# Course Offerings for 2018/19

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.

View graduate-level courses.

## 100-Level Courses

### DATA100: Introduction to Data Analytics

**Winter 2019**

**3 lecture hours; 1.5 lab hours****Credits:** 0.5**Co-requisites:** CP104.

View course outlines, organized by term and includes graduate courses.

### MA100: Introductory Calculus for the Natural Sciences

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 2018 / Winter 2019**

**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 MA101, MA102, MA103, MA110*, MA129. This course may not count for credit in Mathematics programs.

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.

**Winter 2019**

**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.

View course outlines, organized by term and includes graduate courses.

### MA102: Introduction to Functions and Differential Calculus

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 2018**

**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.

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 2018 / Winter 2019**

**3 lecture hours; 1.5 lab hours****Credits:** 0.5**Prerequisites:** MA102, or a minimum score of 70% on the Calculus Preparation Evaluation (CPE); and Grade 12 Calculus or MA100 or MA129.**Exclusions:** MA101, MA110*.

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 2018 / Winter 2019**

**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.

### 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 2018 / Winter 2019**

**Credits:** 0.5

3 lecture/discussion hours; 1.5 lab hours (biweekly)**Exclusions:** MA120.

View course outlines, organized by term and includes graduate courses.

### MA122: Introductory Linear Algebra

Vector geometry in **R ^{2}** and

**R**; the vector space

^{3}**R**and its subspaces; spanning sets, linear independence, bases and dimension; dot product in

^{n}**R**and

^{n}**C**; systems of linear equations and Gaussian elimination; matrices and matrix operations; matrix inverse; matrix rank; linear transformations in

^{n}**R**; introduction to determinants, Cramer's rule; introduction to eigenvalues, eigenvectors and diagonalization of real matrices; applications of linear algebra.

^{n}**Fall 2018 / Winter 2019**

**3 lecture hours;**** 1.5 lab hours (biweekly)****Credits:** 0.5

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 2019**

**Brantford Campus****3 lecture/discussion hours, 1.5 tutorial/seminar hours****Credits:** 0.5**Prerequisites:** Grade 12 U-level math course or equivalent.**Exclusions:** This course can only count for credit for students in the Business Technology Management program. **Notes: **This course should not be counted towards qualifying for a teachable in mathematics.

### MA129: Introductory Calculus for Business and Social Sciences

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 2018 / Winter 2019**

**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:** Prior credit for, or current enrolment in, any of: MA100, MA101, MA102, MA103, MA110*. 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 2018 / Winter 2019**

**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 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 2018**

**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 first-year 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.

## 200-Level 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 2018 / Winter 2019**

**3 lecture hours, 1.5 lab hours (biweekly)****Credits:** 0.5**Prerequisites:** MA122, and one of MA101, MA103. MA104 is recommended. **Exclusions:** MA200.

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 2018 / Winter 2019**

**3 lecture hours, 1.5 lab hours (biweekly)****Credits:** 0.5**Prerequisites:** One of MA101 or MA103.

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 2018**

**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 non-Euclidean geometries.

**Winter 2019**

**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; Gram-Schmidt orthogonalization process; brief review of polynomials; eigenvalues, eigenvectors and diagonalizability of a linear operator; quadratic forms, Sylvester’s law of inertia.

**Fall 2018**

**3 lecture hours****Credits:** 0.5**Prerequisites:** MA121, MA122.

View course outlines, organized by term and includes graduate courses.

### MA235: Introduction to Game Theory

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 2018**

**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, inclusion-exclusion.

**Fall 2018 / Winter 2019**

**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.

### MA250: Introduction to Analysis

A rigorous development of calculus. Topics include sequences, series, convergence, limits, continuity, differentiability, and the Riemann integral.

**Fall 2018 / Winter 2019**

**3 lecture hours; 1.5 lab hours (biweekly)**

**Credits:**0.5

**Prerequisites:**MA121 and MA103.

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 log-normal asset pricing models, introductory no-arbitrage pricing of forwards and **options**, risk analysis.

**Winter 2019**

**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).

View course outlines, organized by term and includes graduate courses.

### 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.

View course outlines, organized by term and includes graduate courses.

### MA287: Mathematical Models for Natural Sciences

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 2018**

**Credits:** 0.5**3 lecture hours, 1.5 lab hours** **(biweekly)****Prerequisites:** One of MA101, MA103, MA110*.**Exclusions:** MA122. This course may not count for credit in Mathematics programs.**Notes:** Not open to students in mathematics, computer science, and physics programs.

