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Undergraduate Course Offerings for 22/23
Departmental course information is provided for your convenience only. Schedules - including times and locations of classes are subject to change and should be confirmed on LORIS under the Student Services tab by accessing the link for Registration. All official academic information, including prerequisites and exclusions, can be found in the academic calendars.
As far as possible, the department attempts to provide a full range of core courses and electives. However, every course listed in this section is not available in every session or every year. Students are encouraged to consult the department to inquire about course offerings each year.
Unless otherwise specified, classes take place on Laurier's Waterloo campus. If no faculty member is named, the instructor is to be announced.
If you would like to take more than 2.5 credits in one term, you will have to fill out a Request for Course Overload Form.
* = Full-year course.
† = Course offered every second or third year.
†† = Course offered occasionally.
View course outlines, organized by term and includes graduate courses.
100-Level Courses
This course provides a broad overview of modern methods and tools for big data analytics. Different stages of data analytics lifecycle including diagnosing, cleaning, preparing, transforming, visualizing and modelling data are considered. Numerical and graphical methods of descriptive statistics are introduced. Data analytic methods are demonstrated using tools such as Excel, Google spreadsheets, Python and the R package.
Fall 2022
3 lecture hours; 1.5 lab hours
Credits: 0.5
Co-requisites: CP104.
This course concentrates on developing mastery of pre-calculus and introductory calculus skills and techniques. Pre-calculus topics include: solving equations and inequalities; algebraic, trigonometric, logarithmic and exponential functions and their properties. Calculus topics include: rates of change and tangents; differentiation of algebraic, trigonometric, exponential and logarithmic functions; integration; and techniques of integration.
Fall 2022 / Winter 2023
3 lecture hours; 1.5 lab hours
Credits: 0.5
Prerequisites: SC101, or a minimum score of 50% on the Calculus Preparation Evaluation (CPE) and 12U Advanced Functions.
Exclusions: Prior credit for, or current enrolment in, any of MA101, MA102, MA103, MA110*, MA129. This course may not count for credit in Mathematics programs.
Review of algebra and trigonometry. Differential calculus of the algebraic, exponential, logarithmic, trigonometric and inverse trigonometric functions of a single variable; introduction to integral calculus; techniques of integration. Introduction to ordinary differential equations. Polar coordinates. Complex numbers. Applications to problems in the natural sciences are emphasized.
Winter 2023 / Spring 2023
3 lecture hours; 1.5 lab hours
Credits: 0.5
Prerequisites: MA100 or permission of the department.
Exclusions: Prior credit for, or current enrolment in, any of: MA103, MA110*. This course may not count for credit in Mathematics programs.
Rational, algebraic, trigonometric, logarithmic and exponential functions; equations and inequalities involving them. Thorough introduction to limits of functions. Continuity and its consequences. Introduction to differential calculus.
Fall 2022
3 lecture hours; 1.5 lab hours
Credits: 0.5
Prerequisites: Completion of the Calculus Preparation Evaluation (CPE) and 12U Advanced Functions.
Exclusions: Prior credit for, or current enrolment in, any of MA100, MA101, MA103, MA110*, MA129.
Notes: Unlike MA103, MA102 does not have Grade 12 Calculus as a prerequisite.
Limits and continuity; differential and integral calculus of functions of a single variable; the Mean Value Theorem; determination of extrema; the Fundamental Theorem of Calculus and techniques of integration; introduction to series.
Fall 2022 / Winter 2023/ Spring 2023
3 lecture hours; 1.5 lab hours
Credits: 0.5
Prerequisites: MA102, or a minimum score of 75% on the Calculus Preparation Evaluation (CPE) and one of MA100, MA129, Grade 12 Calculus.
Exclusions: MA101, MA110*.
Applications of integration; polar coordinates and parametric equations; infinite sequences and series; applications of partial derivatives.
Fall 2022 / Winter 2023 / Spring 2023
3 lecture hours; 1.5 lab hours
Credits: 0.5
Prerequisites: MA101 or MA103.
Exclusions: MA200.
Introduction to sets, functions and relations; elementary logic including logical connectives; proof techniques and induction; basic number theory and applications; basic counting and combinatorics.
Winter 2023
3 lecture/discussion hours
Credits: 0.5
Exclusions: MA121.
An introduction to proofs and to mathematical writing. Methods of proof, such as direct proofs, proofs by contradiction, contrapositive proofs, counterexamples and mathematical induction. Examples of proofs will be illustrated using sets, functions and elementary number theory. Use of precise mathematical language will be emphasized.
