# Course Offerings for 2016/17

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.

For more information, see the undergraduate and graduate academic calendars.

Jump to: Course Outlines (organized by term; includes graduate courses)

Jump to: Graduate-Level Courses

## 100-Level 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 2016; Winter 2017****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.

Jump to: Course Outlines (organized by term; 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 2016; Winter 2017; 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.

### 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 2016; Winter 2017; 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.

Jump to: Course Outlines (organized by term; includes graduate courses)

### MA104: Calculus II

Applications of integration; polar coordinates and parametric equations; infinite sequences and series; applications of partial derivatives.

**Fall 2016; Winter 2017; Spring 2017****3 lecture hours; 1.5 lab hours****Credits:** 0.5**Prerequisites:** MA101 or MA103 (or MA110*) or MA105.**Exclusions:** MA102, MA200.

Jump to: Course Outlines (organized by term; 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.

**Fall-Winter 2016/2017 (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.

Jump to: Course Outlines (organized by term; 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 2016; Winter 2017; Spring 2017****3 lecture hours****Credits:** 0.5

Jump to: Course Outlines (organized by term; includes graduate courses)

### MA122: Introductory Linear Algebra

Systems of linear equations; algebra of complex numbers; algebra of matrices with real and complex entries; determinants and their applications; vector geometry in **R ^{2}** and

**R**; spanning, linear independence and linear transformations in

^{3}**R**and

^{n}**C**; introduction to eigenvalues and eigenvectors; applications of linear algebra.

^{n}**Fall 2016; Winter 2017; Spring 2017****3 lecture hours****Credits:** 0.5

Jump to: Course Outlines (organized by term; 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 2017****Brantford Campus****3 lecture hours, 1.5 tutorial 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.

### 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 2016; Winter 2017; 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.

Jump to: Course Outlines (organized by term; 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 2016; Winter 2017; Spring 2017****3 lecture hours, 1.5 lab hours****Credits:** 0.5**Prerequisites:** 12U Advanced Functions, or equivalent, or permission of the department.

Jump to: Course Outlines (organized by term; 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 2016; Winter 2017; 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).

Jump to: Course Outlines (organized by term; 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 2016; Winter 2017; Spring 2017****3 lecture hours, 1.5 lab hours (biweekly)****Credits:** 0.5**Prerequisites:** MA101, MA102, MA103 (or MA110*), or MA105.

Jump to: Course Outlines (organized by term; includes graduate courses)

### MA215: Set Theory

Equivalence relations and partitions; countable and uncountable sets; ordered sets; development of number systems.

**Fall 2016; Winter 2017****Credits:** 0.5**Prerequisites:** MA121.

Jump to: Course Outlines (organized by term; 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 2017****3 lecture hours****Credits:** 0.5**Prerequisites:** MA121, or consent of the department.

Jump to: Course Outlines (organized by term; includes graduate courses)

### MA222: Linear Algebra

Vector spaces; linear transformations; diagonalizability; applications.

**Fall 2016; Winter 2017; Spring 2017****3 lecture hours****Credits:** 0.5**Prerequisites:** MA121, MA122.

Jump to: Course Outlines (organized by term; 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 2016****3 lecture hours****Credits:** 0.5**Prerequisites:** One of: MA101, MA103 (or MA110*), MA105.

Jump to: Course Outlines (organized by term; 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 2016; Winter 2017****Credits:** 0.5**Prerequisites:** MA121 and an additional 0.5 MA credit.

Jump to: Course Outlines (organized by term; 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.

**Fall 2016; Winter 2017; Spring 20173 lecture hours, 1.5 lab hours (biweekly)**

**Credits:**0.5

**Prerequisites:**One of MA101, MA103, MA105, MA110*.

**Exclusions:**MA141, MA240, PS296.

Jump to: Course Outlines (organized by term; 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 2016; Winter 2017; Spring 20173 lecture hours**

**Credits:**0.5

**Prerequisites:**MA121, and one of MA102 or MA103 (or MA110*).

### 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 20173 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 September 1, 2016.

Jump to: Course Outlines (organized by term; 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 20173 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 September 1, 2016.

Jump to: Course Outlines (organized by term; 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 2016****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.

Jump to: Course Outlines (organized by term; 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 2016Credits:** 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.

Jump to: Course Outlines (organized by term; 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 2017Credits:** 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.]

Jump to: Course Outlines (organized by term; 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.†

**Winter 2017**

**Credits:**0.5

**Prerequisites:**MA104 or MA200, and MA201.

### 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 2016Credits:** 0.5

**Prerequisites:**MA122, MA104 or MA200, MA205 and either a 0.5 credit in computer programming or permission of the department.