View course outlines, organized by term and includes graduate courses.

### 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 2018**

**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 one-way and two-way ANOVA. Problems are analyzed with the aid of appropriate software.

**Winter 2019**

**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.

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 2018**

**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; 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 2019**

**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.

## 300-Level Courses

### MA304: Introduction to Complex Analysis

Functions of a complex variable; transformations; integration; Taylor and Laurent expansions; theory of residues.†

**Fall 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 2018**

** 3 lecture hoursCredits:** 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 curve-fitting; error analysis. Methods will be illustrated by exercises requiring the use of a computer.†

**Fall 2018 / Winter 2018**

**3 lecture hours; 2 lab hours (biweekly)Credits:** 0.5

**Prerequisites:**MA122, MA104, MA201, MA205 and CP104.

**Exclusions:**CP315, MA371, PC315.

**Senate/Editorial Changes**

- Senate Academic Planning Committee March 19, 2018: MA307 Description, prerequisite and exclusion revised; effective September 1, 2018.

View course outlines, organized by term and includes graduate courses.

### MA317: Number Theory

Elementary theory of numbers; arithmetic functions; congruences; quadratic reciprocity; solutions to Diophantine equations.†

**Winter 2019**

**Credits:**0.5

**Prerequisites:**MA121 and 1.0 credit of 200 level Mathematics.

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 2018**

** 3 lecture hoursCredits:** 0.5

**Prerequisites:**MA215 or MA222.

**Exclusions:**MA225.

View course outlines, organized by term and includes graduate courses.

### MA338: Graph Theory

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.

**Winter 2019**

** 3 lecture hours** 0.5

Credits:

**Prerequisites:**MA238

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 Riemann-Stieltjes integral. Introduction to Lebesgue integration.

**Winter 2019**

**3 lecture hoursCredits:** 0.5

**Prerequisites:**MA250.

**Exclusions:**MA303.

View course outlines, organized by term and includes graduate courses.

### MA365: Mathematical Biology

An introduction to the use of differential equations and difference equations for the purpose of studying biological systems, with an emphasis on deterministic models. Material will include Leslie matrix models of population growth, Lotka-Volterra models of predation and competition, and compartmental models of disease spread. Attention will be devoted to both the construction and the analysis of the models. Mathematical analysis will include techniques from stability theory and bifurcation theory.

**Winter 2019**

**3 lecture hoursCredits:** 0.5

**Prerequisites:**MA222, MA205; MA305 is recommended.

View course outlines, organized by term and includes graduate courses.

### MA370: Financial Mathematics II

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 2018 / Winter 2019**

**3 lecture hoursCredits:** 0.5

**Prerequisites:**MA270.

**Co-requisites:**ST359.

**Senate/Editorial Changes**

- Senate Academic Planning Committee March 19, 2018: MA370 Prerequisite and co-requisite revised; effective September 1, 2018.

View course outlines, organized by term and includes graduate courses.

### MA372: Optimization

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 2018**

** 3 lecture hoursCredits:** 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 2018 / Winter 2019**

**3 lecture hoursCredits:** 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 2018**

**3 lecture hoursCredits:** 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 2018**

**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.

## 400-Level Courses

### MA422: Advanced Linear Algebra

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 2018**

** 3 lecture hoursCredits:** 0.5

**Prerequisites:**MA222.

**Exclusions:**MA322.

View course outlines, organized by term and includes graduate courses.

### MA451: Introduction to Stochastic Calculus

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 2018**

**3 lecture hoursCredits:** 0.5

**Prerequisites:**MA350 and ST359.

**Exclusions:**MA351.

**Senate/Editorial Changes**

Senate Academic Planning Committee March 19, 2018: MA451 Description and prerequisite revised; effective September 1, 2018.

View course outlines, organized by term and includes graduate courses.

### 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 2018**

** 3 lecture hoursCredits:** 0.5

**Prerequisites:**MA104 or MA200, MA201 and MA205, and a 0.5 MA credit at the 300 level.

View course outlines, organized by term and includes graduate courses.

### MA470: Financial Mathematics III

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 2019**

**3 lecture/discussion hoursCredits:** 0.5

**Prerequisites:**MA370, MA451.

**Senate/Editorial Changes**

Senate Academic Planning Committee March 19, 2018: MA470 Description and prerequisite revised; effective September 1, 2018.

View course outlines, organized by term and includes graduate courses.

### MA471: Computational Methods in Finance

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 2019**

**3 lecture hours. 2 lab hours every other week.Credits:** 0.5

**Prerequisites:**MA205, MA307, MA370.

View course outlines, organized by term and includes graduate courses.

