Program brochure

MAIT offers one or more core courses each semester, along with a selection of electives and special topics. Schedules, rooms, and time listings may be found at the University registration website www.testudo.umd.edu. For information on how to enroll in the MAIT program or to take courses without enrolling, please see the Application Information page.

Core Program

MAIT 613 Advanced Applied Linear Algebra (3)
(based on the Trefethen or Higham books) 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 623 Modern Mathematical Methods of Signal and Image Processing I (3)
(based on the first half of "A Wavelet Tour of Signal Processing" by Stéphane Mallat) 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 633 Applied Fourier Analysis (3)
Theory, practice, and implementation (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 699 Independent Masters Project (3-6)
The masters project is intended to allow students to apply advanced mathematical methods to practical, real-world problems. Projects will be supervised individually by faculty members associated with the MAIT Program. The nature of the project is flexible and will be determined jointly by the student and faculty supervisor. Ideally, working professional students should be able to use a work-related project for this purpose. The work involved should be equivalent to a 3 credit regular course. A detailed final written report describing the project must be prepared by the student and approved by the faculty supervisor.

Electives

MAIT 615 Quantum Information, Detection, and Computation (3)
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 624 Modern Mathematical Methods of Signal and Image Processing II (3)
(based on the second half of "A Wavelet Tour of Signal Processing" by Stéphane Mallat) Advanced studies with state of the art signal/image processing techniques in the context of applied and numerical harmonic analysis. Topics include stable signal representation techniques (for noise reduction) and erasure channel problems, second-generation wavelets, geometric sub-division schemes for multi-dimensional problems, level set approaches, applications in estimation and analysis of sensor data, non-uniform sampling methods.

MAIT 626 Statistical Pattern Recognition and Classification (3)
(texts of Tribishani and Hastie; "Introduction to Statistical Learning Theory") This is a new course. 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)
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 Helmholtz equations.

MAIT 660 Scientific Computing for Advanced Industrial Mathematics (3)
Fundamental techniques in scientific computation with an introduction to the theory and software of each topic. Topics may include 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.

Special Topics

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 in the subject areas. New 679 courses will be added as areas of interest arise.

MAIT 679A Independent Study (1-3)

Various topics, depending on availability of instructor.

MAIT 679B Introduction to Biomathematics and Applications (3)

The class tailored to applied mathematicians and engineers is intended to serve as an overview of recent developments and the state-of-the-art tools to analyze data in biomedical applications. Only elementary background in linear algebra and calculus, including integration and partial derivatives, are needed. The classes' core topic is multispectral imaging in biomedicine where cutting-edge analysis tools comprise new nonlinear dimension reduction and classification schemes. We will also recall their application to the analysis of microarray gene expression data through a systems biology perspective. New iterative algorithms developed for inverse problems are considered to solve variational optimization problems with sparsity constraints arising in MRI imaging, tomography, and image impainting in which wavelet discretizations play a major role. This technique is also applied to the sparse reconstruction of gene networks modeled through dynamical systems. To provide the perspective of reducing patient's radiology exposure in medical imaging, we will briefly recall compressed sensing and machine learning ideas too. Classical image processing tasks such as denoising are addressed within a PDE framework based on diffusion tensors which is nowadays the most recognized approach. The presented techniques can be usefully applied to a wide range of problems in remote sensing and radar as well.

MAIT 679C Fast Acquisition Techniques in MRI (3)

MAIT 679D Sigma-Delta Methods in Communications and Radar (3)

MAIT 679E Computational Time-Frequency Analysis (3)

The aim of the course will be to cover the algorithms and the discrete transforms necessary to do time-frequency analysis to detect hidden signatures, perform speech recognition, and improve synthetic imaging schemes such as inverse synthetic aperture radar. Topics will include the uncertainty principle, the discrete Fourier transform, the periodicity transforms, the short-time Fourier transform, the spectrogram, the Gabor representation, the ambiguity function, Cohen's classes of time-frequency distributions, the symplectiv transformations, chirplets, the wavelet transform, the Radon transform, and the ridgelet transform. Focus will be on how to appropriately discretize the analytically derived transforms with applications in mind.

MAIT 679F Frames and Applications (3)

Fourier series, Discrete Fourier series (DFT) and the Fast Fourier Transform (FFT); The theory of frames, both finite and infinite; Wavelet and Gabor frames; Sampling theory; Frame potential and the characterization of finite unit norm tight frames; Frame potential and the characterization of finite unit norm tight frames; Quantum detection and finite frames; Grassmannian frames; Compressive sensing; Current research and applications in sampling, frames, and fusion frames including classification.

MAIT 679G Harmonic Analysis and Waveform Design (3)

This course will focus on recent advances in waveform design using tools from the area of Harmonic analysis. Topics include the design and properties of different families of constant amplitude zero-autocorrelation code (CAZAC) sequences, both periodic and aperiodic, in single and multidimensional settings.

MAIT 679M Introduction to Financial Mathematics (3)

MAIT 679N Mathematical Methods in Nanotechnology (3)

MAIT 679R Design and Analysis of RADAR Signals (3)

MAIT 679T Target Tracking and Filtering (3)

This advanced topics course will present the latest advances in tracking technology. The course begins with a review of probability theory, followed by a discussion of the Bayesian estimation techniques. The Kalman filter and its extensions are then introduced and studied. Related techniques including non-linear filters, modified gain techniques, Wiener filters, coordinate systems, and adaptive methods will also be covered. Advanced techniques in particle filtering, as well as tracking problems such as neighbor association and target re-acquisition will also be treated.

MAIT 679Z Short course in RADAR Signal Processing (3)

This course provides a comprehensive introduction to the essential concepts and methods used in digital processing of radar signals. It also surveys several more advanced topics in radar signal processing that are of current interest in connection with the design of advanced radar systems and operational capabilities. The perspective of the course is centered in signal design and processing of received signals. Standard models for propagation and scattering of electromagnetic signals with be employed without emphasis on the underpinning electromagnetic theory.