Course Offerings for 2017/18
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.
* = Fullyear course.
† = Course offered every second or third year.
†† = Course offered occasionally.
View course outlines, organized by term and includes graduate courses.
View graduatelevel courses.
100Level Courses
MA100: Introductory Calculus for the Natural Sciences
This course concentrates on developing mastery of precalculus and introductory calculus skills and techniques. Precalculus 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 2017 / Winter 2018
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.
View course outlines, organized by term and includes graduate courses.
MA101: Calculus I for the Natural Sciences
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.
Fall 2017 / Winter 2018 / Spring 2017
3 lecture hours; 1.5 lab hours
Credits: 0.5
Prerequisites: MA100 or permission of the department.
Exclusions: MA103, MA105, MA110*, MA130. This course may not count for credit in Mathematics programs.
View course outlines, organized by term and includes graduate courses.
MA103: Calculus I
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 partial derivatives.
Fall 2017 / Winter 2018 / Spring 2017
3 lecture hours; 1.5 lab hours
Credits: 0.5
Prerequisites: A minimum score of 70% on the Calculus Preparation Evaluation (CPE); and Grade 12 Calculus or MA100 or MA129.
Exclusions: MA101, MA102, MA105, MA110*, MA130.
View course outlines, organized by term and includes graduate courses.
MA104: Calculus II
Applications of integration; polar coordinates and parametric equations; infinite sequences and series; applications of partial derivatives.
Fall 2017 / Winter 2018 / Spring 2017
3 lecture hours; 1.5 lab hours
Credits: 0.5
Prerequisites: MA101 or MA103 (or MA110*) or MA105.
Exclusions: MA102, MA200.
View course outlines, organized by term and includes graduate courses.
MA110*: Introduction to Differential and Integral Calculus
A thorough introduction to limits of functions. Continuity and its consequences. Rational, algebraic and transcendental functions and geometric relationships. Theory and applications of differential and integral calculus of functions of a single variable. The Fundamental Theorem of Calculus and techniques of integration. Introduction to multivariable calculus and applications.
FallWinter 2017/18 (Both Terms)
3 lecture hours; 1.5 lab hours (biweekly)
Credits: 0.5
Prerequisites: Completion of the Calculus Preparation Evaluation (CPE).
Exclusions: MA100, MA101, MA102, MA103, MA105, MA129, MA130.
View course outlines, organized by term and includes graduate courses.
MA121: Introduction to Mathematical Proofs
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 2017 / Winter 2018 / Spring 2017
3 lecture hours; 1.5 lab hours (biweekly)
Credits: 0.5
Senate/Editorial Changes
 Senate Academic Planning Committee Revision Feb. 21, 2017: MA121 Contact hours changed; effective Sept. 1, 2017.
View course outlines, organized by term and includes graduate courses.
MA122: Introductory Linear Algebra
Vector geometry in R^{2} and R^{3}; the vector space R^{n} and its subspaces; spanning sets, linear independence, bases and dimension; dot product in R^{n} and C^{n}; systems of linear equations and Gaussian elimination; matrices and matrix operations; matrix inverse; matrix rank; linear transformations in R^{n}; introduction to determinants, Cramer's rule; introduction to eigenvalues, eigenvectors and diagonalization of real matrices; applications of linear algebra.
Fall 2017 / Winter 2018 / Spring 2017
3 lecture hours; 1.5 lab hours (biweekly)
Credits: 0.5
Senate/Editorial Changes
 Senate Academic Planning Committee Revision Jan. 19, 2017: MA122 Description change; effective Sept. 1, 2017.
 Senate Academic Planning Committee Revision Feb. 21, 2017: MA122 Contact hours changed; effective Sept. 1, 2017.
View course outlines, organized by term and includes graduate courses.
MA127: Mathematics for Business Technology Management
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 2018
Brantford Campus
3 lecture hours, 1.5 tutorial hours
Credits: 0.5
Prerequisites: Grade 12 Ulevel math course or equivalent.
Exclusions: This course can only count for credit for students in the Business Technology Management program.
