Advanced and Applied Linear Algebra
Advanced Linear Algebra
Advanced topics in linear algebra with applications to data analysis, algorithms, dynamics and differential equations, and more. (1) General vector spaces, linear transformations, spaces isomorphisms; (2) spectral theory - normal matrices and their spectral properties, Rayleigh quotient, Courant-Fischer Theorem, Jordan forms, eigenvalue perturbations; (3) least squares problem and the Gauss-Markov Theorem; (4) singular value decomposition, its approximation properties, matrix norms, PCA and CCA.
MATH METHODS IN CHEMICAL ENGIN
Mathematical description of chemical engineering problems and the application of selected methods for their solution. General modeling principles, including model hierarchies. Linear and nonlinear ordinary differential equations and their systems, including those with variable coefficients. Partial differential equations in Cartesian and curvilinear coordinates for the solution of chemical engineering problems.
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Instructor:
Vivian F McNeill
Info - 3 points
Computing with Brain Circuits of Model O
Building the functional map of the fruit fly brain. Molecular transduction and spatio-temporal encoding in the early visual system. Predictive coding in the Drosophila retina. Canonical circuits in motion detection. Canonical navigation circuits in the central complex. Molecular transduction and combinatorial encoding in the early olfactory system. Predictive coding in the antennal lobe. The functional role of the mushroom body and the lateral horn. Canonical circuits for associative learning and innate memory. Projects in Python.
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Instructor:
Aurel A Lazar
h-index: 53 Info - 3 points
NANOTECHNOLOGY
The science and engineering of creating materials, functional structures and devices on the nanometer scale. Carbon nanotubes, nanocrystals, quantum dots, size dependent properties, self-assembly, nanostructured materials. Devices and applications, nanofabrication. Molecular engineering, bionanotechnology. Imaging and manipulating at the atomic scale. Nanotechnology in society and industry. Offered in alternate years.
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Instructor:
Yuan Yang
h-index: 49 Info - 3 points
STOCHASTIC MODELS
Some of the main stochastic models used in engineering and operations research applications: discrete-time Markov chains, Poisson processes, birth and death processes and other continuous Markov chains, renewal reward processes. Applications: queueing, reliability, inventory, and finance.
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Instructor:
Antonius B Dieker
CULPA: 10 h-index: 19 Info - 3 points
MODERN OPTICS
Ray optics, matrix formulation, wave effects, interference, Gaussian beams, Fourier optics, diffraction, image formation, electromagnetic theory of light, polarization and crystal optics, coherence, guided wave and fiber optics, optical elements, photons, selected topics in nonlinear optics.
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Instructor:
Nanfang Yu
h-index: 48 Info - 3 points
TRANSPORT IN FLUID MIXTURES
Develops and applies non-equilibrium thermodynamics for modeling of transport phenomena in fluids and their mixtures. Continuum balances of mass, energy and momentum for pure fluids; non-equilibrium thermodynamic development of Newtons law of viscosity and Fouriers law; applications (conduction dominated energy transport, forced and free convection energy transport in fluids); balance laws for fluid mixtures; non-equilibrium thermodynamic development of Ficks law; applications (diffusion-reaction problems, analogy between energy and mass transport processes, transport in electrolyte solutions, sedimentation).
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Instructor:
Christopher J Durning
CULPA: 3 Info - 3 points
OPERATING SYSTEMS I
Design and implementation of operating systems. Topics include process management, process synchronization and interprocess communication, memory management, virtual memory, interrupt handling, processor scheduling, device management, I/O, and file systems. Case study of the UNIX operating system. A programming project is required.
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Instructor:
Hubertus Franke
Info - 3 points
COMPUTER NETWORKS
Introduction to computer networks and the technical foundations of the Internet, including applications, protocols, local area networks, algorithms for routing and congestion control, security, elementary performance evaluation. Several written and programming assignments required.
PREV&RESOL OF CONSTR DISPUTES
Contractual relationships in the engineering and construction industry and the actions that result in disputes. Emphasis on procedures required to prevent disputes and resolve them quickly and cost-effectively. Case studies requiring oral and written presentations.
- 3 points
REAL ESTATE FIN/CONST MANAG
REAL ESTATE FIN/CONST MANAGEME
Introduction to financial mechanics of public and private real-estate development and management. Working from perspectives of developers, investors and taxpayers, financing of several types of real estate and infrastructure projects are covered. Basics of real-estate accounting and finance, followed by in-depth studies of private, public, and public/private-partnership projects and their financial structures. Focused on U.S.-based financing, with some international practices introduced and explored. Financial risks and rewards, and pertinent capital markets and their financing roles. Impacts and incentives of various government programs, such as LEED certification and solar power tax credits. Case studies provide opportunity to compare U.S. practices to several international methods.