**Exclusions:**MA308.

Jump to: Course Outlines (organized by term; 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 20163 lecture hours; 2 lab hours (biweekly)Credits:** 0.5

**Prerequisites:**MA122, MA104, MA201 and CP104 (or equivalent).

**Exclusions:**MA371.

Jump to: Course Outlines (organized by term; 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 2016Credits:** 0.5

**Prerequisites:**MA215 or MA222.

**Exclusions:**MA225.

Jump to: Course Outlines (organized by term; 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 2017Credits:** 0.5

**Prerequisites:**MA238.

Jump to: Course Outlines (organized by term; includes graduate courses)

### MA340: Probability Theory

Discrete and continuous probability models; formal probability spaces and random variables; multivariate and conditional distributions; mathematical expectation; conditioning; moment generating function and other transforms; functions of random variables; modes of convergence and limit theorems.†

**Fall 20163 lecture hoursCredits:** 0.5

**Prerequisites:**MA201, and one of ST259 or MA240 (or permission of the department).

Jump to: Course Outlines (organized by term; 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; Neyman-Pearson Lemma and likelihood ratio testing.†

**Winter 2017Credits:** 0.5

**Prerequisites:**MA201, and one of MA141, or MA240 (or permission of the department).

**Exclusions:**ST361.

Jump to: Course Outlines (organized by term; 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 2017; Spring 20173 lecture hoursCredits:** 0.5

**Prerequisites:**MA250.

**Exclusions:**MA303.

Jump to: Course Outlines (organized by term; 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, reaction-diffusion models, neural networks, discrete optimization, and signal and image processing. Mathematical techniques may include differential and difference equations, PDEs, Fourier analysis, optimization, game theory, calculus of variations, and numerical methods. Topics covered may vary from year to year.

**Winter 2018 (This course is offered every other year)3 lecture hoursCredits:** 0.5

**Prerequisites:**MA205, MA222, and one of MA200, MA201, MA250.

Jump to: Course Outlines (organized by term; 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 20173 lecture hoursCredits:** 0.5

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

Jump to: Course Outlines (organized by term; 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.

**Winter 2017; Spring 20173 lecture hoursCredits:** 0.5

**Prerequisites:**MA270; and either MA340 or ST359.

Jump to: Course Outlines (organized by term; 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 2017Credits:** 0.5

**Prerequisites:**MA201, MA222.

Jump to: Course Outlines (organized by term; 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 2016; Spring 2017****3 lecture hoursCredits:** 0.5

**Prerequisites:**MA201, ST259.

**Exclusions:**MA340.

**Note:**Senate Academic Planning Revision March 21, 2016: ST359 Prerequisite changed; effective September 1, 2016.

Jump to: Course Outlines (organized by term; 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.

**Winter 2017****3 lecture hoursCredits:** 0.5

**Prerequisites:**MA201, ST260 or (ST259 and one of MA241, ST230).

**Exclusions:**MA341.

**Note:**Senate Academic Planning Revision March 21, 2016: ST361 New course; effective September 1, 2016.

Jump to: Course Outlines (organized by term; 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 2016**

**3 lecture hours, 1 lab hour (biweekly)**

Credits:0.5

Credits:

**Prerequisites:**MA122, ST260 or (ST259 and one of MA241, ST230).

**Exclusions:**MA242, EC245, EC295, EC355.

**Note:**Senate Academic Planning Revision March 21, 2016: ST362 New course; effective September 1, 2016.

Jump to: Course Outlines (organized by term; includes graduate courses)

## 400-Level Courses

### MA422: Advanced Linear Algebra

Cayley-Hamilton Theorem; real and complex inner product spaces; Spectral Theorem; bilinear and quadratic forms; canonical forms.

**Fall 2016Credits:** 0.5

**Prerequisites:**MA222.

**Exclusions:**MA322.

### 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 hoursCredits:** 0.5

**Prerequisites:**MA222, MA323.

**Exclusions:**MA325.

Jump to: Course Outlines (organized by term; includes graduate courses)

### MA451: Introduction to Stochastic Calculus

Conditional expectations, sigma-algebras, and filtrations; martingales and stopping times; Gaussian processes and Brownian motion; stochastic integration and Ito’s formula; diffusion processes and stochastic differential equations; the Feynman-Kac theorem.

**Fall 20163 lecture hoursCredits:** 0.5

**Prerequisites:**MA350; and either MA340 or ST359.

**Exclusions:**MA351.

Jump to: Course Outlines (organized by term; 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 2016; Spring 2017Credits:** 0.5

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

Jump to: Course Outlines (organized by term; includes graduate courses)

### MA470: Financial Mathematics III

Continuous-time financial models and riskless asset pricing. Black-Scholes theory. 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 20173 lecture hoursCredits:** 0.5

**Prerequisites:**MA370, MA451 (or MA351), MA455.

Jump to: Course Outlines (organized by term; 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 2018 (This course is offered every other year)3 lecture hours. 2 lab hours every other weekCredits:** 0.5

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

Jump to: Course Outlines (organized by term; 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 2017Credits:** 0.5

**Prerequisites:**MA222, MA323.

Jump to: Course Outlines (organized by term; 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 2017Credits:** 0.5

**Prerequisites:**MA205, MA307 or MA371 or CP315/PC315.

Jump to: Course Outlines (organized by term; 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 2016/17****Credits:** 0.5**Prerequisites: **Permission of the department.