MA129: Introductory Calculus for Business and Social Sciences
This course concentrates on developing mastery of precalculus and introductory calculus skills and techniques. Precalculus 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 2017 / Winter 2018 / Spring 2017
3 lecture hours, 1.5 tutorial hours
Credits: 0.5
Prerequisites: Completion of the Calculus Preparation Evaluation (CPE) and 12U Advanced Functions or permission of the department.
Exclusions: If a student has successfully passed, or is currently enrolled in MA100, MA101, MA103, MA110*, or MA130, then MA129 will not be eligible for credit. This course may not count for credit in mathematics programs.
View course outlines, organized by term and includes graduate courses.
MA170: Introduction to Mathematics for Finance
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 2017 / Winter 2018 / Spring 2017
3 lecture hours, 1.5 lab hours
Credits: 0.5
Prerequisites: 12U Advanced Functions, or equivalent, or permission of the department.
View course outlines, organized by term and includes graduate courses.
SC101: Essential Skills for Mathematics
Thorough review of preuniversity 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 2017
3 lecture hours
Prerequisites: One of: 12U Advanced Functions, 3U Functions and Relations, 3M Functions; or permission of the Department of Mathematics.
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 firstyear students enrolled in one of: Biology, Chemistry, Health Science, Environmental Science, Applied Water Science, Psychology.
Senate/Editorial Changes
 Senate Academic Planning Committee Revision March 20, 2017: SC101 New course; effective Sept. 1, 2017.
View course outlines, organized by term and includes graduate courses.
200Level Courses
MA201: Multivariable Calculus
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 2017 / Winter 2018 / Spring 2017
3 lecture hours, 1.5 lab hours (biweekly)
Credits: 0.5
Prerequisites: MA122, and one of MA101, MA102, MA103 (or MA110*) or MA105 (MA104 is recommended).
View course outlines, organized by term and includes graduate courses.
MA205: Differential Equations I
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 2017 / Winter 2018 / Spring 2017
3 lecture hours, 1.5 lab hours (biweekly)
Credits: 0.5
Prerequisites: One of MA101, MA102, MA103 (or MA110*), or MA105.
View course outlines, organized by term and includes graduate courses.
MA215: Set Theory
Equivalence relations and partitions; countable and uncountable sets; ordered sets; development of number systems.
Fall 2017
3 lecture hours
Credits: 0.5
Prerequisites: MA121.
View course outlines, organized by term and includes graduate courses.
MA218: Euclidean Geometry
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 nonEuclidean geometries.
Winter 2018
3 lecture hours
Credits: 0.5
Prerequisites: MA121, or consent of the department.
View course outlines, organized by term and includes graduate courses.
MA222: Linear Algebra
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; GramSchmidt orthogonalization process; brief review of polynomials; eigenvalues, eigenvectors and diagonalizability of a linear operator; quadratic forms, Sylvester’s law of inertia.
Fall 2017 / Winter 2018 / Spring 2017
3 lecture hours
Credits: 0.5
Prerequisites: MA121, MA122.
View course outlines, organized by term and includes graduate courses.
MA233: Problem Solving in Mathematics
A comprehensive study of techniques in mathematical problem solving, including topics from classical and contemporary mathematics. Examples will be taken from such areas as calculus, algebra, logic, geometry, elementary number theory, combinatorics and graph theory. Problems from various mathematical contests and competitions will be discussed.
Winter 2018
3 lecture hours
Credits: 0.5
Prerequisites: MA103 (or MA110*), MA121.
View course outlines, organized by term and includes graduate courses.
MA235: Introduction to Game Theory
An introduction to gametheoretic methods and their applications. Topics include the preference relation and von NeumannMorgenstern utility, noncooperative 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 2017
3 lecture hours
Credits: 0.5
Prerequisites: One of: MA101, MA103 (or MA110*), MA105.
View course outlines, organized by term and includes graduate courses.
MA238: Discrete Mathematics
Basic graph theory, Euler circuits and Hamilton cycles in graphs, planar graphs, graph colouring, trees, relations, partial orders, introduction to counting, recurrence relations, inclusionexclusion.
Fall 2017 / Winter 2018
3 lecture hours
Credits: 0.5
Prerequisites: MA121 and an additional 0.5 MA credit.
View course outlines, organized by term and includes graduate courses.
