Review of electromagnetism; electromagnetic nature of light, radiation, geometrical optics, Gaussian beams, transformation of Gaussian beams; electromagnetic modes of an optical resonator, interaction of light with matter, classical theory of absorption and dispersion, broadening processes, Rayleigh scattering, quantum theory of spontaneous and stimulated emission, optical amplification, theory of laser oscillation, examples of laser systems, Q switching and mode locking of lasers.

Supervised Adaptive Filtering (Least Mean Square, Recursive Least Squares, Fast Algorithms), Unsupervised Adaptive Filtering (Higher Order Statistics Methods, Blind Deconvolution, Blind Source Separation, Independent Component Analysis), Model Based Signal Processing (Sparsity, Boundedness, Subspace Algorithms), Multirate Signal Processing, Filter-banks and Wavelets.

The optoelectronic devices such as light-emitting diodes, lasers, photodetectors, etc. are widely used in modern lighting, information and telecommunication technologies. We will discuss the following topics with mathematical derivations and exciting practical examples: wave nature of light, dielectric waveguides and optical fibers, semiconductor science and light-emitting diodes, stimulated emission devices: optical amplifiers and lasers, photodetectors and image sensors, and polarization and modulation of light.

Design, simulation, and optimization of integrated photonics structures, the notion of fabless silicon photonics, metal and dielectric waveguides, planar waveguide modes, coupled mode theory, integrated passive couplers and splitters, Mach-Zehnder Interferometers, ring and disk resonators, adiabatic couplers, Bragg gratings, grating and edge couplers, photonic crystal waveguides and structures, principles of integrated modulator and detector operation, fabrication-dependent design considerations, use of transfer matrix, eigenmode expansion, and finite difference time-domain simulation techniques throughout the semester, design oriented and simulation based assignments and term project.

Recent applications of wearable devices, design fundamentals of physiological monitoring systems, overview of physiological signals (SCG, ECG, PPG, EEG, EMG, etc.). Tools for biomedical signal analysis: digital filters, feature extraction, data visualization and machine learning (regression and classification).

A capstone design course where students apply engineering and science knowledge in an electrical-electronics engineering design project. Development, design, implementation and management of a project in teams under realistic constraints and conditions. Emphasis on communication, teamwork and presentation skills..

Discrete and continuous random variables and processes, functions of random variables, independence of random variables. Central Limit Theorem. Discrete-time random processes, continuous-time random processes, stationary random processes, ergodicity, auto and cross correlation functions, power spectral density; spectral estimation, white noise processes, Markov chains.

Linear Algebra Review, Normal Matrices, Quadratic Forms and Semidefinite Matrices, Inner Product and Norm Spaces, State Space Descriptions for Continuous and Discrete Time Systems, Controllability, Observability, Stability, Realization Theory.

Review of multi-dimensional sampling theory, aliasing, and quantization, fundamentals of color, human visual system, 2-D Block transforms, DFT, DCT and wavelets. Image filtering, edge detection, enhancement, and restoration. Basic video file formats, resolutions, and bit rates for various digital video applications. Motion analysis and estimation using 2D and 3D models. Motion-compensated filtering methods for noise removal, de-interlacing, and resolution enhancement. Digital image and video compression methods and standards, including JPEG/JPEG2000 and MPEG-1/2 and 4. Content-based image and video indexing and MPEG-7.

Characterization of communication signals & systems, digital modulation schemes, optimum reception for the additive white Gaussian noise (AWGN) channel, signal design for band-limited channels, Nyquist criterion, intersymbol interference (ISI), optimum reception for channels with ISI and AWGN, linear equalization, decision feedback equalization, adaptive equalization, channel capacity & coding, linear block codes, convolutional codes, multichannel and multicarrier systems, spread spectrum signals for digital communications, multiuser communications. Design oriented exercises using computer aids.

Introduction to mathematical formulations and computational techniques for the modeling and simulation of engineering and other kinds of systems, including electronic, mechanical, biological, biochemical, virtual, abstract and multi-domain dynamical systems. Applications from various engineering disciplines and the sciences. Matrix formulation of equations for linear problems. Formulation of equations for nonlinear problems & linearization. Numerical solution of linear algebraic equations. Gaussian elimination, computations with sparse & structured matrices. Floating point number representation & arithmetic. Numerical conditioning, ill-conditioned problems. Numerical solution of nonlinear algebraic equations. Fixed point iteration & Newton’s method in one dimension. Newton’s method for system of coupled nonlinear algebraic equations. Improving convergence of Newton’s method. Numerical solution of ordinary differential equations. Forward & backward Euler, trapezoidal rule. Multistep methods, accuracy & stability. Implicit vs explicit techniques, region of stability, stiff problems.