Fall 2023 / Winter 2023 / Spring 2023
Credits: 0.5
3 lecture/discussion hours; 1 lab hour
Prerequisites: 0.5 credit in MA (one of MA101, MA102, MA122, or MA170)
Exclusions: MA120.
Vector geometry in R2 and R3; the vector space Rn and its subspaces; spanning sets, linear independence, bases and dimension; dot product in Rn and Cn; systems of linear equations and Gaussian elimination; matrices and matrix operations; matrix inverse; matrix rank; linear transformations in Rn; introduction to determinants, Cramer's rule; introduction to eigenvalues, eigenvectors and diagonalization of real matrices; applications of linear algebra.
Fall 2023 / Spring 2023
3 lecture hours; 1 lab hours
Credits: 0.5
This course covers the basic mathematical concepts used in business. Topics will include basic algebra; ratios; solving and manipulating equations; functions and graphs; inequalities; introduction to linear algebra and matrices; inverse of a matrix; an introduction to linear programming; simple and compound interest; annuities.
Winter 2023
Brantford Campus
3 lecture/discussion hours, 1.5 tutorial/seminar hours
Credits: 0.5
Prerequisites: Grade 12 U-level math course or equivalent.
Corequisites: Honours Business Technology Management program
Exclusions: This course does not satisfy mathematics requirements outside of the Business Technology anagement program.
Notes: This course should not be counted towards qualifying for a teachable in mathematics.
This course concentrates on developing mastery of pre-calculus and introductory calculus skills and techniques. Pre-calculus topics include: solving equations and inequalities; algebraic, logarithmic and exponential functions and their properties; matrix representation and solution of systems of linear equations. Calculus topics include: rates of change and tangents; differentiation of algebraic, exponential and logarithmic functions; optimization; introduction to integration.
Fall 2023 / Winter 2023 / Spring 2023
3 lecture hours, 1.5 lab hours
Credits: 0.5
Prerequisites: Completion of the Calculus Preparation Evaluation (CPE) and 12U Advanced Functions or permission of the department.
Exclusions: Prior credit for, or current enrolment in, any of: MA100, MA101, MA102, MA103, MA110*. This course may not count for credit in mathematics programs.
An introduction to the theory of interest. Mathematical models and their analysis for problems involving fixed interest rates. Simple and compound interest. Cash flows, annuities, amortization and sinking funds. (Zero-)coupon bonds.
Fall 2022 / Winter 2023 / Spring 2023
3 lecture hours, 1.5 lab hours
Credits: 0.5
Prerequisites: 12U Advanced Functions, or equivalent, or permission of the department.
Thorough review of pre-university skills in algebra, trigonometry and functions. Topics discussed will include: algebraic manipulations used to simplify expressions and solve equations and inequalities; analytic geometry; and polynomial, rational, exponential, logarithmic and trigonometric functions. Also integrated with the course content will be discussion of specific learning strategies to help students with the transition from high school mathematics to university level expectations. The course will not count towards satisfying program requirements in mathematics.
Fall 2023 / Winter 2023
3 lecture hours
Prerequisites: Completion of the Calculus Preparation Evaluation (CPE), and one of: 12U Advanced Functions, 3U Functions and Relations, 3M Functions.
Exclusions: If a student has successfully passed, or is currently enrolled in MA100, MA101, MA103, MA110*, or MA129, then SC101 will not be eligible for credit. This course will not count for credit in mathematics programs. Additionally, the course will not count towards satisfying program requirements in mathematics.
Note: Open to first-year students enrolled in one of: Biology, Chemistry, Health Science, Environmental Science, Water Science and Environmental Health, Psychology.
200-Level Courses
In this course concepts and techniques introduced in DATA100 will be reinforced. Students will explore the data science lifecycle, including question formulation, data collection and cleaning, exploratory data analysis and visualization, statistical inference and prediction, and decision-making. This course will focus on quantitative critical thinking and key principles and techniques needed to carry out this cycle. The main topics include languages for transforming, querying and analyzing data; algorithms for machine learning methods including regression, classification and clustering; principles behind creating informative data visualizations; statistical concepts of measurement error and prediction; and techniques for scalable data processing. The statistical computing software R will primarily be used to demonstrate the techniques. Other programming tools may include Excel and Python.