MA241: Statistical Methods for the Life Sciences
Data reduction methods; discrete and continuous random variables; hypothesis testing and confidence intervals; linear regression and linear models, analysis of variance and correlation methods. Introduction to experimental design. Problems drawn primarily from biology and related sciences are used to illustrate the concepts, and are analyzed with the aid of an appropriate software package.
Spring 2017
3 lecture hours, 1.5 lab hours (biweekly)
Credits: 0.5
Prerequisites: One of MA101, MA103, MA105, MA110*.
Exclusions: MA141, MA240, PS296.
Senate/Editorial Changes
 Editorial Revision: April 17, 2017: Exclusion added; effective Sept. 1, 2017.
View course outlines, organized by term and includes graduate courses.
MA250: Introduction to Analysis
A rigorous development of calculus. Topics include sequences, series, convergence, limits, continuity, differentiability, and the Riemann integral.
Fall 2017 / Winter 2018 / Spring 2017
3 lecture hours; 1.5 lab hours (biweekly)
Credits: 0.5
Prerequisites: MA121, and one of MA102 or MA103 (or MA110*).
Senate/Editorial Change

Planning Committee Revision Jan. 19, 2017;
 MA250 Contact hour change; effective Sept. 1, 2017.
View course outlines, organized by term and includes graduate courses.
MA270: Financial Mathematics I
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 lognormal asset pricing models, introductory noarbitrage pricing of forwards and options, risk analysis.
Winter 2018
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).
Senate Academic Planning Deletion March 21, 2016: MA270 Exclusions BU205 and BU255 deleted; effective Sept. 1, 2016.
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MA273: Introduction to Actuarial Mathematics
Survival distributions, life tables, life annuities, and life insurance. Calculation of premiums and reserves. Introduction to policy valuation.
Winter 2018
3 lecture hours
Credits: 0.5
Prerequisites: MA103 (or MA110*), MA170, ST259 or MA240 or a similar course in probability and statistics such as EC255 and EC285.
Senate Academic Planning Deletion March 21, 2016: MA273 Prerequisite BU255 deleted; effective Sept. 1, 2016.
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ST230: Introduction to Probability and Statistics for Science
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 2017
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, MA241, BU205, BU255, EC205, EC255, EC285, ST260.
View course outlines, organized by term and includes graduate courses.
ST231: Statistical Methods for Life and Health Sciences
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 oneway and twoway ANOVA. Problems are analyzed with the aid of appropriate software.
Fall 2017 / Winter 2018
Credits: 0.5
3 lecture hours, 1.5 lab hours (biweekly)
Prerequisites: One of: MA101, MA103, MA110*.
Exclusions: EC205, EC255, EC285, MA141, MA240, MA241, PS296, ST230, ST260.
Senate Editorial Change
Senate Academic Planning Committee March 20, 2017: ST231 New course; effective Sept. 1, 2017.
View course outlines, organized by term and includes graduate courses.
ST259: Probability I
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 2017
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.
View course outlines, organized by term and includes graduate courses.
ST260: Introduction to Statistics
Numerical and visual exploratory data analysis; probability models; point and interval estimation; bias and mean squared error of estimators; singlesample, 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 2018
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.]
View course outlines, organized by term and includes graduate courses.
300Level Courses
MA304: Introduction to Complex Analysis
Functions of a complex variable; transformations; integration; Taylor and Laurent expansions; theory of residues.†
Winter 2018
3 lecture hours
Credits: 0.5
Prerequisites: MA104 or MA200, and MA201.
View course outlines, organized by term and includes graduate courses.
MA305: Differential Equations II
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 2017
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.
View course outlines, organized by term and includes graduate courses.
MA307: Numerical Analysis
Numerical solution of equations and systems of equations; numerical integration; methods of interpolation, extrapolation and curvefitting; error analysis. Methods will be illustrated by exercises requiring the use of a computer.†
Fall 2017
3 lecture hours; 2 lab hours (biweekly)
Credits: 0.5
Prerequisites: MA122, MA104, MA201 and CP104 (or equivalent).
Exclusions: MA371.
View course outlines, organized by term and includes graduate courses.
