Master of Science in Electrical Engineering

The course is designed to give the student an introduction to the important subject of random signals and noise. Random signals and processes play a particularly important role in the fields of communications, signal processing, and control, as well as in many other fields, as far-fetched as the stock market and biological sciences. Understanding the nature of random signals and noise is critically important for detecting signals and for reducing and minimizing the effects of noise in applications such as communications and control systems. Outlining a variety of techniques and explaining when and how to use them, Random Signals and Noise: A Mathematical Introduction focuses on applications and practical problem solving rather than probability theory. We will also discuss some practical analysis applications of random processes and noise in different fields, e.g., calculating signal-to-noise ratios in communication systems. (3 credits)

Engineering Analysis covers topics in Linear Algebra, an extremely useful branch of mathematics for many application areas, and the basics of MATLAB, a powerful computing language for solving linear algebra problems and much more. Specific topics include solving systems of linear equations, linear independence, linear transformations, matrix inverses, vector spaces, and least-squares problems. We will also cover a sequence of case studies showing different applications of these concepts. No programming or linear algebra background is assumed. (3 credits).

Survey of advanced mathematics topics needed in the study of engineering. Topics include review of complex numbers, multivariate calculus, and analytic geometry. Study of polar, cylindrical, and spherical coordinates, vector differential calculus, vector integral calculus, and vector integral theorems. Examples are provided from electromagnetic, fluid mechanics, physics, and geometry. (3 credits)

Contemporary topics at the advanced graduate elective level. Faculty present advanced elective topics not included in the established curriculum. The course should be approved by the departmental committee. (3 credits)

In this course, the students will learn the basic skills that are essential to becoming a successful researcher. The objective of the course is to teach research skills in a systematic fashion, early in a student’s graduate program. Lecture topics will include research methodology, experimental design, professional ethics and academic integrity, and oral and written presentation techniques. Students will be required to perform a literature survey (on a topic in their own research area), construct a research proposal that includes an experimental design, and write a paper summary in the style of a formal scientific paper (3 credits)

A candidate for the Master of Science in Electrical Engineering is required to perform a study, a design of investigation, under the direction of a faculty advisory committee. A written thesis is required to be presented, defended orally and submitted to the faculty advisory committee for approval. (6 credits)

A quantitative study of the issues in design, analysis and operation of computer communication and telecommunication networks as they evolve towards the integrated networks of the future employing both packet and circuit switching technology. The course emphasizes a fundamental understanding of basic network design, routing, dimensioning and control. The students will study various network functions such as error-recovery algorithms, flow control, congestion control, routing, multi-access, switching, etc. They will also study these in the context of current Internet solutions (e.g. TCP, IP, etc.) and future open problems, and possible solutions. (3 credits)

The course gives an overview of the designs of digital communication systems. We explain the mathematical foundation of decomposing the systems into separately designed source codes and channel codes. We introduce the principles and some commonly used algorithms in each component, to convert continuous time waveforms into bits, and vice versa. We give a comprehensive introduction to the basics of information theory, a rather thorough treatment of Fourier transforms and the sampling theorem, and an overview of the use of vector spaces in signal processing. The course would be beneficial particularly to students who are interested in doing research in fields related to communications, networks, and signal processing (3 credits)

Overview of existing and emerging wireless communications systems; interference, blocking, and spectral efficiency; radio propagation and fading models; performance of digital modulation in the presence of fading; diversity techniques; Code-Division Multiple Access. (3 credits)

Introducing advanced optimization techniques. Emphasis on nonlinear optimization and recent developments in the field. Topics include unconstrained optimization methods such as gradient and incremental gradient, conjugate direction, Newton and quasi-Newton methods; constrained optimization methods such as projection, feasible directions, barrier and interior point methods; duality theory and methods; convex duality; and stochastic approximation algorithms. Introduction to modern convex optimization including semi-definite programming, conic programming, and robust optimization. Applications drawn from control, production and capacity planning, resource allocation, communication and sensor networks, and bioinformatics. (3 credits)

Introduction to the concepts, key issues, and motivating examples for adaptive filters; Discrete time linear systems and filters; Random variables and random processes, covariance matrices; Z transforms of stationary random processes. Optimum Linear Systems – Error surfaces and minimum mean square error; Optimum discrete time Wiener filter; Principle of orthogonality and canonical forms; Constrained optimization; Method of steepest descent – convergence issues; Stochastic gradient descent LMS – convergence in the mean and mis adjustment Case study. Least squares and recursive least squares. Linear Prediction – Forward and backward linear prediction; Levinson Durbin; Lattice filters. (3 credits)

The objective of this course is to introduce the students to the fundamental techniques and algorithms used for acquiring, processing, and extracting useful information from digital images. Particularly emphasis will be placed on covering methods used for image sampling and quantization, image transforms, image enhancement and restoration, image encoding, image analysis and pattern recognition. In addition, the students will learn how to apply the methods to solve real-world problems in several areas including medical, remote sensing and surveillance and develop the insight necessary to use the tools of digital image processing (DIP) to solve any new problem. (3 credits)

