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Course Offerings for 2021/22
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 must complete a Request for Course Overload Form.
View course outlines, organized by term and includes graduate courses.
* = Full-year course.
† = Course offered every second or third year.
†† = Course offered occasionally.
Course Registration Resources
500-Level Courses
Functions of a complex variable; transformations; integration; Taylor and Laurent expansions; theory of residues.
Fall 2021
Credits: 0.5
Exclusions: MA304 or equivalent
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 2020
Credits: 0.5Exclusions: MA305 or equivalent
Elementary theory of numbers; arithmetic functions; congruences; quadratic reciprocity; solutions to Diophantine equations.
Winter 2022
Credits: 0.5Exclusions: MA317 or equivalent
Notes: Formerly offered as MA617 (Number Theory and Cryptography)
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 2022
Credits: 0.5
Exclusions:MA350, MA686J or equivalent
Properties of continuous and discrete Fourier transformations; the Sampling Theorem; Inverse Fourier Transformations 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 2022
Credits: 0.5
Exclusions:MA355 or equivalent
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 2021
Credits: 0.5
Exclusions:ST359 or equivalent
This course presents a rigorous development of: point and interval estimation; sufficiency, efficiency, unbiasedness, and consistency. Topics include: maximum likelihood and Bayesian estimation; exchangeability; invariance; decision theory; large sample theory; optimality criteria and most powerful tests; likelihood ratio tests; and robustness.
Fall 2021
Credits: 0.5
Exclusions:ST361, MA641, or equivalent
Notes:Formerly offered as MA641 (Advanced Theory of Statistics)
Regression analysis including estimation, hypothesis testing, analysis of variance, variable selection techniques; regression diagnostics; generalized linear regression; nonlinear regression; nonparametric regression.
Fall 2021/ Spring 2022
Credits: 0.5
Exclusions:ST362, MA642, MA686F, or equivalent
Notes:Formerly offered as MA642 (Regression Analysis)
This course introduces discrete-time financial models and their application to risk-neutral asset pricing and hedging. Students learn the concepts of arbitrage, martingale measure, and complete and incomplete markets. Using these concepts and models, students learn how to replicate payoffs of contingent claims using a portfolio or other securities and to construct martingale measures, hence providing both a value and hedging strategy for the claim. This analysis is carried out in both complete and incomplete market models. Students are introduced to American-style options and are able to value them using stopping times. Students are also introduced to Black-Scholes theory for pricing options and computing sensitivities of options prices to input parameters. Optional topics include an introduction to single-factor interest rate modelling and pricing of fixed income securities.
Fall 2021
Credits: 0.5
View course outlines, organized by term and includes graduate courses.
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. Modelling and applications.
Winter 2022
Credits: 0.5
Exclusions: MA372 or equivalent
600-Level Courses
Determinants; Caley-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 2021
Credits: 0.5
Exclusions: MA422 or equivalent
This course introduces the fundamentals of stochastic calculus. Topics include probability measures and random variables; the Itô integral calculus; Itô's Lemma; Markov chains; random walks; the Wiener process; Brownian and geometric Brownian motion; filtrations; adaptive processes; Martingales and super-Martingales; the Martingale Stopping Time Theorem; Girsanov's Theorem and the Radon-Nikodym derivative; stochastic differential equations for single and multiple random processes; Kolmogorov equations and the Feynman-Kac Theorem. Applications include the modelling of continuous diffusion processes, and the development of solution techniques for stochastic differential equations. Topics may include stochastic optimization and jump processes.
Fall 2021
Credits: 0.5
Prerequisites: ST559 - Intermediate Probability Theory or equivalent
Exclusions: MA451 or equivalent
Notes: Formerly offered as MA551 (Stochastic Analysis)
View course outlines, organized by term and includes graduate courses.
Canonical forms of linear second order PDEs. Ill-posed and well-posed problems. General frameworks for linear PDEs: sself-adjoint and positive definite linear operators, minimization principle, Rayleigh quotient, Eigenfunction series. Green's functions in the planar case and spatial case and higher dimensional; delta-function in higher dimensions. Additional topics may include: Finite elements and weak solutions. Linear and nonlinear evolution equations, linearization and stability. Heat and forced heat equations, maximum principle. Nonlinear diffusion. Dispersion and solitons.
