Graduate Courses for Masters in the Mathematics of Advanced Industrial Tech (MAIT)

Schedule of Classes: Fall | Winter | Spring | Summer
(Only current and next semester available)

MAIT 613 Advanced Applied Linear Algebra (3 credits)
Prerequisite: Knowledge of basic linear algebra and computation or permission of instructor.
Tools and techniques of computational linear algebra for applications. Topics include: linear systems and least squares problems, error analysis, accuracy and stability, matrix decompositions, iterative solvers, Krylov subspace methods, symmetric and non-symmetric eigenvalue problems, singular value decomposition.

MAIT 615 Quantum Information, Detection, and Computation (3 credits)
Introduction to information processing tasks implemented on fundamentally quantum mechanical systems. Topics include background physics, mathematics, and information theory, quantum cryptography, teleportation, super-dense coding, quantum computation, Shor's algorithm, quantum error correction, quantum limits in detection and estimation.

MAIT 623 Modern Mathematical Methods of Signal and Image Processing I (3 credits)
Prerequisite: Knowledge of advanced calculus and applications or permission of instructor.
Introduction to current signal/image processing techniques, including wavelets and frames, in the context of applied and numerical harmonic analysis. Topics include time-frequency and time-scale representations, sub-band filterbanks, and applications to compression and denoising.

MAIT 624 Modern Mathematical Methods of Signal and Image Processing II (3 credits)
Prerequisite: MAIT623 or permission of instructor.
Advanced studies of state of the art signal/image processing using applied/numerical harmonic analysis. Topics include stable signal representation and erasure channel problems, 2nd-generation wavelets, geometric sub-division schemes for multi-dimensional problems, level set approaches, estimation and analysis of sensor data, and non-uniform sampling methods.

MAIT 626 Statistical Pattern Recognition and Classification (3 credits)
Mathematical and statistical tools for decision making based on categorization of patterns present in data. Topics include regression, feature extraction, dimensionality reduction, parametric and non- parametric approaches to decision, estimation, and classification problems.

MAIT 627 Fast Multipole Methods (3 credits)
Introduction to the fast multipole method, a matrix compression computational scheme analyzing wide classes of structured operators arising in physics, data analysis, and visualization. Topics include: single and multi-level FMM, iterative solvers, non-uniform interpolation schemes, Fast Gauss Transform, solutions of Laplace and Helmhotz equations.

MAIT 633 Applied Fourier Analysis (3 credits)
Prerequisite: Knowledge of advanced calculus or permission of instructor.
Theory, practice, and implementation (e.g. MATLAB) of Fourier analysis with applications in signal processing. Topics include the Fourier transform for periodic and non-periodic functions in continuous and discrete time, generalized functions, sampling theorems, fast computational algorithms for transforms and convolutions, filterbanks and multirate systems.

MAIT 660 Scientific Computing for Advanced Industrial Mathematics (3 credits)
Data analysis, signal and image processing with control, non-traditional mathematical modeling, Fourier and wavelet transform methods, second generation wavelets for graphics, inverse problems and scattering. Fundamental techniques in scientific computation with an introduction to the theory and software of each topic.

MAIT 679 Special Topics in Mathematics of Advanced Industrial Technology (3 credits)
Special topics courses are intended to expose students to the latest developments in mathematical applications. As such, the content will vary depending on the instructor and the current state-of-the-art. 679 will appear with a letter appended to distinguish different topics. New 679 courses will be added as areas of interest arise.

MAIT 699 Independent Masters Project (1-3 credits)
Permission of instructor. Repeatable to 12 credits if content differs.
This course allows students to apply advanced mathematical methods to practical, real-world problems. Projects are supervised individually by faculty members from the MAIT Program. The project's nature is flexible and determined jointly by the student and supervisor. A detailed final report must be prepared by the student and approved by the supervisor.