This class introduces information theory. Information measures: entropy, mutual information, relative entropy, and differential entropy. These topics are connected to practical problems in communications, compression, and inference, including lossless data compression, Huffman coding, asymptotic equipartition property, channel capacity, Gaussian channels, rate distortion theory, and Fisher information. (3 credits)

The course covers the Basics of optimization theory, numerical algorithms, and applications. The course is divided into three main parts: linear programming (simplex method, duality theory), unconstrained methods (optimality conditions, descent algorithms and convergence theorems), and constrained minimization (Lagrange multipliers, Karush-Kuhn-Tucker conditions, active set, penalty, and interior point methods). Applications in engineering, operations, finance, statistics, etc. will be emphasized. Students will also use MATLAB’s optimization toolbox to obtain practical experience with the material. (3 credits)

The course explores state-space, time-domain techniques for analyzing and designing optimal and robust linear control systems. Introduces basic concepts of dynamic optimization and applies them to problems of short-term and long-term optimal control, path planning and stabilization, state estimation, and filtering. Emphasizes linear quadratic optimization, H2 control, Hinfinity control, and mu-synthesis. Reviews pertinent linear systems concepts and discusses connections with a geometric intuition relating quadratic optimization to projections. (3 credits)

Introducing advanced optimization techniques. Emphasis on nonlinear optimization and recent developments in the field. Topics include unconstrained optimization methods such as gradient and incremental gradient, conjugate direction, Newton and quasi-Newton methods; constrained optimization methods such as projection, feasible directions, barrier and interior point methods; duality theory and methods; convex duality; and stochastic approximation algorithms. Introduction to modern convex optimization including semi-definite programming, conic programming, and robust optimization. Applications drawn from control, production and capacity planning, resource allocation, communication and sensor networks, and bioinformatics. (3 credits)

The course explores the State space theory of dynamic estimation in discrete and continuous time. Linear state space models driven by white noise, Kalman filtering and its properties, optimal smoothing, nonlinear filtering, extended and second order Kalman filters, particle filters, graphical models and sequential detection. Applications to radar, sonar, multiobject tracking, parameter identification. (3 credits)

The course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We start with dynamic models of random phenomena, and in particular, the most popular classes of such models: Markov chains and Markov decision processes. We then consider optimal control of a dynamical system over both a finite and an infinite number of stages. We will also discuss approximation methods for problems involving large state spaces. This includes systems with finite or infinite state spaces, as well as perfectly or imperfectly observed systems. Applications of dynamic programming in a variety of fields will be covered in recitations. (3 credits)

An introduction to a broad range of topics in deep learning, covering mathematical and conceptual background, deep learning techniques used in industry, and research perspectives. his book introduces a broad range of topics in deep learning. The course offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. (3 credits)

Introduction to data analytics introduces you to the basics of data science and data analytics for handling of massive databases. The course covers concepts data mining for big data analytics and introduces you to the practicalities of map-reduce while adopting the big data management life cycle. (3 credits)

In this course we study the algorithms and the associated distributed computing systems used in analyzing massive datasets, or big data, and in large-scale machine learning. We focus on two fundamental ideas for scaling analysis to large datasets: (i) distributed computing, and (ii) randomization. In the former, we study how to design, implement, and evaluate data analysis algorithms for the distributed computing platforms MapReduce/Hadoop and Spark. In the latter, we explore techniques such as locality sensitive hashing, Bloom filters, and data stream mining. These fundamental ideas are applied to applications such as finding similar items, market-basket analysis, clustering, and building recommendation systems—all on massive datasets. They are the foundation of modern data analysis in companies such as Google, Facebook, and Netflix. (3 credits)

Robotics as an application draws from many different fields and allows automation of products as diverse as cars, vacuum cleaners, and factories. This course is a challenging introduction to basic computational concepts used broadly in robotics. Topics include simulation, kinematics, control, optimization, and probabilistic inference. The mathematical basis of each area is emphasized, and concepts are motivated using common robotics applications and programming exercises. Students will participate in a series of projects over the course of the semester, in which they will implement algorithms that apply each of the topics discussed in class to real robotics problems. (3 credits)

In this course, we will review several recent advancements in cyberphysical systems (CPS) and intelligent control. Topics will include core principles of CPS, differential equations to model physical processes, graph theory and CPS communication structures, control loops in CPS, intelligent control, game theoretic frameworks for secure control, control, and estimation over lossy and attacked networks, intrusion and fault detection in CPS, differential and temporal logic for safety of execution, machine learning in CPS. (3 credits)

This course emphasizes learning algorithms and theory including concept, decision tree, neural network, computational, Bayesian, evolutionary, and reinforcement learning. The course will give the student the basic ideas and intuition behind modern machine learning methods as well as a bit more formal understanding of how, why, and when they work. The underlying theme in the course is statistical inference as it provides the foundation for most of the methods covered. (3 credits)