normal distribution; inferences about a mean vector; multivariate linear regression analysis; principal components; factor analysis; canonical correlation analysis.
***Prerequisite: STAT 351 and STAT 354.***

STAT 456 - Applied Stochastic Processes

An introduction to stochastic processes; Markov chains; Poisson processes; renewal processes; Brownian motion; simulation.
***Prerequisite: STAT 351.***
*Note: Credit can be earned for only one of STAT 456, ACSC 456, or STAT 856.*

STAT 470 - Bootstrap Methods

A first course in Bootstrap techniques. Topics include bootstrap and jackknife procedures, confidence intervals, hypothesis testing, standard errors, regression models. Additional topics may vary.
***Prerequisite: STAT 351 and STAT 354***
*Note: Credit cannot be received for both STAT 470 and STAT 870*

STAT 472 - Large Sample Methods

Asymptotic behavior of estimators and test statistics, asymptotic relative efficiency, large sample theory for regression models.
***Prerequisite: STAT 351.***
*Note: Students may receive credit for one of STAT 472 or STAT 495AE.*

STAT 485 - Design and Analysis of Experiments

Theory and application of analysis of variance for standard experimental designs including blocked, nested, factorial, Latin square, and split-plot designs; fixed and random effects; multiple comparisons; analysis of covariance.
***Prerequisite: STAT 354***

STAT 489 - Statistical Consulting and Communications

This course aims to provide students with an understanding of the nature of applied statistical consulting and skills for communicating technical statistical contents with non-statisticians. Topics include the general principles for solving statistical problems, oral and written communication skills, ethics, and collaborative project.
***Prerequisite: STAT 301 and STAT 354.***

STAT 495AC - Readings in Mathematical Finance

This course presents a selection of readings in the theory of mathematical finance, as chosen by the instructor.
*** Prerequisite: STAT 351 with a minimum grade of 80% ***

STAT 495AD - Topics in Probability Theory

In depth study of selected topics in probability theory.
***Prerequisite: STAT 451 ***

STAT 496 - Data Science Capstone

This is a capstone course for data science majors. This course aims to enhance students’ competencies by applying data scientific methodologies to the challenges imposed by real data and skills to effectively communicate project requirements and findings. This course also covers ethical issues and responsible practices in data science.
***Prerequisite: STAT 300, STAT 301, STAT 354, CS 280, and one of CS 412 or CS 465.***

STAT 497 - Honours Seminar

This is the first of two honours seminars. This course must be taken by all honours students in their fourth year. Students are required to attend the seminars and to work in consultation with an assigned supervisor on an independent research project. To receive credit for STAT 497, students must present a seminar on their preliminary work.
*Note: This seminar is restricted to honours standing students in statistics.*

STAT 498 - Honours Seminar

This is the second of two honours seminars. This course must be taken by all honours students in their fourth year. Students are required to attend the seminars and to work in consultation with an assigned supervisor on an independent research project. To receive credit for STAT 498, students must present their project in both written form and as a seminar.
*Note: This seminar is restricted to honours standing students in statistics.*