### MA475: Ring and Field Theory

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 2019**

**Credits:** 0.5**Prerequisites: **MA222, MA323.

View course outlines, organized by term and includes graduate courses.

### MA477: Quantitative Financial Risk Management

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. copulate).

**Fall 2018**

**Credits:** 0.5**Prerequisites: **MA270, MA307 or MA371, ST260.

View course outlines, organized by term and includes graduate courses.

### MA487: Mathematical Modelling in the Applied Sciences and Finance

An introduction to modelling tools used in modern applications of mathematics, with examples from the applied sciences and finance. The course will focus on the translation of real-world problems into an appropriate mathematical context, and on their subsequent solution, with emphasis on the uniformity of the modelling approach over various disciplines.

**Winter 2019**

**3 lecture hoursCredits:** 0.5

**Prerequisites:**MA205, MA307 or CP315/PC315.

View course outlines, organized by term and includes graduate courses.

### 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.)

**Fall-Winter 2018/19**

**Credits:** 0.5**Prerequisites: **Permission of the department.

View course outlines, organized by term and includes graduate courses.

### MA490: Stochastic Processes

Markov Chains in discrete and continuous time; birth-death processes; renewal theory; renewal-reward theory; Markov processes; stationary processes; introduction to queuing theory.††

**Winter 2019**

**3 lecture hoursCredits:** 0.5

**Prerequisites:**ST359 (or MA340).

View course outlines, organized by term and includes graduate courses.

### MA492/EC455: Time Series Analysis

A survey of the econometrics of time series analysis and recent advances in regression methods.

(Cross-listed as EC455.)

**Winter 2019**

**Winter 2019**

**3 lecture/discussion hours; 1 lab (biweekly).****Credits: **0.5

**EC355 or MA242 or ST362.**

**Prerequisites:****Notes: **Lab pertains to MA492 sections.

View course outlines, organized by term and includes graduate courses.

### 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 2019**

** 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).

**Exclusions:**MA495H

View course outlines, organized by term and includes graduate courses.

### MA570: Financial Mathematics in Discrete Time

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 2018**

**Credits:** 0.5

View course outlines, organized by term and includes graduate courses.

## 600-Level Courses

### MA641: Advanced Theory of Statistics

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 2018**

**Credits:** 0.5

View course outlines, organized by term and includes graduate courses.

### MA642: Advanced Regression Analysis

Regression analysis including estimation, hypothesis testing, analysis of variance, variable selection techniques; regression diagnostics; generalized linear regression; nonlinear regression; nonparametric regression.

**Fall 2018**

**Credits:** 0.5**Exclusions:** MA686F, ST362.

View course outlines, organized by term and includes graduate courses.

### MA647: 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 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 2019**

**Credits:** 0.5

**Exclusions****:**MA547, ST474.- View course outlines, organized by term and includes graduate courses.

### 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 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 2018**

**Credits:** 0.5**Notes:** Formerly offered as MA551 (Stochastic Analysis).

View course outlines, organized by term and includes graduate courses.

### MA665: Mathematical Biology

An introduction to the use of dynamical systems for the purpose of studying biological systems. Models will be chosen from ecology and epidemiology, including structured populations, as well as genetics and systems biology. Mathematical analysis will include techniques from stability analysis, bifurcation theory and persistence theory applied to ordinary differential equations, partial differential equations, difference equations, delay equations, stochastic equations or integral equations.

**Winter 2019**

**Credits:** 0.5**Prerequisites:** MA660 is recommended.

View course outlines, organized by term and includes graduate courses.

### MA670: Financial Mathematics: Continuous-Time 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 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 2019**

**Credits: **0.5**Exclusions:** MA470.

View course outlines, organized by term and includes graduate courses.

### MA671: Computational Methods in Finance

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 2019**

**Credits: **0.5**Exclusions:** MA686B, MA471.

View course outlines, organized by term and includes graduate courses.

### 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 2018**

**Credits:** 0.5

View course outlines, organized by term and includes graduate courses.

### MA686E: Special Topics: Topics in Abstract Algebra

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 2019**

**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.

**Winter 2019**

**Credits:** 0.5**Prerequisites:** Permission of the Department of Mathematics.

View course outlines, organized by term and includes graduate courses.

### 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 2019**

**Credits:** 0.5**Prerequisites:** Permission of the Department of Mathematics.

View course outlines, organized by term and includes graduate courses.

