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Course Catalog

TF501/Matrix Analysis

School: SIST

Course Level: Graduate

Grading: The grading option will be decided by the instructor when the class is offered.

Credit: 3

Prerequisites: Linear Algebra

Course Description: Basic concepts and algorithms of matrix theory and linear algebra (norm, floating point arithmetic, error and sensitivity analysis, matrix decomposition, solution of linear systems, least squares problems, eigenvalue problems), and their applications in other parts of mathematics and other fields such as engineering, physics, statistics and data mining.

 

TF502/Numerical Analysis

School: SIST

Course Level: Graduate

Grading: The grading option will be decided by the instructor when the class is offered.

Credit: 3

Prerequisites: Mathematical Analysis, Linear Algebra

Course Description: Programming for numerical calculations, round-off error, approximation and interpolation, numerical quadrature, solutions to linear equations, iterative solution of systems of nonlinear equations, evaluation of eigenvalues and eigenvectors of matrices, convergence of optimization algorithms.

 

EE542/Compressive Sensing

School: SIST

Course Level: Graduate

Grading: The grading option will be decided by the instructor when the class is offered.

Credit: 3

Prerequisites: Linear Algebra and Matrix Analysis, Programming Languages and Data Structures, Probability and Statistics, Convex Optimization, Digital Signal Processing

Course Description: Compressive sensing has become the fundamental corner stone of modern massive high-dimensional data analysis. This is an advanced course that systematically introduces the modern mathematical theory, optimization algorithms, and practical applications of compressive sensing of low-dimensional structures from high dimensional data. Representative structures include sparse signals and low-rank matrices. This course will cover the fundamental high-dimensional statistical and geometric principles, as well as some of its remarkable applications to image processing, computer vision, and data science.

 

CS512/Parallel Computing and Distributed Systems

School: SIST

Course Level: Graduate

Grading: The grading option will be decided by the instructor when the class is offered.

Credit: 3

Prerequisites: Undergraduate Parallel Computing and Distributed Systems

Course Description: An advanced foundation in various programming models and varieties of parallelism in current hardware.

Topics include

 implicit vs. explicit parallelism,

 shared vs. non-shared memory,

 synchronization mechanisms, and

 Parallel programming models

 

CS550/Artificial Intelligence

School: SIST

Course Level: Graduate

Grading: The grading option will be decided by the instructor when the class is offered.

Credit: 3

Prerequisites: Programming Languages and Data Structures, Algorithms, Discrete Mathematics, Probability and Statistics

Course Description: Advanced topics in artificial intelligence, such as: graphical models, stochastic relational learning, probabilistic logics, stochastic grammars, image and video understanding, semantic web, etc.

 

CS551/Computer Vision

School: SIST

Course Level: Graduate

Grading: The grading option will be decided by the instructor when the class is offered.

Credit: 3

Prerequisites: Programming Languages and Data Structures, Probability and Statistics, Undergraduate Artificial Intelligence, Undergraduate Image Processing and Computer Vision

Course Description: Introduction to modern foundations of Computer Vision and Image Understanding. Physics and geometry of image formation, illumination and reflectance models. Human visual perception principles and its inspiration for image understanding paradigms: low-level image feature extraction and representations, image segmentation and parsing, reconstruction of 3D geometry and textures, high-level image representation and object recognition.

 

CS552/Computer Graphics

School: SIST

Course Level: Graduate

Grading: The grading option will be decided by the instructor when the class is offered.

Credit: 3

Prerequisites: Programming Languages and Data Structures, Algorithms, Undergraduate Computer Graphics

Course Description: Advanced techniques for object and scene modeling for computer rendering and animation. Mathematical tools for curve, surface, and solid shape representations and manipulations. Components of computer graphics rendering pipeline. Physical models of surface reflectance, refraction, and transparency etc. Motion capture, representation, and manipulation for purpose of animation. Modern graphics display devices and 3D printing etc.

 

CS553/Natural Language Processing

School: SIST

Course Level: Graduate

Grading: The grading option will be decided by the instructor when the class is offered.

Credit: 3

Prerequisites: Programming Languages and Data Structures, Algorithms, Discrete Mathematics, Probability and Statistics

Course Description: The theory and technology of natural language processing, including: words, n-gram models, part-of-speech, context-free grammars, syntactic parsing, semantics, text mining, information retrieval, machine translation, etc.

 

CS554/Machine Learning Theory and Algorithms

School: SIST

Course Level: Graduate

Grading: The grading option will be decided by the instructor when the class is offered.

Credit: 3

Prerequisites: Linear Algebra and Matrix Analysis, Programming Languages and Data Structures, Probability and Statistics, Convex Optimization, Artificial Intelligence

Course Description: This course provides an introduction to theoretical foundations, algorithms, and methodologies for machine learning, emphasizing the role of probability and optimization and exploring a variety of real-world applications. Regression, classification, clustering, graphical model inference, Bayesian inference, statistical learning, and neural networks.

 

CS555/Generalized Principal Component Analysis

School: SIST

Course Level: Graduate

Grading: The grading option will be decided by the instructor when the class is offered.

Credit: 3

Prerequisites: Linear Algebra and Matrix Analysis, Programming Languages and Data Structures, Probability and Statistics, Convex Optimization, Digital Signal Processing

Course Description: This is an advanced course on the modeling and analysis of high-dimensional data and signals (such as images) using models of a single or multiple low-dimensional subspaces (or manifolds). The course aims to systematically introduce the modern theory, optimization algorithms, and applications of principal component analysis and its robust generalizations. Through this class of models, one will gain first hand experience with fundamental principles from mathematical modeling, statistical inferences, and optimization. This is a course suitable for students in the area of signal processing, data science, optimization, and machine learning.