Credits: 0.5
Prerequisites: MA506 or MA655 or equivalent
Exclusions: Not available for students holding WLU credit for MA406
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 epidemiology. 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 2022
Credits: 0.5Prerequisites: MA505 Ordinary Differential Equations or MA660- Dynamical Systems or equivalent
Exclusions:MA365, MA464, MA665, or equivalent
Notes:Formerly offered as MA665 (Mathematical Biology)
This course develops the mathematical framework for option pricing in continuous time for equity and interest rate derivatives. Topics include: asset pricing and interest rate processes; derivation of the Black-Scholes partial differential equation; pricing of standard European, American and multi-asset options under geometric Brownian motions; stochastic asset price models; multi-factor interest rate stochastic modelling; bond pricing and interest rate option pricing and calibration; and path dependent options. Topics may include: transformation techniques for solving parabolic PDEs; Green's functions; path integral methodologies for pricing and hedging options; Monte Carlo simulation and stochastic mesh methods for pricing complex multi-asset derivatives.
Winter 2022
Credits: 0.5
Prerequiites: MA570 - Financial Mathematics in Discrete Time or equivalent, and MA651 - Stochastic Analysis or equivalent
Exclusions: MA470.
View course outlines, organized by term and includes graduate courses.
Numerical methods used in financial engineering and risk management, including numerical solutions of ordinary 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 2022
Credits: 0.5
Prerequisites: MA570 - Financial Mathematics in Discrete Time or equivalent, and MA507 - Numerical Analysis or MA571 - Computational Methods fro Data Analysis or equivalent
Exclusions: MA686B, MA471.
View course outlines, organized by term and includes graduate courses.
Monte Carlo techniques and simulation methods are studied in detail. Applications include mathematical modelling and computation of numerical solutions; evaluation of multi-dimensional integrals through pseudo-random numbers, quasi-random numbers, Sobol sequences and other sequences of lattice points. Topics include: sampling algorithms; simulated annealing; Markov processes; variance reduction techniques; importance sampling; adaptive and recursive Monte Carlo methods. Applications include numerical integration of multivariate functions in high dimensions; approximation algorithms for solving partial differential equations; stochastic lattice approaches and path expansions. Additional topics may include parallel algorithms for Monte Carlo simulations.
Winter 2022
Credits: 0.5Prequisites: ST559 - Intermediate Probability Theory or equivalent
Exclusions: ST474, MA547, MA647 or equivalent
Notes: Formerly offered as MA647 (Monte Carlo and Simulation Methods)
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 2022
Credits: 0.5Prequisites: MA523 - Introduction to Groups and Rings or equivalent
Exclusions: MA475 or MA686E (Ring and Field Theory version)
This course will introduce students to a variety of topics in risk management. Topics might include (but will not necessarily be limited to) some of the following:
- introduction to risk measures such as the value at risk (VaR), conditional tail expectation and expected shortfall
- Introduction to credit scoring
- Introduction to economic and regulatory capital modeling, 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 2021
Credits: 0.5
Prequisites: MA570- Financial Mathematics in Discrete Time or equivalent and MA507- Numerical Analysis or MA571 or equivalent
Exclusions: MA477, MA686I (Quantitative Financial Risk Management)
This seminar course is designed to develop the capacity to abstract salient features of problems in financial mathematics and the scientific disciplines, and to develop, analyse, and interpret models. Problems from financial mathematics and science, using undergraduate mathematics in modelling and analysis, are studied in detail. Commonality of mathematical methods and structures across disciplines is emphasized. Students work individually and in groups, and produce both written and oral reports on their projects.
Fall 2021
Credits: 0.5
View course outlines, organized by term and includes graduate courses.
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 2022
Credits: 0.5Prerequisites: ST559-- Intermediate Probability Theory or equivalent
Exclusions: MA490, ST490, MA686G or equivalent
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 2022
Credits: 0.5
Prerequisites: ST541 or ST562 - Regression Analysis or equivalent
Exclusions: EC455, MA492, ST492, MA686H (Time Series Analysis) or equivalent
This course is designed for students who take the course-based option in the MSc in mathematics. This seminar course introduces the students to a broad range of topics in mathematics, finance, statistics, data science and other multidisciplinary areas. The course material is presented through lectures, hands-on computational labs and guest-speaker series. The students' performance is evaluated based on the written report and oral presentations.
Spring 2022
Credits: 0.5
View course outlines, organized by term and includes graduate courses.
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, and Regression. The unsupervised learning methods include Hierarchical Clustering, K-means, and Model-based Clustering methods. Furthermore, the course also covers dimension 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 2022
Credits: 0.5
Prerequisites: ST562 - Regression Analysis or equivalent
Exclusions: ST494, MA686K (Statistical Learning) or equivalent
800-Level Courses
The Research Proposal and Qualifying Examination is designed for students to demonstrate broad knowledge in their research area, in addition to their expertise in a specific research topic within one or more of the application domains of mathematical and statistical modelling. It is normally completed in the 4th, and not later than the 5th term of registration.