Winter 2023
3 lecture hours, 1.5 lab hours (biweekly)
Credits: 0.5
Prerequisites: DATA100
Co-requisites: One of: ST230,ST231,ST260, or equivalent.
Infinite sequences and series; Taylor and Maclaurin series; partial derivatives (limits and continuity, tangent planes, linear approximations, chain rule, directional derivative, gradient, max/min values, Lagrange multipliers); multiple integrals (double integrals, iterated integrals, triple integrals, polar/spherical coordinates).
Winter 2023
3 lecture hours, 1.5 lab hours (biweekly)
Credits: 0.5
Prerequisites: MA122 and one of MA101, MA103.
Exclusions: MA104 and MA201.
Vector functions; differential and integral calculus of functions of several variables, including vector fields; line and surface integrals including Green's Theorem, Stokes' Theorem and the Divergence Theorem.
Fall 2022 / Winter 2023 / Spring 2023
3 lecture hours, 1.5 lab hours (biweekly)
Credits: 0.5
Prerequisites: MA122, and one of MA101, MA103. MA104 is recommended.
Exclusions: MA200.
First order differential equations; linear differential equations of second and higher order; methods of undetermined coefficients and variation of parameters; Laplace transforms; power series solutions.
Fall 2022 / Spring 2023
3 lecture hours, 1.5 lab hours (biweekly)
Credits: 0.5
Prerequisites: MA101 or MA103.
This course provides an introduction to the use of several commercial and open-source software packages which are useful to mathematics students and professional mathematicians. The students will acquire a knowledge of basic programming concepts through computer-aided lectures and projects and learn how to use each system for symbolic and numerical problem solving and visualization. Examples will be taken from linear algebra (operations with vectors and matrices, solving linear equations), discrete mathematics (elementary combinatorics, basic graphs), visualization of functions, numerical solution of nonlinear equations, descriptive statistics, elementary probability and simulations. The software (e.g. Maple, Matlab, R) presented in the course will enhance each student's presentation, visualization, and problem-solving skills.
Spring 2023
3 lecture hours, 1.5 lab hours (biweekly)
Credits: 0.5
Prerequisites: MA103,MA122
Equivalence relations and partitions; countable and uncountable sets; ordered sets; development of number systems.
Fall 2022
3 lecture hours
Credits: 0.5
Prerequisites: MA121.
Elements of Euclidean geometry emphasizing the axiomatic approach; geometric shapes and measurements; Euler line and nine point circle; straightedge and compass constructions; transformations in Euclidean geometry; notions of non-Euclidean geometries.
3 lecture hours
Credits: 0.5
Prerequisites: MA121
This is an introductory course in mathematical methods with an aim of addressing problems arising from the data analysis, computing and modelling. Selected topics from matrix algebra, discrete mathematics and calculus will be presented.
3 lecture hours
Credits: 0.5
Prerequisites: One of MA101 ot MA103
Notes: Course offered online only
Abstract vector spaces, bases and dimension; linear transformations, matrix of a linear transformation, kernel, range, dimension theorem; change of basis; inner product spaces; orthogonal bases; Gram-Schmidt orthogonalization process; brief review of polynomials; eigenvalues, eigenvectors and diagonalizability of a linear operator; quadratic forms, Sylvester’s law of inertia.
Fall 2022 / Winter 2023
3 lecture hours
Credits: 0.5
Prerequisites: MA122 and either MA120 or MA121
An introduction to game-theoretic methods and their applications. Topics include the preference relation and von Neumann-Morgenstern utility, non-cooperative games in strategic form and extensive form, perfect and imperfect information, complete and incomplete information, and cooperative game theory including bargaining solutions and the Shapley value. Illustrative examples include game models from economics, political science, business, and other disciplines.
Fall 2022
3 lecture hours
Credits: 0.5
Prerequisites: MA101 or MA103 or MA129.
Basic graph theory, Euler circuits and Hamilton cycles in graphs, planar graphs, graph colouring, trees, relations, partial orders, introduction to counting, recurrence relations, inclusion-exclusion.
Fall 2022 / Winter 2023
3 lecture hours
Credits: 0.5
Tutorial/Seminar: 1.5 (biweekly)
Prerequisites: MA122 and either MA120 or MA121
A rigorous development of calculus. Topics include sequences, series, convergence, limits, continuity, differentiability, and the Riemann integral.
