From random walk to Brownian motion, quadratic variation and volatility, stochastic integrals, martingale property, Ito formula, geometric Brownian motion, solution of Black-Scholes equation, stochastic differentialequations, Feynman-Kac theorem, Cox-Ingersoll-Ross and Vasicek term structure models, Girsanov's theorem and risk neutral measures, Heath-Jarrow-Morton term structure model, exchange-rate instruments.

Foundations of fluid mechanics introduced at an advanced level. Aspects of kinetic theory as it applies to formulation of continuum fluid dynamics. Introduction to tensor analysis and derivation of Navier Stokes equations and energy equation for compressible fluids. Boundary conditions and surface phenomena. Viscous flows, boundary layer theory, potential flows and vorticity dynamics. Introduction to turbulence and turbulent flows.

Numerical methods for elliptic, parabolic, hyperbolic and mixed type partial differential equations arising in fluid flow and heat transfer problems. Finite-difference, finite-volume and some finite-element methods. Accuracy, convergence, and stability; treatment of boundary conditions and grid generation. Review of current methods. Assignments require programming a digital computer.

Geometric, physics-based, and probabilistic modeling methodology and associated computational tools for interactive simulation: computer programming, numerical methods, graphical modeling and programming, physics-based and probabilistic modeling techniques.

Topics will be announced when offered.

Free electron theory of metals. Crystal lattices. Reciprocal lattice. Classification of Bravais lattices. X-ray diffraction and the determination of crystal structures. Electrons in a periodic potential. Tight binding method. Band structures. Semi-classical theory of conduction in metals. Fermi surface. Surface effects.

Classification of solids. Theory of harmonic crystals. Phonons and phonon dispersion relations. Anharmonic effects in crystals. Phonons in metals. Dielectric properties of insulators. Semiconductors. Diamagnetism and paramagnetism. Electron interactions and magnetic structure. Magnetic ordering. Superconductivity.

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.

Provides hands-on teaching experience to graduate students in undergraduate courses. Reinforces students' understanding of basic concepts and allows them to communicate and apply their knowledge of the subject matter.

The principles and computational methods to study the biological data generated by genome sequencing, gene expressions, protein profiles, and metabolic fluxes. Application of arithmetic, algebraic, graph, pattern matching, sorting and searching algorithms and statistical tools to genome analysis. Applications of Bioinformatics to metabolic engineering, drug design, and biotechnology.

Sound and human speech systems, phonetics and phonology, speech signal representations, role of pitch and formants, pitch-scale and time-scale modifications, basics of speech coding and VoIP systems, fundamentals of pattern and speech recognition, search algorithms for speech recognition.

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.

Study of computational models of visual perception and their implementation in computer systems. Topics include: image formation; edge, corner and boundary extraction, segmentation, matching, pattern recognition and classification techniques; 3-D Vision: projection geometry, camera calibration, shape from stereo/silhouette/shading, model-based 3D object recognition; color texture, radiometry and BDRF; motion analysis.

Theory and practice of 3D computer graphics. Topics covered include graphics systems and models; geometric representations and transformations; graphics programming; input and interaction; viewing and projections; compositing and blending; illumination and color models; shading; texture mapping; animation; rendering and implementation; hierarchical and object-oriented modeling; scene graphs; 3D reconstruction and modeling.

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.

Introduction to distributed computing, overview of operating systems, process synchronization and deadlocks, threads and thread synchronization, communication protocols, synchronization in distributed systems, management of time, causality, logical clocks, consistent global states, distributed mutual exclusion, distributed deadlock detection, election algorithms, agreement protocols, consensus, multicast communication, distributed transactions, replication, shared memory model, scheduling, distributed file systems, fault tolerance in distributed systems, distributed real-time systems.

Next generation communication systems, wireless cellular networks, machine-to-machine communications, Internet of things, software defined networking, physical layer data transmission, channel propagation characteristics, modulation, demodulation, medium access control layer, data link layer, forward and backward error control, routing layer, optimal routing, transport layer, flow control, congestion control.

Fundamental concepts of concurrency, non-determinism, atomicity, race-conditions, synchronization, mutual exclusion. Overview of parallel architectures, multicores, distributed memory. Parallel programming models and languages, multithreaded, message passing, data driven, and data parallel programming. Design of parallel programs, decomposition, granularity, locality, communication, load balancing. Patterns for parallel programming, structural, computational, algorithm strategy, concurrent execution patterns. Performance modeling of parallel programs, sources of parallel overheads.

Review of multimedia (image, video and audio) source coding/compression techniques and standards (JPEG, MPEG, H26x); Review of communication and networking architectures and IP networks; QoS, delay, jitter, rate control, scheduling, and traffic engineering for real-time multimedia delivery; Reliability, error control, error concealment and resilience techniques; Streaming media and real-time communication techniques and protocols, RTP/RTCP, IntServ, DiffServ, MPLS; Transmission of multimedia over Internet, wireless channels, mobile cellular networks, GSM, 3G, 4G wireless systems, and satellite networks; Current and future applications of multimedia communications, e.g., voice-over-IP (VoIP), Internet Video conferencing, SIP, IMS, video-on-demand, digital video broadcasting systems, real-time delivery of 3DTV; Current state-of-the-art and future visions in multimedia communications research.

Overview of Computer Security Techniques, Conventional Encryption, Public-Key Cryptography, Key Management, Message Authentication, Hash Functions and Algorithms, Digital Signatures, Authentication Protocols, Access Control Mechanisms, Network Security Practice, TCP/IP Security, Web Security, SSL (Secure Socket Layer), Denial-of-Service Attacks, Intrusion Detection, Viruses.

Applications of artificial intelligence in user interfaces. Design, implementation, and evaluation of user interfaces that use machine learning, computer vision and pattern recognition technologies. Supporting tools for classification, regression, multi-modal information fusion. Gaze-tracking, gesture recognition, object detection, tracking, haptic devices, speech-based and pen-based interfaces.

Basic linear models for classification and regression; stochastic gradient descent (backpropagation) learning; multi-layer perceptrons, convolutional neural networks, and recurrent neural networks; recent advances in the field; practical examples from machine translation, computer vision; practical experience in programming, training, evaluating and benchmarking deep learning models.