MA323: Introduction to Groups and Rings
Examples and basic properties of groups and rings including their substructures, quotient structures and homomorphisms.
Fall 2017
3 lecture hours
Credits: 0.5
Prerequisites: MA215 or MA222.
Exclusions: MA225.
View course outlines, organized by term and includes graduate courses.
MA341: Introduction to the Theory of Statistics
Review of problems and objectives of parametric statistics; likelihood function; methods of finding estimators; properties of estimators; interval estimation; hypothesis testing procedures; NeymanPearson Lemma and likelihood ratio testing.†
Fall 2017
3 lecture hours
Credits: 0.5
Prerequisites: MA201, and one of MA141, or MA240 (or permission of the department).
Exclusions: ST361.
View course outlines, organized by term and includes graduate courses.
MA348: Statistical Methods for Data Analysis
This course provides a broad overview of modern statistical methods for data analysis. Statistical methodology may include linear and generalized linear models, multilevel modelling, nonparametric methods, resampling theory, pointprocesses, survival analysis and functional data analysis.
Winter 2018
3 lecture hours; 1 lab hour
Credits: 0.5
Prerequisites: ST362 or equivalent courses from other departments.
Senate/Editorial Changes
Editorial Revision March 28, 2017: MA348 Prerequisite revised; effective Sept. 1, 2017
View course outlines, organized by term and includes graduate courses.
MA350: Real Analysis
Topics in metric spaces including open and closed sets, compactness, uniform continuity. Sequences and series of functions. The RiemannStieltjes integral. Introduction to Lebesgue integration.
Winter 2018 / Spring 2017
3 lecture hours
Credits: 0.5
Prerequisites: MA250.
Exclusions: MA303.
View course outlines, organized by term and includes graduate courses.
MA360: Topics in Applied Mathematics
The formulation, analysis and interpretation of mathematical models in various areas of application. Possible topics include population modelling, fluid mechanics, classical and quantum systems, reactiondiffusion 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 2018
This course is offered every other year.
3 lecture hours
Credits: 0.5
Prerequisites: MA205, MA222, and one of MA200, MA201, MA250.
View course outlines, organized by term and includes graduate courses.
MA370: Financial Mathematics II
Discretetime 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 riskneutral pricing. Stopping times and American option pricing. Introduction to the BlackScholes theory and sensitivity analysis for options. Optional topics: introduction to singlefactor interest rate modelling and pricing of fixed income securities.
Winter 2018 / Spring 2017
3 lecture hours
Credits: 0.5
Prerequisites: MA270; and either MA340 or ST359.
View course outlines, organized by term and includes graduate courses.
MA372: Optimization
Linear programming algorithms, duality theory and postoptimum sensitivity analysis. Integer programming. Deterministic and stochastic dynamic programming. KuhnTucker conditions for optimality. Quadratic programming. Nonlinear programming. Network optimization. Modeling and applications.
Winter 2018
3 lecture hours
Credits: 0.5
Prerequisites: MA201, MA222.
View course outlines, organized by term and includes graduate courses.
ST359: Probability II
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 2017 / Spring 2017
3 lecture hours
Credits: 0.5
Prerequisites: MA201, ST259.
Exclusions: MA340.
View course outlines, organized by term and includes graduate courses.
ST361: Mathematical Statistics
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 2017
3 lecture hours
Credits: 0.5
Prerequisites: MA201, ST260 or (ST259 and one of MA241, ST230).
Exclusions: MA341.
View course outlines, organized by term and includes graduate courses.
ST362: Regression Analysis
Regression analysis including estimation, hypothesis testing, analysis of variance, variable selection techniques; regression diagnostics; generalized linear regression; nonlinear regression; nonparametric regression.
Fall 2017
3 lecture hours, 1 lab hour (biweekly)
Credits: 0.5
Prerequisites: MA122, ST260 or (ST259 and one of MA241, ST230).
Exclusions: MA242, EC245, EC295, EC355.
View course outlines, organized by term and includes graduate courses.
400Level Courses
MA419: Differential Geometry
Geometry of curves and surfaces, curvature, geodesics, first and second fundamental forms, the Gauss Theorema Egregium and the GaussBonnet theorem. Differential forms and vector fields. Line and surface integrals. The divergence and Stoke’s theorems.