Winter 2023 / Spring 2023
3 lecture hours; 1.5 lab hours (biweekly)
Credits: 0.5
Prerequisites: MA121 and MA103.
An introduction to mathematical methods from linear algebra, calculus, and probability theory used in the financial analysis of problems in areas such as bond pricing, capital budgeting, making decisions under certainty/uncertainty, utility theory, portfolio optimization, binomial and log-normal asset pricing models, introductory no-arbitrage pricing of forwards and options, risk analysis.
Winter 2023
3 lecture hours, 1.5 lab hours (biweekly)
Credits: 0.5
Prerequisites: MA103 (or MA110*), MA122, MA170, ST259 (or MA240) or a similar course in probability and statistics (e.g., EC205, EC255, EC285).
This is an introductory course in mathematical models with an aim of addressing problems arising from the natural sciences. Selected topics from linear algebra, differential equations, and multivariate calculus will be presented along with models used in chemistry, biology, and health sciences.
Fall 2022
Credits: 0.5
3 lecture hours, 1.5 lab hours (biweekly)
Prerequisites: One of MA101, MA103, MA110*.
Exclusions: This course may not count for credit in Mathematics programs.
Notes: Not open to students in mathematics, computer science, and physics programs.
Data collection and description including univariate and bivariate frequency tables, histograms and summary statistics; elementary probability theory; random variables and expectations; sampling theory and the Central Limit Theorem; estimation and hypothesis testing for data from one and two normal populations.
Fall 2022 / Spring 2023
Credits: 0.5
3 lecture hours, 1.5 lab hours (biweekly)
Prerequisites: One of: MA101, MA103, or MA110
Exclusions: MA240, MA241, BU205, BU255, EC205, EC255, EC285, ST231; prior credit for ST260, current enrolment in ST260.
This course covers all basic statistical concepts, and includes relevant examples for life and health science students. The course introduces descriptive and inferential statistics; basic probability theory; discrete and continuous random variables with focus on binomial and normal random variables; statistical inference for population means and population proportions, both for one and two populations, with focus on confidence intervals and tests of hypotheses. Furthermore, simple and multiple linear regression methods are covered as well as one-way and two-way ANOVA. Problems are analyzed with the aid of appropriate software.
Winter 2023 / Spring 2023
Credits: 0.5
3 lecture hours, 1.5 lab hours (biweekly)
Prerequisites: One of: MA100, MA101, MA102, MA103, MA100.
Exclusions: EC205, EC255, EC285, MA141, MA240, MA241, PS296, ST230; prior credit for ST260; current enrolment in ST260.
Notes: This course may not count for credit in Honours Mathematics, Financial Mathematics, or Data Science programs.
Elementary probability theory; conditional probability and independence; discrete and continuous random variables; expected value, variance, covariance and correlation; introduction to Moment Generating Functions, the Law of Large Numbers and the Central Limit Theorem.
Fall 2022 / Spring 2023
Credits: 0.5
3 lecture hours, 1.5 lab hours (biweekly)
Prerequisites: MA104, or (one of MA101, MA103, MA110*, and either MA121 or MA122).
Exclusions: MA240.
Numerical and visual exploratory data analysis; probability models; point and interval estimation; bias and mean squared error of estimators; single-sample, paired and two- sample inference and hypothesis testing; introduction to experimental design and analysis of variance; introduction to goodness of fit and categorical data analysis; a thorough development of the simple linear regression model.
Winter 2023
Credits: 0.5
3 lecture hours, 1.5 lab hours (biweekly)
Prerequisites: ST259.
Exclusions: MA240, MA241, EC205, EC255, EC285, [Note: Students holding credit in statistical quantitative methods courses other than those listed above are strongly advised to consult with their home departments before registering in ST260.]
300-Level Courses
Functions of a complex variable; transformations; integration; Taylor and Laurent expansions; theory of residues.
Fall 2022
3 lecture hours
Credits: 0.5
Prerequisites: MA104 and MA201
Numerical solutions of differential equations and boundary value problems; linear systems of differential and difference equations including their solution by matrix methods and their stability; introduction to dynamical systems. Numerical methods will be illustrated by exercises requiring the use of a computer.†
Fall 2022
3 lecture hours
Credits: 0.5
Prerequisites: MA122, MA104 or MA200, MA205 and either a 0.5 credit in computer programming or permission of the department.
Exclusions: MA308.