### MA686I: Special Topics: Quantitative Financial Risk Management

**Fall 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

## 800-Level Courses

### MA820: Interdisciplinary Seminar in Modelling and its Applications

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.

To document attendance of the Interdisciplinary Seminar, students are required to complete a brief statement indicating which presentations they attended (speaker name, institution, title, date) and a two to three sentence summary or critique of each seminar. This seminar attendance form shall be included in the annual report as an appendix. Students are required to attend a minimum of six presentations every year.

Graded as complete/incomplete.

**Fall/Winter 2018/19 **

**Credits:** 0.0

View course outlines, organized by term and includes graduate courses.

### MA880: Graduate Seminar in Mathematical and Statistical Modelling

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 2018 **

**Credits:** 0.5**Prerequisites:** Permission of the Department of Mathematics.

View course outlines, organized by term and includes graduate courses.

### MA899: Doctoral Dissertation

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 2018, Winter 2019, Spring 2019**

**Credits:** 0.5

View course outlines, organized by term and includes graduate courses.

### Fall 2018

**100-Level Courses**

- MA100: Introductory Calculus for the Natural Sciences
- MA102: Introduction to Functions and Differential Calculus
- 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
- MA170OC1: Introduction to Mathematics for Finance
- SC101: Essential Skills for Mathematics

**200-Level 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
- MA287: Mathematical Models for Natural Sciences
- ST230: Introduction to Probability and Statistics for Science
- ST259: Probability I

**300-Level Courses**

- MA304: Introduction to Complex Analysis
- MA305: Differential Equations II
- MA307: Numerical Analysis
- MA323: Introduction to Groups and Rings
- MA370: Financial Mathematics II
- ST359: Probability II
- ST361: Mathematical Statistics
- ST362: Regression Analysis

**400-Level Courses**

- MA422: Advanced Linear Algebra
- MA451: Introduction to Stochastic Calculus
- MA455: Partial Differential Equations
- MA477: Quantitative Financial Risk Management
- MA489: Honours Seminar

**Graduate-Level Courses**

**500-Level Courses**

**600-Level Courses**

- MA641: Advanced Theory of Statistics
- MA642: Advanced Regression Analysis
- MA651: Stochastic Analysis
- MA680: Seminar in Mathematical Modelling in Finance and Science
- MA686I: Special Topics: Quantitative Financial Risk Management

**800-Level Courses**

- MA820: Interdisciplinary Seminar in Modelling and its Applications
- MA880: Graduate Seminar in Mathematical and Statistical Modelling

### Spring 2018

**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
- MA129: Introductory Calculus for Business and Social Sciences
- MA170: Introduction to Mathematics for Finance
- MA170OC1: Introduction to Mathematics for Finance

**200-Level Courses**

- MA201: Multivariable Calculus
- MA205: Differential Equations I
- MA222: Linear Algebra
- MA250: Introduction to Analysis
- ST231: Statistical Methods for Life and Health Sciences
- ST259: Probability I

**300-Level Courses**

**400-Level Courses**

### Winter 2019

**100-Level Courses**

- DATA100: Introduction to Data Analytics
- MA100: Introductory Calculus for the Natural Sciences
- 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
- MA170OC2: Introduction to Mathematics for Finance

**200-Level Courses**

- MA201: Multivariable Calculus
- MA205: Differential Equations I
- MA218: Euclidean Geometry
- 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

**300-Level Courses**

- MA307: Numerical Analysis
- MA317: Number Theory
- MA338: Graph Theory
- MA350: Real Analysis
- MA365: Mathematical Biology
- MA370: Financial Mathematics II
- MA372: Optimization
- ST359: Probability II

**400-Level Courses**

- MA470: Financial Mathematics III
- MA471: Computational Methods in Finance
- MA475: Ring and Field Theory
- MA487: Mathematical Modelling in the Applied Sciences and Finance
- MA489: Honours Seminar
- MA490: Stochastic Processes
- MA492/EC455: Time Series Analysis
- ST474: Monte Carlo Methods

**Graduate-Level Courses**

**600-Level Courses**

- MA647: Monte Carlo and Simulation Methods
- MA665: Mathematical Biology
- MA670: Financial Mathematics: Continuous-Time Option Pricing
- MA671: Computational Methods in Finance
- MA686E: Special Topics: Topics in Abstract Algebra
- MA686G: Special Topics: Stochastic Processes
- MA686H: Special Topics: Time Series Analysis

**800-Level Courses**

- MA820: Interdisciplinary Seminar in Modelling and its Applications