### 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.††

**Fall 20163 lecture hoursCredits:** 0.5

**Prerequisites:**MA340 or ST359.

Jump to: Course Outlines (organized by term; includes graduate courses)

### MA492/EC455: Time Series Analysis

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

**Winter 2017**

**3 lecture hours; 1 lab hour**(biweekly)**Credits:**0.5**Prerequisites:**EC355 or MA242 or ST362.Notes: Lab pertains to MA492 sections.

Jump to: Course Outlines (organized by term; 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 2017**(biweekly)

3 lecture/discussion hours; 1 lab hour

**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).

**(biweekly)**

3 lecture hours; 1 lab hour3 lecture hours; 1 lab hour

**Exclusions:**MA495H

?Jump to: Course Outlines (organized by term; includes graduate courses)

## 500-Level Courses

### 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 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 2017Credits:** 0.5

**Note:**Formerly offered as MA647 (Monte Carlo and Simulation Methods)

Jump to: Course Outlines (organized by term; includes undergraduate courses)

## 600-Level 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 2016Credits:** 0.5

**Note:**Formerly offered as MA551 (Stochastic Analysis).

Jump to: Course Outlines (organized by term; includes undergraduate 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 continuous-time systems and of discrete-time 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 2016Credits:** 0.5

Jump to: Course Outlines (organized by term; includes undergraduate 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 2017Credits:** 0.5

**Prerequisite:**MA660 is recommended

Jump to: Course Outlines (organized by term; includes undergraduate 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 2017Credits:** 0.5

Jump to: Course Outlines (organized by term; includes undergraduate 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 2016Credits:** 0.5

Jump to: Course Outlines (organized by term; includes undergraduate 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.

**Winter 2017Credits:** 0.5

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

Jump to: Course Outlines (organized by term; includes undergraduate 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.

**Fall 2016Credits:** 0.5

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

Jump to: Course Outlines (organized by term; includes undergraduate 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 2017Credits:** 0.5

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

Jump to: Course Outlines (organized by term; includes undergraduate courses)

### MA695: Major Project

### MA699: Master's Thesis

### Spring 2017

**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
- MA170 OC1: Introduction to Mathematics for Finance

**200-Level Courses**

- MA201: Multivariable Calculus
- MA205: Differential Equations I
- MA222: Linear Algebra
- MA241: Statistical Methods for the Life Sciences
- MA250: Introduction to Analysis

**300-Level Courses**

**400-Level Courses**

### Winter 2017

**100-Level 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

**200-Level Courses**

- MA201: Multivariable Calculus
- MA205: Differential Equations I
- MA215: Set Theory
- MA218: Euclidean Geometry
- MA222: Linear Algebra
- MA238: Discrete Mathematics
- MA241: Statistical Methods for the Life Sciences
- MA250: Introduction to Analysis
- MA270: Financial Mathematics I
- MA273: Introduction to Actuarial Mathematics
- ST259: Probability I
- ST260: Introduction to Statistics

**300-Level Courses**

- MA304: Introduction to Complex Analysis
- MA338: Graph Theory
- MA341: Introduction to the Theory of Statistics
- MA350: Real Analysis
- MA365: Mathematical Biology
- MA370: Financial Mathematics II
- MA372: Optimization
- ST361: Mathematical Statistics

**400-Level Courses**

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

**Graduate-Level Courses**

### Fall 2016

**100-Level 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

**200-Level Courses**

- MA201: Multivariable Calculus
- MA205: Differential Equations I
- MA215: Set Theory
- MA222: Linear Algebra
- MA235: Introduction to Game Theory
- MA238: Discrete Mathematics
- MA241: Statistical Methods for the Life Sciences
- MA250: Introduction to Analysis
- ST230: Introduction to Probability and Statistics for Science
- ST259: Probability I

**300-Level Courses**

- MA305: Differential Equations II
- MA307: Numerical Analysis
- MA323: Introduction to Groups and Rings
- MA340: Probability Theory
- ST359: Probability II
- ST362: Regression Analysis

**400-Level Courses**

- MA422: Advanced Linear Algebra
- MA451: Introduction to Stochastic Calculus
- MA455: Partial Differential Equations
- MA489: Honours Seminar
- MA490: Stochastic Processes