First order partial differential equations and the method of characteristics. Fourier series and convergence. Separation of variables for diffusion, wave and Laplace equations. Eigenfunction series solutions. Generalized functions and Green's functions for one-dimensional boundary value problems. Fourier transform and convolution.
Fall 2022/ Spring 2023
3 lecture hours
Credits: 0.5
Prerequisites: MA205; and either MA200 or both MA104 and MA201.
Exclusions: MA455, MA406
Fall 2022/ Spring 2023
3 lecture hours
Credits: 0.5
Prerequisites: MA205; and either MA200 or both MA104 and MA201.
Exclusions: MA455, MA406
Numerical solution of equations and systems of equations; numerical integration; methods of interpolation, extrapolation and curve-fitting; error analysis. Methods will be illustrated by exercises requiring the use of a computer.†
Fall 2022 / Winter 2023
3 lecture hours; 2 lab hours (biweekly)
Credits: 0.5
Prerequisites: MA122, MA205; either CP104 or MA207; either MA200 or both MA104 and MA201.
Exclusions: CP315, MA371, PC315.
Examples and basic properties of groups and rings including their substructures, quotient structures and homomorphisms.
Fall 2022
3 lecture hours
Credits: 0.5
Prerequisites: MA215 or MA222.
Selected topics may include graph colouring, extremal graph theory, planar graphs, random graphs, network flows, algebraic methods in graph theory, Ramsay theory for graphs, matching theory, graph algorithms; application of graph theory, such as applications to scheduling, VLSI circuits, compiler design, computer vision and the design of internet search engines.
3 lecture hours
Credits: 0.5
Prerequisites: MA238
Topics in metric spaces including open and closed sets, compactness, uniform continuity. Sequences and series of functions. The Riemann-Stieltjes integral. Introduction to Lebesgue integration.
Winter 2023
3 lecture hours
Credits: 0.5
Prerequisites: MA250.
Exclusions: MA303.
Properties of continuous and discrete Fourier transforms; the Sampling Theorem; Inverse Fourier Transforms and convolution; introduction to wavelet analysis; Fast Fourier Transform (FFT), Fourier-Cosine (COS) method, and other algorithms; Laplace transform. Applications will be selected from applied sciences and quantitative finance.
Winter 2023
3 lecture hours; 1.5 lab hours (biweekly)
Credits: 0.5
Prerequisites: MA201 and MA205.
Exclusions: MA255.
The formulation, analysis and interpretation of mathematical models in various areas of application. Possible topics include population modelling, fluid mechanics, classical and quantum systems, reaction-diffusion models, neural networks, discrete optimization, and signal and image processing. Mathematical techniques may include differential and difference equations, PDEs, Fourier analysis, optimization, game theory, calculus of variations, and numerical methods. Topics covered may vary from year to year.†
Winter 2023
3 lecture hours
Credits: 0.5
Prerequisites: MA205, MA222, and one of MA200, MA201, MA250.
Discrete-time financial models and riskless asset pricing. Notion of arbitrage, martingale measure, and complete and incomplete markets. Fundamental theorems of asset pricing. Static and dynamic hedging and replication. Change of numeraire and equivalent martingale measures. Introduction to options and risk-neutral pricing. Stopping times and American option pricing. Introduction to the Black-Scholes theory and sensitivity analysis for options. Optional topics: introduction to single-factor interest rate modelling and pricing of fixed income securities.
Fall 2022
3 lecture hours; Tutorial/Seminar: 1.5 (biweekly)
Credits: 0.5
Prerequisites: MA270.
Co-requisites: ST359.
Linear programming algorithms, duality theory and post-optimum sensitivity analysis. Integer programming. Deterministic and stochastic dynamic programming. Kuhn-Tucker conditions for optimality. Quadratic programming. Non-linear programming. Network optimization. Modeling and applications.
Winter 2023
3 lecture hours
Credits: 0.5
Prerequisites: MA201, MA222.
Survival distributions, life tables, life annuities, and life insurance. Calculation of premiums and reserves. Introduction to policy valuation.
Winter 2023
3 lecture hoursCredits: 0.5
Prerequisites: MA103 (or MA110), MA170, ST259 (or MA240) or a similar course in probability and statistics such as EC255 and EC285.
Exclusions: MA273.