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Instructor:
Kevin J Riordan
Info - 3 points
PUBLIC-PRIVATE PARTNERSHIP IN GLOBAL INF
Delivery of infrastructure assets through Public-Private Partnerships (PPP). Value for Money analysis. Project organization. Infrastructure sector characterization. Risk analysis, allocation and mitigation. Monte Carlo methods and Real Options. Project finance and financing instruments. Case studies from transportation, water supply and energy sectors.
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Instructor:
Patrick Foye
Info - 3 points
MATERIALS THERMODYN/PHASE DIAG
Review of laws of thermodynamics, thermodynamic variables and relations, free energies and equilibrium in thermodynamic system. Statistical thermodynamics. Unary, binary, and ternary phase diagrams, compounds and intermediate phases, solid solutions and Hume-Rothery rules, relationship between phase diagrams and metastability, defects in crystals. Thermodynamics of surfaces and interfaces, effect of particle size on phase equilibria, adsorption isotherms, grain boundaries, surface energy, electrochemistry, statistical mechanics.
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Instructor:
Renata M Wentzcovitch
Info - 3 points
KINETICS OF TRANSFORMATIONS
Review of thermodynamics, irreversible thermodynamics, diffusion in crystals and noncrystalline materials, phase transformations via nucleation and growth, overall transformation analysis and time-temperature-transformation (TTT) diagrams, precipitation, grain growth, solidification, spinodal and order-disorder transformations, martensitic transformation.
THEORY CRYSTALL MAT: ELECTRONS
Phenomenological theoretical understanding of electrons in crystalline materials. Both translational and point symmetry employed to block diagonalize the Schrödinger equation and compute observables related to electrons. Topics include nearly free electrons, tight-binding, electron-electron interactions, transport, magnetism, optical properties, topological insulators, spin-orbit coupling, and superconductivity. Illustrated using both minimal model Hamiltonians in addition to accurate Hamiltonians for real materials.
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Instructor:
Chris A Marianetti
Info - 3 points
MECH BEHAVIOR OF MATERIALS
Review of states of stress and strain and their relations in elastic, plastic, and viscous materials. Dislocation and elastic-plastic concepts introduced to explain work hardening, various materials-strengthening mechanisms, ductility, and toughness. Macroscopic and microstructural aspects of brittle and ductile fracture mechanics, creep and fatigue phenomena. Case studies used throughout, including flow and fracture of structural alloys, polymers, hybrid materials, composite materials, ceramics, and electronic materials devices. Materials reliability and fracture prevention emphasized.
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Instructor:
William Bailey
CULPA: 12 Info - 3 points
Interfacial Engineering for Sustainable
Cross disciplinary interfacial engineering principles and applications in sustainable energy and material science. Surface science and systems analysis across different technology sectors - material production and processing, waste management, device manufacture, composites, coatings, ceramics, membranes, biomaterials, and microelectronics.
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Instructor:
Raymond Farinato
CULPA: 1 Info - 3 points
Advanced Algorithms
Introduces classic and modern algorithmic ideas that are central to many areas of Computer Science. The focus is on most powerful paradigms and techniques of how to design algorithms, and how to measure their efficiency. The intent is to be broad, covering a diversity of algorithmic techniques, rather than be deep. The covered topics have all been implemented and are widely used in industry. Topics include: hashing, sketching/streaming, nearest neighbor search, graph algorithms, spectral graph theory, linear programming, models for large-scale computation, and other related topics
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Instructor:
Alexandr Andoni
CULPA: 2 h-index: 34 Info - 3 points
COMPUT MATH:INTRO-NUMERCL METH
Programming experience in Python extremely useful. Introduction to fundamental algorithms and analysis of numerical methods commonly used by scientists, mathematicians and engineers. Designed to give a fundamental understanding of the building blocks of scientific computing that will be used in more advanced courses in scientific computing and numerical methods for PDEs (e.g. APMA E4301, E4302). Topics include numerical solutions of algebraic systems, linear least-squares, eigenvalue problems, solution of non-linear systems, optimization, interpolation, numerical integration and differentiation, initial value problems and boundary value problems for systems of ODEs. All programming exercises will be in Python.
