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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.
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Applied Mathematics
501
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Seminar in Applied Mathematics
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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
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The Mathematics of Wavelets, Signal and Image Processing
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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
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Calculus on Manifolds
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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
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Introduction to Relativity Theory
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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
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Analytical Dynamics
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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
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Advanced Futures and Options
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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.
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Applied Mathematics
601
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Topics in Applied Mathematics
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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
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Differential Equations III
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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
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Partial Differential Equations II
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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
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Analysis IV
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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
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Research Seminar
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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
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Perturbation Theory
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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
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Numerical Linear Algebra
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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
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Approximation Theory
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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
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Numerical Solution of Partial Differential Equations
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Explicit and implicit methods for PDE, difference equations.
Course Hours:
H(3-0)
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.
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Courses of Instruction