This course provides an introduction to two related areas of statistics -- experimental design and survey sampling. Topics covered in experimental design include randomization and replication; completely randomized and randomized complete block experiments; designs and analysis of variance (ANOVA) tables for fixed, random and mixed effects models; and efficiency of designs. The survey sampling part of the course provides a basic understanding of sample surveys and emphasizes the statistical aspects of taking and analyzing survey samples. Topics include: common sampling methods such as simple random, cluster and stratified sampling; sampling with unequal probabilities, sampling weights; complex surveys and its application to statistical modelling.
Fall 2022
3 lecture hours
Credits: 0.5
Prerequisites: ST260 or (ST259 and one of ST230, ST231).
Exclusions: MA344
Formal probability spaces and random variables; multivariate and conditional distributions; functions of jointly distributed random variables; mathematical expectation; conditioning; moment generating function and other transforms; functions of random variables; modes of convergence and limit theorems; introduction to topics in applied probability.
Fall 2022
3 lecture hours; tutorial/Seminar: 1.5 (biweekly)
Credits: 0.5
Prerequisites: MA200 or MA201, ST259.
Exclusions: MA340.
Parametric statistics; principles of data reduction including sufficiency and likelihood function; point estimation including methods of finding estimators and properties of estimators; interval estimation; hypothesis testing including likelihood ratio testing; introduction to Bayesian analysis.
Fall 2022
3 lecture hours
Credits: 0.5
Prerequisites: MA200 or MA201, ST260 or (ST259 and one of ST230, ST231).
Exclusions: MA341.
Regression analysis including estimation, hypothesis testing, analysis of variance, variable selection techniques; regression diagnostics; generalized linear regression; nonlinear regression; nonparametric regression.
Fall 2022 / Spring 2023
3 lecture/discussion hours, 1.5 lab hour (biweekly)
Credits: 0.5
Prerequisites: MA122, ST260 or (ST259 and one of ST230, ST231).
Exclusions: MA242
400-Level Courses
Canonical forms of linear second order PDEs. Ill-posed and well-posed problems. General framework for linear PDEs: self-adjoint and positive definite linear operators, minimization principle, Rayleigh quotient, Eigenfunction series. Green’s functions in the planar case; delta-function in higher dimensions. Introduction to numerical methods for PDEs.Additional topics may include: Weak solutions. Linear and nonlinear evolution equations, linearization and stability. Heat and forced heat equations, maximum principle. Nonlinear diffusion. Dispersion and solitons.
3 Lecture/discussion hours
Credits: 0.5
Prequisites: MA222, MA250, MA306
Exclusions: MA455
Geometry of curves and surfaces, curvature, geodesics, first and second fundamental forms, the Gauss Theorema Egregium and the Gauss-Bonnet theorem. Differential forms and vector fields. Line and surface integrals. The divergence and Stoke's theorems.
3 lecture hours
Credits: 0.5
Prerequisites: MA201, MA222, MA205, and a 0.5 MA credit at the 300 level.
Exclusions: MA419
Determinants; Cayley-Hamilton theorem; bilinear forms; adjoint, self-adjoint, and normal linear operators; the spectral theorem for normal operators; orthogonal and Hermitian operators; the Jordan canonical form of matrices and linear operators.
Fall 2022
3 lecture hours
Credits: 0.5
Prerequisites: MA222
Exclusions: MA322
Conditional expectations, sigma-algebras, and filtrations; martingales and stopping times; the Riemann-Stieltjes integral; Gaussian processes and Brownian motion; stochastic integration and Ito's formula; diffusion processes and stochastic differential equations; the Feynman-Kac theorem.
Fall 2022
3 lecture hours
Credits: 0.5
Prerequisites: MA250 and ST359.
Exclusions: MA351.
An introduction to the use of dynamical systems for the purpose of studying biological systems, with an emphasis on deterministic models. Models will be chosen from ecology and epidemology. Attention will be devoted to both the construction and the analysis of the models. Mathematical analysis will involve linear algebra, differential equations, and techniques from stability theory.
Winter 2023
3 lecture hoursCredits: 0.5
Prerequisites: MA222 and MA305
Exclusions: MA365
Continuous-time financial models and riskless asset pricing. The Black-Scholes theory (including the Black-Scholes PDE). Arbitrage free pricing of European, American, and exotic options. Optional topics: stochastic volatility and jump-diffusion models; continuous-time interest rate models; pricing bonds and derivatives on interest rates.
Winter 2023
3 lecture/discussion hours
Credits: 0.5
Prerequisites: MA370, MA451.