NUMERICAL METHODS/PDE'S
Numerical solution of differential equations, in particular partial differential equations arising in various fields of application. Presentation emphasizes finite difference approaches to present theory on stability, accuracy, and convergence with minimal coverage of alternate approaches (left for other courses). Method coverage includes explicit and implicit time-stepping methods, direct and iterative solvers for boundary-value problems.
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Instructor:
Qiang Du
Wikipedia h-index: 67 Info - 3 points
Applied Stochastic Analysis
Provides elementary introduction to fundamental ideas in stochastic analysis for applied mathematics. Core material includes: (i) review of probability theory (including limit theorems), and introduction to discrete Markov chains and Monte Carlo methods; (ii) elementary theory of stochastic process, Ito's stochastic calculus and stochastic differential equations; (iii) introductions to probabilistic representation of elliptic partial differential equations (the Fokker-Planck equation theory); (iv) stochastic approximation algorithms; and (v) asymptotic analysis of SDEs.
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Instructor:
Liliana Borcea
Info - 3 points
Biomechanics of Developmental Biology
BIOMECHANICS DEVELOPMENTA
Biophysical mechanisms of tissue organization
during embryonic development: conservation laws, reaction-diffusion, finite elasticity, and fluid mechanics are reviewed and applied to a broad range of topics in developmental biology, from early development to later organogenesis of the central nervous, cardiovascular, musculoskeletal, respiratory, and gastrointestinal systems. Subdivided into modules on patterning (conversion of diffusible cues into cell fates) and morphogenesis (shaping of tissues), the course will include lectures, problem sets, reading of primary literature, and a final project.
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Instructor:
Nandan L Nerurkar
Info - 3 points
Green Chemical Engineering & Innovation
Approaches used in chemistry and chemical engineering to design green, sustainable products and processes; focus of using the tenets of green chemistry as a means for chemical innovation. Technical and design practice and measuring the impacts of green and conventional approaches emphasized. Themes of business, regulatory, ethical, and social considerations relevant to chemical engineering practice.
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Instructor:
Christopher S Chen
Info - 3 points
PRIN OF ULTRASOUND IN MEDICINE
ULTRASOUND IN DIAGNOSTC IMAGNG
Fourier analysis. Physics of diagnostic ultrasound and principles of ultrasound imaging instrumentation. Propagation of plane waves in lossless medium; ultrasound propagation through biological tissues; single-element and array transducer design; pulse-echo and Doppler ultrasound instrumentation, performance evaluation of ultrasound imaging systems using tissue-mimicking phantoms, ultrasound tissue characterization; ultrasound nonlinearity and bubble activity; harmonic imaging; acoustic output of ultrasound systems; biological effects of ultrasound.
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Instructor:
Elisa Konofagou
Wikipedia h-index: 71 Info - 3 points
MICRO/NANO STRUCT CELL ENG
Design, fabrication, and application of micro-/nanostructured systems for cell engineering. Recognition and response of cells to spatial aspects of their extracellular environment. Focus on neural, cardiac, coculture, and stem cell systems. Molecular complexes at the nanoscale.
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Instructor:
Lance Kam
CULPA: 7
h-index: 38
Info
- 3 points
FOUND OF NANOBIOSCI/NANOBIOTECH
Fundamentals of nanobioscience and nanobiotechnology, scientific foundations, engineering principles, current and envisioned applications. Includes discussion of intermolecular forces and bonding, of kinetics and thermodynamics of self-assembly, of nanoscale transport processes arising from actions of biomolecular motors, computation and control in biomolecular systems, and of mitochondrium as an example of a nanoscale factory.
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Instructor:
Henry Hess
CULPA: 1 h-index: 45 Info - 3 points
BIOMEMS:CELL/MOLECULAR APPLIC
Topics include biomicroelectromechanical, microfluidic, and lab-on-a-chip systems in biomedical engineering, with a focus on cellular and molecular applications. Microfabrication techniques, biocompatibility, miniaturization of analytical and diagnostic devices, high-throughput cellular studies, microfabrication for tissue engineering, and in vivo devices.