Winter 2018
3 lecture hours
Credits: 0.5
Prerequisites: MA201, MA222, MA205, and a 0.5 MA credit at the 300 level.
Exclusions: MA303.
View course outlines, organized by term and includes graduate courses.
MA422: Advanced Linear Algebra
CayleyHamilton Theorem; real and complex inner product spaces; Spectral Theorem; bilinear and quadratic forms; canonical forms.
Fall 2017
3 lecture hours
Credits: 0.5
Prerequisites: MA222.
Exclusions: MA322.
Senate/Editorial Changes
 Senate Academic Planning Committee Revision Jan. 19, 2017: MA422 Description change; effective Sept. 1, 2017.
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MA425: Group Theory
Monoids and groups, subgroups, quotient groups and group homomorphisms: groups acting on sets, conjugacy and the class equation; the Sylow theorems; free gropus; finitely generated Abelian groups.
Winter 2018
This course is offered every other year.
3 lecture hours
Credits: 0.5
Prerequisites: MA222, MA323.
Exclusions: MA325.
View course outlines, organized by term and includes graduate courses.
MA451: Introduction to Stochastic Calculus
Conditional expectations, sigmaalgebras, and filtrations; martingales and stopping times; Gaussian processes and Brownian motion; stochastic integration and Ito’s formula; diffusion processes and stochastic differential equations; the FeynmanKac theorem.
Fall 2017
3 lecture hours
Credits: 0.5
Prerequisites: MA350; and ST359 (or MA340).
Exclusions: MA351.
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MA455: Partial Differential Equations
Hyperbolic, parabolic and elliptic differential equations; boundary value problems of applied mathematics including such partial differential equations as the heat equation, the wave equation and Laplace's equation. Techniques will include separation of variables, canonical transformations and integral transform methods.†
Fall 2017 / Spring 2017
3 lecture hours
Credits: 0.5
Prerequisites: MA104 or MA200, MA201 and MA205, and a 0.5 MA credit at the 300 level.
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MA470: Financial Mathematics III
Continuoustime financial models and riskless asset pricing. BlackScholes theory. Arbitrage free pricing of European, American, and exotic options. Optional topics: stochastic volatility and jumpdiffusion models; continuoustime interest rate models; pricing bonds and derivatives on interest rates.
Winter 2018
3 lecture hours
Credits: 0.5
Prerequisites: MA370, MA451 (or MA351), MA455.
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MA489: Honours Seminar
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.)
FallWinter 2017/18
Credits: 0.5
Prerequisites: Permission of the department.
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MA490: Stochastic Processes
Markov Chains in discrete and continuous time; birthdeath processes; renewal theory; renewalreward theory; Markov processes; stationary processes; introduction to queuing theory.††
Fall 2017
3 lecture hours
Credits: 0.5
Prerequisites: MA340 or ST359.
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MA492/EC455: Time Series Analysis
A survey of the econometrics of time series analysis and recent advances in regression methods.
Winter 2018
3 lecture hours; 1 lab hour (biweekly)
Credits: 0.5
Prerequisites: EC355 or MA242 or ST362.
Notes: Lab pertains to MA492 sections.
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MA495I: Special Topics: Game Theory II
A detailed examination of a special topic not covered by the Department's regular course offerings. The topic and evaluation scheme must be approved by the Department.
Winter 2018
3 lecture hours
Credits: 0.5
Prerequisites: Permission of the Department of Mathematics.
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ST474: Monte Carlo Methods
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 2018
3 lecture/discussion hours; 1 lab hour (biweekly)
Credits: 0.5
Prerequisites: CP104, MA201, ST260 or (ST259 and one of MA241, ST230), and a 0.5 MA/ST credit at the 300 level (MA307 is recommended).