Numerical methods used in financial engineering and risk management, including numerical solutions of ordinarily differential equations, finite difference methods, numerical optimization, Monte Carlo and quasi-Monte Carlo methods, numerical solutions of stochastic differential equations, fast Fourier and other discrete transform methods. The computational methods are illustrated with the use of programming languages such as MAPLE, MATLAB and VBA.
Winter 2023
3 lecture hours; 2 lab (biweekly)
Credits: 0.5
Prerequisites: MA205; MA370; and either MA307 or MA371
Rings; subrings, quotient rings and ring homomorphisms; ideal theory; polynomial rings; integral domains and divisor theory; fields and field extensions; the Fundamental Theorem of Galois Theory.††
Winter 2023
Credits: 0.5
Prerequisites: MA222, MA323.
This course will introduce students to a variety of topics in risk management. The defining feature of this course is that it will cover topics that are not typically covered in the traditional mathematical finance curriculum. As such it will be an important differentiator for the program. Topics might include (but will not necessarily be limited to) some of the following:
● Introduction to risk measures such as value at risk (VaR), conditional tail expectation and expected shortfall.
● Introduction to credit scoring.
● Introduction to economic and regulatory capital modelling, especially as it relates to compliance with Basel III.
● Advanced treatment of hedging derivatives portfolios.
● Introduction to credit risk models such as the Merton and/or Black-Cox models, as well as linear factor models and alternative models of dependence (e.g. copulae).
Fall 2022
Credits: 0.5
Prerequisites: MA270, MA307 or MA371, ST260.
An introduction to modelling tools used in modern applications of mathematics, including: dimensional analysis and scaling; discrete and continuous models; finite and infinite dimensional systems; variational modeling. Other topics may include: Financial bubbles. Interbank networks. Diffusion. Chemical kinetics. Stochastic models. Population models. Basic continuum mechanics.
Winter 2023
3 lecture hours
Credits: 0.5
Prerequisites: MA205, MA307 or CP315/PC315.
Completion of an appropriate individual project under faculty supervision, including submission of a final report and presentation in a department seminar. (Consult department for details.)
Fall 2022/ Winter 2023
Credits: 0.5
Completion of an appropriate individual project under faculty supervision, including submission of a final report and presentation in a department seminar. (Consult department for details.)
Simulating random numbers from various probability distributions; transformations of uniform variates; sampling from multivariate distributions; simulation of stochastic processes; (quasi-)Monte Carlo methods; variance reduction techniques. Applications may include: numerical integration of multivariate functions in high dimensions; approximation algorithms for solving matrix equations, partial differential equations and integral equations; pricing financial securities; MCMC methods; resampling techniques and other topics of computational statistics.
Winter 2023
3 lecture/discussion hours; 1.5 lab hours (biweekly)
Credits: 0.5
Prerequisites: CP104 or MA207; MA200 or MA201; ST260 or (ST259 and one of ST230, ST231); and a 0.5 MA/ST credit at the 300 level (MA307 is recommended).
Exclusions: MA495H
Classification of stochastic processes; Markov Chains in discrete and continuous time including Poisson processes and birth-death processes; renewal theory; introduction to queuing theory.
Winter 2023
3 lecture hours
Credits: 0.5
Prerequisites: ST359.
Exclusions: MA490.
This course provides a survey of time series analysis methods. General topics include models for stationary and nonstationary time series, ARIMA specification, parameter estimation, model diagnostics, forecasting and seasonal models. Advanced topics such as GARCH, VAR and other time series methodologies in econometrics and finance are also covered.
Winter 2023
3 lecture/discussion hours; 1.5 lab hours (biweekly)
Credits: 0.5
Prerequisites: ST362 or EC295.
Exclusions: MA492.
(Cross-listed as EC455.)
The course covers the most current techniques used in statistical learning and data analysis, and their background theoretical results. Two basic groups of methods are covered in this course: supervised learning (classification and regression) and unsupervised learning (clustering). The supervised learning methods include Recursive Partitioning Tree, Random Forest, Linear Discriminant and Quadratic Discriminant Analysis, Neural Network, Support Vector Machine, K-nearest neighbour, linear and generalized models, and generalized additive models. The unsupervised learning methods include Hierarchical Clustering, K-means, model-based clustering methods. Furthermore, the course also covers the dimensional reduction techniques such as LASSO and Ridge Regression, and model checking criteria. Some data visualization methods will be introduced in this course as well.
Winter 2023
3 lecture/discussion hours; 1.5 lab (biweekly).