Review of electromagnetism; geometrical optics, analysis of optical systems; wave properties of light, Gaussian beams, beam optics; interaction of light with matter, spontaneous and stimulated emission, optical amplification, theory and applications of lasers, optical interactions in semiconductors, light emitting diodes and diode lasers; detectors, noise in detection systems; light propagation in anisotropic crystals, Pockels and Kerr effect, light modulators; nonlinear optics, second harmonic generation, phase matching, nonlinear optical materials.

Supervised Adaptive Filtering (Least Mean Square, Recursive Least Squares, Fast Algorithms), Unsupervised Adaptive Filtering (Higher Order Statistics Methods, Blind Deconvolution, Blind Source Separation, Independent Component Analysis), Model Based Signal Processing (Sparsity, Boundedness, Subspace Algorithms), Multirate Signal Processing, Filter-banks and Wavelets.

The optoelectronic devices such as light-emitting diodes, lasers, photodetectors, etc. are widely used in modern lighting, information and telecommunication technologies. We will discuss the following topics with mathematical derivations and exciting practical examples: wave nature of light, dielectric waveguides and optical fibers, semiconductor science and light-emitting diodes, stimulated emission devices: optical amplifiers and lasers, photodetectors and image sensors, and polarization and modulation of light.

Design, simulation, and optimization of integrated photonics structures, the notion of fabless silicon photonics, metal and dielectric waveguides, planar waveguide modes, coupled mode theory, integrated passive couplers and splitters, Mach-Zehnder Interferometers, ring and disk resonators, adiabatic couplers, Bragg gratings, grating and edge couplers, photonic crystal waveguides and structures, principles of integrated modulator and detector operation, fabrication-dependent design considerations, use of transfer matrix, eigenmode expansion, and finite difference time-domain simulation techniques throughout the semester, design oriented and simulation based assignments and term project.

Recent applications of wearable devices, design fundamentals of physiological monitoring systems, overview of physiological signals (SCG, ECG, PPG, EEG, EMG, etc.). Tools for biomedical signal analysis: digital filters, feature extraction, data visualization and machine learning (regression and classification).

Mathematical questions around machine learning and deep learning, geometrical aspects of high dimensional learning models, geometric stability priors, geometry of optimization, smooth and non-smooth optimization method including gradient methods, proximal methods, mirror descent, Nesterov's acceleration, ADMM, stochastic optimization, variance reduction, and distributed optimization.

A series of lectures given by faculty or outside speakers.

A series of lectures given by faculty or outside speakers.

The course aims to help students advance their reading, listening, writing and speaking skills (moving from B2 level English to C1-C2) through exposure to a variety of texts in English dealing with themes varying from citizenship, sense of responsibility, integrity, civic involvement, community work, ethical standards in education, business and management, use of technology, and other related academic fields. Main objectives: communicating effectively in written and oral form, focusing on academic conventions and style to produce and present academic work; developing critical thinking skills, formulating an argument and supporting ideas through finding appropriate and effective sources, synthesizing information, evaluating the reliability of information.

The following objectives will be met through extensive reading, writing and discussion both in and out of class.Build a solid background in academic discourse, both written and spoken. Improve intensive and extensive critical reading skills. Foster critical and creative thinking. Build fundamental academic writing skills including summary, paraphrase, analysis, synthesis. Master cohesiveness as well as proper academic citation when incorporating the work of others.

Introduction to probability, sets, conditional probability, total probability theorem and Bayes rule; Independence, counting; Discrete random variables, functions of random variables, expectation, mean and variance; Continuous random variables, probability density functions, and cumulative distribution functions; Multiple random variables; Sums of random variables; Limit theorems; Covariance and correlation; Introduction to Stochastic Processes

Introduction to probability, sets, conditional probability, total probability theorem and Bayes rule; Independence, counting; Discrete random variables, functions of random variables, expectation, mean and variance; Continuous random variables, probability density functions, and cumulative distribution functions; Multiple random variables; Sums of random variables; Limit theorems; Covariance and correlation; Introduction to Stochastic Processes

Descriptive statistics; measures of association, correlation, simple regression; probability theory, conditional probability, independence; discrete and continuous random variables; probability distributions; functions of random variables; sampling distributions; estimation; inference (confidence intervals and hypothesis testing). Topics are supported by computer applications and specific examples from engineering applications.