Basics of linear algebra and their applications to data-centric real-world problems with real-time coding and demonstrations. Vectors and matrices, eigenvalues, eigenvectors and singular value decomposition: mathematical foundations, geometrical intuitions and practical applications. Least Squares for data fitting and classification, Markov Chains, Principal Component Analysis (PCA), low-rank approximation and compression, clustering, gradient descent (batch- minibatch and stochastic) and basics of neural networks.

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.

Entropy, Relative Entropy and Mutual Information; Asymptotic Equipartition Theory; Entropy Rates of a Stochastic Process; Data Compression; Kolmogorov Complexity; Channel Capacity; Differential Entropy; The Gaussian Channel; Maximum Entropy and Spectral Estimation; Rate Distortion Theory, Network Information Theory.

The cellular concept, channel assignment strategies, frequency reuse, handoff strategies, interference sources, mobile radio propagation, large-scale path loss, small-scale fading and multipath, modulation techniques for mobile radio, diversity combining, transmit and receive antennas for wireless communication systems, multiple access techniques in wireless, error correction codes and ARQ schemes, wireless networking, OFDM and multiple-input multiple-output systems, wireless systems & standards: GSM, IS-95, cdma2000, W-CDMA, LTE (4G), LTE-Advanced and 5G New Radio, advanced topics and current trends in wireless communications,design oriented exercises using MATLAB aids.

Principles of computer networks and network protocols; Internet protocol stack with emphasis on application, transport, network and link layers; network edge and network core; client/server and peer-to-peer models; routing algorithms; reliable data transfer; flow and congestion control; protocol design and analysis; network performance metrics; software-defined networks; network programming and distributed applications.

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; 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.

Parameter Estimation, Cramer-Rao Lower Bound, Maximum Likelihood/ Maximum A Posteriori Estimation, Stochastic Least Squares Estimation, Wiener and Kalman Filtering, Hypothesis Testing, Signal Detection

Electrical excitation mechanisms of biological cells, bio-electronic systems. Electrically active membranes and their resistance and capacitance, diffusion and fields across membranes, Nernst equilibrium, ion channels, action potentials, impulse propagation, electrical stimulation, and biomedical electronic systems

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.

Entropy, Relative Entropy and Mutual Information; Asymptotic Equipartition Theory; Entropy Rates of a Stochastic Process; Data Compression; Kolmogorov Complexity; Channel Capacity; Differential Entropy; The Gaussian Channel; Maximum Entropy and Spectral Estimation; Rate Distortion Theory, Network Information Theory.

The cellular concept, channel assignment strategies, frequency reuse, handoff strategies, interference sources, mobile radio propagation, large-scale path loss, small-scale fading and multipath, modulation techniques for mobile radio, diversity combining, transmit and receive antennas for wireless communication systems, multiple access techniques in wireless, wireless system design for delay intolerant services, wireless system design for delay tolerant services, error correction coding and ARQ schemes, wireless networking, wireless systems & standards: GSM, IS-95, cdma2000, W-CDMA, 3GPP2 1xEV-DO, 3GPP2 1xEV-DV, fourth generation wireless system proposals. 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.

Hypothesis Testing, Signal Detection, Parameter Estimation, Cramer-Rao Lower Bound, Maximum Likelihood/ Maximum a Posteriori Estimation, Stochastic Least Squares Estimation and Kalman Filtering.

Electrical excitation mechanisms of biological cells, bio-electronic systems. Electrically active membranes and their resistance and capacitance, diffusion and fields across membranes, Nernst equilibrium, ion channels, action potentials, impulse propagation, electrical stimulation, and biomedical electronic systems

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.