3 lecture hours; 1 lab hour (biweekly)
Exclusions: MA495H
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MA547: Monte Carlo and Simulation Methods
Monte Carlo techniques and simulation methods are studied in detail. Applications include mathematical modelling and computation of numerical solutions; evaluation of multidimensional integrals through pseudorandom numbers, quasirandom 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 2018
Credits: 0.5
Note: Formerly offered as MA647 (Monte Carlo and Simulation Methods)
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600Level Courses
MA632: Optimization
Fundamental concepts of linear and nonlinear optimization theory for developing algorithms and models are discussed. Topics include: duality and problem structure for finding, recognizing and interpreting solutions; network optimization problems; problems with integer constraints; combinatorial optimization problems; the simplex algorithm for linear programming; linear programming duality and complementary slackness; the network simplex algorithm; Newton and gradient methods for unconstrained optimization; Lagrange multipliers; penalty and barrier methods for constrained optimization; and an introduction to interiorpoint methods for linear and convex programming. Search techniques for hard problems may be included. The output of appropriate computer packages is analyzed.
Fall 2017
Credits: 0.5
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MA651: Stochastic Analysis
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 superMartingales; the Martingale Stopping Time Theorem; Girsanov's Theorem and the RadonNikodym derivative; stochastic differential equations for single and multiple random processes; Kolmogorov equations and the FeynmanKac 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 2017
3 lecture hours
Credits: 0.5
Prerequisites: MA350; and ST359 (or MA340).
Exclusions: MA351.
View course outlines, organized by term and includes graduate courses.
MA660: Dynamical Systems
This course studies the qualitative and quantitative theory of dynamical systems. Topics include: extensions of Picard's theorems; stability properties of continuoustime systems and of discretetime iterative maps; linearization; Lyapunov direct method; centre manifold; and bifurcation. Other topics may include: delay/feedback equations, limit cycles, strange attractors and deterministic chaos. Applications to neural networks and complex ecosystems are examined.
Fall 2017
Credits: 0.5
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MA670: Financial Mathematics: ContinuousTime Option Pricing
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 BlackScholes partial differential equation; pricing of standard European, American and multiasset options under geometric Brownian motions; stochastic asset price models; multifactor 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 multiasset derivatives.
Winter 2017
Credits: 0.5
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MA680: Seminar in Mathematical Modelling in Finance and Science
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 2017
Credits: 0.5
View course outlines, organized by term and includes graduate courses.
MA686A: Special Topics: Introduction to Theory of Statistics
A detailed examination of a special topic not covered by the Department's regular course offerings. The topic and evaluation scheme must be approved by the Department.
Fall 2017
Credits: 0.5
Prerequisites: Permission of the Department of Mathematics.
View course outlines, organized by term and includes graduate courses.
MA686C: Special Topics: Game Theory II
A detailed examination of a special topic not covered by the Department's regular course offerings. The topic and evaluation scheme must be approved by the Department.
Winter 2018
Credits: 0.5
Prerequisites: Permission of the Department of Mathematics.
View course outlines, organized by term and includes graduate courses.
MA686D: Special Topics: Advanced Data Analysis
A detailed examination of a special topic not covered by the Department's regular course offerings. The topic and evaluation scheme must be approved by the Department.
Winter 2018
Credits: 0.5
Prerequisites: Permission of the Department of Mathematics.
View course outlines, organized by term and includes graduate courses.
MA686E: Special Topics: Topics in Abstract Algebra: Ring and Field Theory
A detailed examination of a special topic not covered by the Department's regular course offerings. The topic and evaluation scheme must be approved by the Department.
Winter 2018
Credits: 0.5
Prerequisites: Permission of the Department of Mathematics.
View course outlines, organized by term and includes graduate courses.
MA686F: Special Topics: Advanced Regression Analysis
A detailed examination of a special topic not covered by the Department's regular course offerings. The topic and evaluation scheme must be approved by the Department.
Fall 2017
Credits: 0.5
Prerequisites: Permission of the Department of Mathematics.
View course outlines, organized by term and includes graduate courses.
MA686G: Special Topics: Stochastic Processes
A detailed examination of a special topic not covered by the Department's regular course offerings. The topic and evaluation scheme must be approved by the Department.
Fall 2017
Credits: 0.5
Prerequisites: Permission of the Department of Mathematics.
MA686H: Special Topics: Time Series Analysis
A detailed examination of a special topic not covered by the Department's regular course offerings. The topic and evaluation scheme must be approved by the Department.
Winter 2018
Credits: 0.5
Prerequisites: Permission of the Department of Mathematics.