Credits: 0.5
Prerequisites: ST362.
100-Level Courses
- MA101: Calculus I for the Natural Sciences
- MA103: Calculus I
- MA104: Calculus II
- MA121: Introduction to Mathematical Proofs
- MA122: Introductory Linear Algebra
- MA129OC1: Introductory Calculus for Business and Social Sciences
- MA170OC1: Introduction to Mathematics for Finance
200-Level Courses
- MA201: Multivariable Calculus
- MA205: Differential Equations I
- MA250: Introductions to Analysis
- ST230: Introduction to Probability and Statistics for Science
- ST231: Statistical Methods for Life and Health Sciences
- ST259: Probability I
300-Level Courses
- ST362: Regression Analysis
400-Level Courses
- MA451:Introduction to Stochastic Calculus
100-Level Courses
- MA100:Intro Calc for Natural Science
- MA101:Calculus I for Natural Science
- MA101:Calculus I for Natural Science
- MA103:Calculus I
- MA104:Calculus II
- MA120:Intro to Discrete Structures
- MA121:Intro to Mathematical Proofs
- MA127:Math for Business Tech Mgmt
- MA129:Intro Calc for Bus/Soc Science
- MA129:Intro Calc for Bus/Soc Science
- MA129:Intro Calc for Bus/Soc Science
- MA170:Intro to Math for Finance
200-Level Courses
- DATA200:Data Analytics
- MA200:Advanced Calculus
- MA201:Multivariable Calculus
- MA218:Euclidean Geometry
- MA222:Linear Algebra
- MA250:Intro to Analysis
- MA270:Financial Mathematics I
300-Level Course
- MA307:Numerical Analysis
- MA338:Graph Theory
- MA350:Real Analysis
- MA355:Continuous Discrete Transforms
- MA361:Methods in Applied Math
400-Level Courses
- MA405:Dynamical Systems
- MA425:Group Theory
- MA464:Mathematical Biology
- MA470:Financial Mathematics III
- MA471:Comp. Methods in Finance
- MA487:Math Modelling
- MA489:Honours Seminar
100-Level Courses
- MA101: Calculus I for the Natural Sciences
- MA103: Calculus I
- MA104: Calculus II
- MA121: Introduction to Mathematical Proofs
- MA122: Introductory Linear Algebra
- MA129OC1: Introductory Calculus for Business and Social Sciences
- MA170OC1: Introduction to Mathematics for Finance
200-Level Courses
- MA201: Multivariable Calculus
- MA205: Differential Equations I
- MA250: Introductions to Analysis
- ST230: Introduction to Probability and Statistics for Science
- ST231: Statistical Methods for Life and Health Sciences
- ST259: Probability I
300-Level Courses
- ST362: Regression Analysis
400-Level Courses
- MA451:Introduction to Stochastic Calculus
- MA455: Partial Differential Equations
100-Level Courses
- MA100: Introductory Calculus for the Natural Sciences
- MA101: Calculus I for the Natural Sciences
- MA103: Calculus I
- MA104: Calculus II
- MA120: Introduction to Discrete Structures
- MA121: Introduction to Mathematical Proofs
- MA127: Mathematics for Business Technology Management
- MA129: Introductory Calculus for Business and Social Sciences
- MA170: Introduction to Mathematics for Finance
- MA170OC2: Introduction to Mathematics for Finance
200-Level Courses
- DATA200: Data Analytics
- MA200: Advanced Calculus
- MA201: Multivariable Calculus
- MA222: Linear Algebra
- MA238: Discrete Mathematics
- MA250: Introduction to Analysis
- MA270: Financial Mathematics I
- ST231: Statistical Methods for Life and Health Sciences
- ST260: Introduction to Statistics
300-Level Courses
- MA307: Numerical Analysis
- MA317: Numbers Theory
- MA350: Real Analysis
- MA355: Continuous and Discrete Transforms
- MA360: Topics in Applied Mathematics
- MA372: Optimization
- MA373: Introduction to Actuarial Math
400-Level Courses
- MA464: Mathematical Biology
- MA470: Financial Mathematics III
- MA471: Computational Methods in Finance
- MA475: Ring and Field Theory
- MA487: Math Modelling
- ST490: Stochastic Processes
- ST492/EC455: Time Series Analysis
- MA495I: Special Topics
- ST474: Monte Carlo Methods
- ST494: Statistical Learning