A written Research Proposal and an oral presentation is required. Based on the candidate's defence of the research proposal and responses to the questions, the examining committee will render a decision of pass/decision deferred/fail. In the case of a deferred decision or a failing grade, the candidate may be allowed to take the examination once more, for a total of two attempts. The examination may be repeated no later than 6 months from the date of the first attempt. In the event the second attempt results in a failing grade, the Graduate Co-ordinator will recommend to the Faculty of Graduate and Postdoctoral Studies that the student be required to withdraw from the program.
Fall 2021 / Winter 2022 / Spring 2022
Credits: 0.5
View course outlines, organized by term and includes graduate courses.
All students in the program must attend the Seminar in the fall and winter terms, for the duration of their time in the program. The seminar will include presentations from guest speakers, as well as faculty from the program, and may occasionally be combined with the existing MS2Discovery Seminar Series events devoted to mathematical and statistical modelling. Such events frequently feature world-renowned researchers in all application domains of the program. This seminar not only will expose students to the challenges of real-world problems, but also will teach them from first-hand experience how to communicate the modelling tools in the application domains with their own technical language. Students are also expected to attend other specialized research seminars, as appropriate.
Students are required to attend a minimum of 6 presentations and write a short summary of at least 6 presentations each year (September to April).
Graded as complete/incomplete.
Fall 2021 / Winter 2022
Credits: 0.0
View course outlines, organized by term and includes graduate courses.
This course is designed to develop the capacity to abstract salient features of problems in all three identified application domains of mathematical and statistical modelling, and to develop, analyse, and interpret models. This course sets the tone by introducing the students to all aspects of modelling, including formulating a mathematical representation of the real-world problem of interest, solving that problem, and interpreting the results in the context of the application domain. Commonality of mathematical and statistical methods and structures across disciplines is emphasized. Students work individually and in groups, and produce both written and oral reports on their projects.
Fall 2021
Credits: 0.5
View course outlines, organized by term and includes graduate courses.
Each student must prepare a dissertation on his or her original research in mathematical and statistical modelling within one or more of the application domains identified for this program, and present this dissertation to the Dissertation Examination Committee (DEC) in accordance with the university's regulations and procedures governing the doctoral dissertation.
Fall 2021/ Winter 2022/ Spring 2022
Credits: 6.0
View course outlines, organized by term and includes graduate courses.
600-Level Courses
- MA651: Introduction to Stochastic Calculus
- MA693: Graduate Seminar
- MA695: Major Project
- MA699: Masters Thesis
800-Level Courses
- MA810:Research Proposal and Qualifying Examination
- MA899: Doctoral Dissertation
- MA664: Mathematical Biology
- MA670: Financial Modelling and Derivative Pricing in Continuous Time
- MA671: Computational Methods in Finance
- MA675: Ring And Field Theory
- MA686: Special Topics
- ST674:Monte Carlo and Sim Methods
- ST690:Stochastic Processes
- ST692:Time Series Analysis
- ST694:Statistical Learning
500-Level Courses
- MA570: Financial Mathematics in Discrete Time
600-Level Courses
- MA641: Advanced Theory of Statistics
- MA642: Regression Analysis
- MA651: Stochastic Analysis
- MA660: Dynamical Systems
- MA680: Seminar in Mathematical Modelling in Finance and Science
- MA686I: Special Topics: Quantitative Financial Risk Management
- MA686L: Advanced PDE's and Applications
800-Level Courses
- MA820: Interdisciplinary Seminar in Modelling and its Applications
- MA880: Graduate Seminar in Mathematical and Statistical Modelling
600-Level Courses
- MA642: Regression Analysis
- MA686L: Advanced PDE's and Applications
- MA693: Graduate Seminar
- MA695: Major Project
- MA699: Masters Thesis
800-Level Courses
- MA810:Research Proposal and Qualifying Examination
- MA899: Doctoral Dissertation
600-Level Courses
- MA647: Monte Carlo and Simulation Methods
- MA665: Mathematical Biology
- MA670: Financial Modelling and Derivative Pricing in Continuous Time
- MA671: Computational Methods in Finance
- MA686C: Special Topics
- MA686E: Special Topics: Topics in Abstract Algebra
- MA686H: Special Topics: Time Series Analysis
- MA686J: Special Topics