View course outlines, organized by term and includes graduate courses.
MA695: Major Project
MA699: Master's Thesis
Winter 2018
100Level Courses
 MA100: Introductory Calculus for the Natural Sciences
 MA101: Calculus I for the Natural Sciences
 MA103: Calculus I
 MA104: Calculus II
 MA110A/B*: Introduction to Differential and Integral Calculus
 MA121: Introduction to Mathematical Proofs
 MA122: Introductory Linear Algebra
 MA129: Introductory Calculus for Business and Social Sciences
 MA170: Introduction to Mathematics for Finance
 MA170OC2: Introduction to Mathematics for Finance
200Level Courses
 MA201: Multivariable Calculus
 MA205: Differential Equations I
 MA218: Euclidean Geometry
 MA222: Linear Algebra
 MA233: Problem Solving in Mathematics
 MA238: Discrete Mathematics
 MA250: Introduction to Analysis
 MA270: Financial Mathematics I
 MA273: Introduction to Actuarial Mathematics
 ST231: Statistical Methods for Life and Health Sciences
 ST260: Introduction to Statistics
300Level Courses
 MA304: Introduction to Complex Analysis
 MA348: Statistical Methods for Data Analysis
 MA350: Real Analysis
 MA360: Topics in Applied Mathematics
 MA370: Financial Mathematics II
 MA372: Optimization
400Level Courses
 MA419: Differential Geometry
 MA425: Group Theory
 MA470: Financial Mathematics III
 MA489: Honours Seminar
 MA492/EC455: Time Series Analysis
 MA495I: Special Topics in Game Theory
 ST474: Monte Carlo Methods
GraduateLevel Courses
 MA547: Monte Carlo and Simulation Methods
 MA670: Financial Mathematics: ContinuousTime Option Pricing
 MA686C: Special Topics: Game Theory II
 MA686D: Special Topics: Advanced Data Analysis
 MA686E: Special Topics: Topics in Abstract Algebra: Ring and Field Theory
 MA686H: Special Topics: Time Series Analysis
 MA695: Major Project
Fall 2017
100Level Courses
 MA100: Introductory Calculus for the Natural Sciences
 MA101: Calculus I for the Natural Sciences
 MA103: Calculus I
 MA104: Calculus II
 MA110A/B*: Introduction to Differential and Integral Calculus
 MA121: Introduction to Mathematical Proofs
 MA122: Introductory Linear Algebra
 MA129: Introductory Calculus for Business and Social Sciences
 MA170: Introduction to Mathematics for Finance
 MA170OC1: Introduction to Mathematics for Finance
 SC101: Essential Skills for Mathematics
200Level Courses
 MA201: Multivariable Calculus
 MA205: Differential Equations I
 MA215: Set Theory
 MA222: Linear Algebra
 MA235: Introduction to Game Theory
 MA238: Discrete Mathematics
 MA250: Introduction to Analysis
 ST230: Introduction to Probability and Statistics for Science
 ST231: Statistical Methods for Life and Health Sciences
 ST259: Probability I
300Level Courses
 MA305: Differential Equations II
 MA307: Numerical Analysis
 MA323: Introduction to Groups and Rings
 MA341: Introduction to the Theory of Statistics
 ST359: Probability II
 ST361: Mathematical Statistics
 ST362: Regression Analysis
400Level Courses
 MA422: Advanced Linear Algebra
 MA451: Introduction to Stochastic Calculus
 MA455: Partial Differential Equations
 MA489: Honours Seminar
 MA490: Stochastic Processes
GraduateLevel Courses
Spring 2017
100Level Courses
 MA101: Calculus I for the Natural Sciences
 MA103: Calculus I
 MA104: Calculus II
 MA121: Introduction to Mathematical Proofs
 MA122: Introductory Linear Algebra
 MA129: Introductory Calculus for Business and Social Sciences
 MA170: Introduction to Mathematics for Finance
 MA170 OC1: Introduction to Mathematics for Finance
200Level Courses
 MA201: Multivariable Calculus
 MA205: Differential Equations I
 MA222: Linear Algebra
 MA241: Statistical Methods for the Life Sciences
 MA250: Introduction to Analysis