Instruction offered by members of the Department of Mathematics and Statistics in the Faculty of Science.
Department Head  T. Bisztriczky
Note: For listings of related courses, see Actuarial Science, Mathematics, Pure Mathematics and Statistics.


Applied Mathematics
217

Calculus for Engineers and Scientists


Functions, limits, continuity, derivatives, Mean Value Theorem, integrals, Fundamental Theorem of Calculus, applications to the physical sciences.
Course Hours:
H(31T1.5)
Prerequisite(s):
A grade of 70% or higher in Pure Mathematics 30 and credit in Mathematics 31; or admission to the Faculty of Engineering including credit in Pure Mathematics 30 and Mathematics 31.
Antirequisite(s):
Note: Credit for more than one of Mathematics 249, 251, 281 or Applied Mathematics 217 will not be allowed.

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Applied Mathematics
307

Differential Equations for Engineers


Definition, existence and uniqueness of solutions, first and second order equations with applications, series solutions about regular points and singular points, special functions. Laplace transform, systems of equations.
Course Hours:
H(31.5T)
Prerequisite(s):
Mathematics 211 or 221; and Applied Mathematics 219 or Mathematics 253.
Antirequisite(s):
Note: Credit for both Applied Mathematics 307 and 311 will not be allowed.

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Applied Mathematics
311

Differential Equations I


Classification of ordinary differential equations, first and second order equations with applications, series solutions about regular points and singular points, special functions, Laplace transform.
Course Hours:
H(31T)
Prerequisite(s):
Mathematics 253 or 263 or 283 or Applied Mathematics 219.
Antirequisite(s):
Note: Credit for both Applied Mathematics 307 and 311 will not be allowed.

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Applied Mathematics
411

Differential Equations II


Existence and uniqueness theorems, comparison and oscillation theorems, Green's functions, SturmLiouville problems, systems of equations, phase portraits, stability.
Course Hours:
H(31T)
Prerequisite(s):
One of Applied Mathematics 311 or 307, and one of Mathematics 331, 353, 381, Applied Mathematics 309, or consent of the Division.
Notes:
It is recommended that students complete Pure Mathematics 435 or 455 before taking this course.

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Applied Mathematics
413

Introduction to Partial Differential Equations


Orthogonal sets of functions, Fourier series, solution of potential equation, heat equation and wave equation. Numerical solution of partial differential equations.
Course Hours:
H(31T)
Prerequisite(s):
One of Mathematics 353, 381, Applied Mathematics 309, Mathematics 331; or consent of the Division.
Antirequisite(s):
Note: Credit for both Applied Mathematics 413 and 407 will not be allowed.

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Applied Mathematics
425

Introduction to Optimization


Examples of optimization problems. Quadratic forms, minimum energy and distance. Least squares, generalized inverse. Location and classification of critical points. Variational treatment of eigenvalues. Lagrange multipliers. Linear programming.
Course Hours:
H(31T)
Prerequisite(s):
Mathematics 311; and Mathematics 353 or 381 or Applied Mathematics 309 or Mathematics 331.

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Applied Mathematics
481

Introduction to Mathematical Finance


Introduction to financial markets and derivatives, asset price random walks, BlackScholes option pricing model, American options and other generalizations.
Course Hours:
H(31T)
Prerequisite(s):
Mathematics 323 and one of 353 or 381.

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Applied Mathematics
483

Computational Methods in Mathematical Finance


Review of financial models, MonteCarlo simulation, binomial and trinomial trees, finitedifference method, aspects of time series and parameter estimation, volatility modelling and estimation.
Course Hours:
H(31T)
Prerequisite(s):
Applied Mathematics 481 and 491.

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Applied Mathematics
501

Seminar in Applied Mathematics


Topics will be chosen according to the interests of instructors and students and could include analysis of optimization algorithms, approximation theory, control theory, differential equations, mathematical physics.
Course Hours:
H(30)
Prerequisite(s):
Consent of the Division.
MAY BE REPEATED FOR CREDIT

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Applied Mathematics
503

The Mathematics of Wavelets, Signal and Image Processing


Continuous and discrete Fourier transforms, the Fast Fourier Transform, wavelet transforms, multiresolution analysis and orthogonal wavelet bases, and applications.
Course Hours:
H(31T)
Prerequisite(s):
Applied Mathematics 491 or Computer Science 491.

