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About the University of Calgary
 Graduate Studies Calendar 2012-2013 Courses of Instruction Course Descriptions A Applied Mathematics AMAT
Applied Mathematics AMAT
AMAT 501 503 505 507 509 581 601 605 613 617 621 643 671 673 677 681 683
 

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 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(3-0)
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(3-0)
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(3-0)
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. Electro-dynamics. General Relativity.
Course Hours: H(3-0)
Prerequisite(s): Applied Mathematics 505 or consent of the Division.
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Applied Mathematics 509       Analytical Dynamics
Symplectic geometry, Hamilton's equation, Hamilton-Jacobi theory, constraints and reduction.
Course Hours: H(3-0)
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 risk-neutral valuation, interest rate models, energy and commodity markets, value-at-risk and risk management.
Course Hours: H(3-0)
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(3-0)
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. Poincare-Bendixson.
Course Hours: H(3-0)
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, non-linear problems.
Course Hours: H(3-0)
Prerequisite(s): Consent of the Division.
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Applied Mathematics 617       Analysis IV
Analysis in abstract spaces. Function spaces.
Course Hours: H(3-0)
Prerequisite(s): Pure Mathematics 545.
Also known as: (formerly Pure Mathematics 617)
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Applied Mathematics 621       Research Seminar
Reports on studies of the literature or of current research.
Course Hours: Q(2S-0)
Notes: All graduate students in Mathematics and Statistics are required to participate in one of Applied Mathematics 621, Pure Mathematics 621, Statistics 621 each semester.
MAY BE REPEATED FOR CREDIT NOT INCLUDED IN GPA
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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(3-0)
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(3-0)
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(3-0)
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(3-0)
Prerequisite(s): Applied Mathematics 311 and 491.
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Applied Mathematics 681       Stochastic Calculus for Finance
Martingales in discrete and continuous time, risk-neutral valuations, discrete- and continuous-time (B,S)-security markets, Cox-Ross-Rubinstein formula, Wiener and Poisson processes, Ito formula, stochastic differential equations, Girsanov’s theorem, Black-Scholes and Merton formulas, stopping times and American options, stochastic interest rates and their derivatives, energy and commodity models and derivatives, value-at-risk and risk management.
Course Hours: H(3-0)
Prerequisite(s): Applied Mathematics 481.
Antirequisite(s): Credit for both Applied Mathematics 681 and 581 will not be allowed.
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Applied Mathematics 683       Computational Finance

Review of financial asset price and option valuation models; model calibration; tree-based methods; finite-difference methods; Monte Carlo simulation; Fourier methods.
Course Hours: H(3-0)
Prerequisite(s): Applied Mathematics 481 and 491.
Antirequisite(s): Credit for both Applied Mathematics 683 and 583 will not be allowed.
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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.