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Applied Mathematics
505

Calculus on Manifolds


Integral and differential calculus on manifolds including tensor fields, covariant differentiation, Lie differentiation, differential forms, Frobenius' theorem, Stokes' theorem, flows of vector fields.
Course Hours:
H(30)
Prerequisite(s):
Pure Mathematics 445 or 545; and one of Applied Mathematics 311 or 307; or consent of the Division.

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Applied Mathematics
507

Introduction to Relativity Theory


Mathematical theories of space and time. Special Relativity. Electrodynamics. General Relativity.
Course Hours:
H(30)
Prerequisite(s):
Applied Mathematics 505 or consent of the Division.

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Applied Mathematics
509

Analytical Dynamics


Symplectic geometry, Hamilton's equation, HamiltonJacobi theory, constraints and reduction.
Course Hours:
H(30)
Prerequisite(s):
Applied Mathematics 505 or consent of the Division.

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Applied Mathematics
581

Advanced Futures and Options


Stochastic calculus and the dynamics of asset prices, martingale theory and riskneutral valuation, interest rate models, energy and commodity markets, valueatrisk and risk management.
Course Hours:
H(30)
Prerequisite(s):
Applied Mathematics 483 and Statistics 407.

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Graduate Courses
In addition to the prerequisites listed below, consent of the Applied Mathematics Division is a prerequisite for all graduate courses in Applied Mathematics.

Applied Mathematics
601

Topics in Applied Mathematics


Topics will be chosen according to the interests of instructors and students.
Course Hours:
H(30)
Prerequisite(s):
Consent of the Division.
MAY BE REPEATED FOR CREDIT

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Applied Mathematics
605

Differential Equations III


Linear systems, classification. Nonlinear systems: Existence and uniqueness. Flow and one parameter groups of transformations. Stability theory. Hyperbolicity, Unstable/Stable/Center manifold theorems. PoincareBendixson.
Course Hours:
H(30)
Prerequisite(s):
Applied Mathematics 411 and Pure Mathematics 445 or 545 or equivalents.

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Applied Mathematics
613

Partial Differential Equations II


Fundamental solutions, integral equations, eigenvalue problems, nonlinear problems.
Course Hours:
H(30)
Prerequisite(s):
Consent of the Division.

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Applied Mathematics
617

Analysis IV


Analysis in abstract spaces. Function spaces.
Course Hours:
H(30)
Prerequisite(s):
Pure Mathematics 545.
Also known as:
(formerly Pure Mathematics 617)

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Applied Mathematics
643

Perturbation Theory


Perturbation problems for ordinary differential equations, matrices and more general operators. Applications. Methods will be motivated by discussion of physical problems.
Course Hours:
H(30)
Prerequisite(s):
Familiarity with complex variables, linear algebra and differential equations.

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Applied Mathematics
671

Numerical Linear Algebra


Iterative and elimination methods for linear systems of equations, determination of eigenvalues, linear and convex programming.
Course Hours:
H(30)
Prerequisite(s):
Applied Mathematics 441 or Mathematics 411; and Applied Mathematics 491.

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Applied Mathematics
673

Approximation Theory


Existence, uniqueness of minimal solutions, Haar systems, characterization by alternation, Remez algorithm, monotone operators, spline approximation.
Course Hours:
H(30)
Prerequisite(s):
Applied Mathematics 491; and Pure Mathematics 435 or 455.

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Applied Mathematics
677

Numerical Solution of Partial Differential Equations


Explicit and implicit methods for PDE, difference equations.
Course Hours:
H(30)
Prerequisite(s):
Applied Mathematics 311 and 491.

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In addition to the numbered and titled courses shown above, the department offers a selection of advanced level graduate courses specifically designed to meet the needs of individuals or small groups of students at the advanced doctoral level. These courses are numbered in the series 800.01 to 899.99. Such offerings are, of course, conditional upon the availability of staff resources.