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Instructor:
Samuel Sia
CULPA: 1 h-index: 39 Info - 3 points
DISCRETE CONTROL SYSTEMS
Digital Control Systems
The course studies control strategies and their implementation in the discrete domain. Introduction with examples; review of continuous control and Laplace Transforms; review of continuous state-space representation and Solutions; review of difference equations, discretization in time and frequency, the WKS (aka Shannon) sampling theorem, windowing, filters, Transforms: Fourier series, Fourier transform, z-transform and their inverses; Ideal sampler, Sample-and-hold devices, zero, one, polygonal, and slewer hold; Transfer functions, block diagrams, and signal flow graphs for discrete systems; Discrete State-Space transformation, controllabililty, observability, and stability in the state-space domain. Discrete time and z domain analysis, steady state analysis, discrete-time root-locus, and pole-zero placement; Discrete Nyquist stability criterion, Bode plot, Gain and Phase Margin analysis, Nichols chart, bandwidth and sensitivity analysis; Design criteria, self-tuning regulator, Kalman filter, and simulation, followed by advanced stability analysis such as Lyapunov stability; Overview of the discrete Euler-Lagrange equations, discrete maximum and minimum principle, optimal linear discrete regulator design, optimality and dynamic programming.
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Instructor:
Homayoon Beigi
Info - 3 points
TOPICS IN SOFT MATERIALS
Self-contained treatments of selected topics in soft materials (e.g. polymers, colloids, amphiphiles, liquid crystals, glasses, powders). Topics and instructor may change from year to year. Intended for junior/senior level undergraduates and graduate students in engineering and the physical sciences.
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Instructor:
Christopher J Durning
CULPA: 3 Info - 3 points
CHEMICAL ENGINEERING DATA ANALYSIS
CHEM E DATA ANALYSIS
Course is aimed at senior undergraduate and graduate students. Introduces fundamental concepts of Bayesian data analysis as applied to chemical engineering problems. Covers basic elements of probability theory, parameter estimation, model selection, and experimental design. Advanced topics such as nonparametric estimation and Markov chain Monte Carlo (MEME) techniques are introduced. Example problems and case studies drawn from chemical engineering practice are used to highlight the practical relevance of the material. Theory reduced to practice through programming in Mathematica. Course grade based on midterm and final exams, biweekly homework assignments, and final team project.
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Instructor:
Kyle Bishop
h-index: 42 Info - 3 points
INTRO TO FINANCIAL ENGINEERING
Prerequisite(s): IEOR E4106 or E3106. Required for undergraduate students majoring in OR:FE. Introduction to investment and financial instruments via portfolio theory and derivative securities, using basic operations research/engineering methodology. Portfolio theory, arbitrage; Markowitz model, market equilibrium, and the capital asset pricing model. General models for asset price fluctuations in discrete and continuous time. Elementary introduction to Brownian motion and geometric Brownian motion. Option theory; Black-Scholes equation and call option formula. Computational methods such as Monte Carlo simulation.
ARTIFICIAL INTELLIGENCE
Prior knowledge of Python is recommended. Provides a broad understanding of the basic techniques for building intelligent computer systems. Topics include state-space problem representations, problem reduction and and-or graphs, game playing and heuristic search, predicate calculus, and resolution theorem proving, AI systems and languages for knowledge representation, machine learning and concept formation and other topics such as natural language processing may be included as time permits.
NATURAL LANGUAGE PROCESSING
Computational approaches to the analysis, understanding, and generation of natural language text at scale. Emphasis on machine learning techniques for NLP, including deep learning and large language models. Applications may include information extraction, sentiment analysis, question answering, summarization, machine translation, and conversational AI. Discussion of datasets, benchmarking and evaluation, interpretability, and ethical considerations.
Due to significant overlap in content, only one of COMS 4705 or Barnard COMS 3705BC may be taken for credit.
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Instructor:
Andrei A Simion
Info - 3 points
Ethical and Responsible AI
ETHIC AND RESPONSIBLE AI
Principles of Ethical Artificial Intelligence across technical and societal dimensions. Combines technical AI and machine learning implementations and ethical analysis. Students will learn to build, audit, and mitigate ethical risks in AI systems using tools like fairness libraries, explainability frameworks, and privacy-preserving techniques. Emphasizes coding, algorithmic critique, and real-world cases.
Topics include: foundations of AI ethics, fairness, interpretability, explainability, accountability, privacy, robustness, alignment, safety, and societal benefit.
Assessments include coding projects, bias auditing assignments, and ethical analysis papers.
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Instructor:
Ansaf Salleb-Aouissi
CULPA: 21 h-index: 16 Info - 3 points
Pharmacokinetics for Engineers
Pharmacokinetics for Engr
Develop process models of the human body to predict pharmaceutical effects as a function of time and organ (or cell) type to work for a wide variety of pharmaceuticals, including small molecules, biologics, and chemotherapy agents. Computer models of pharmacokinetic behavior will be developed and then used to analyze and design drug delivery regimens. Covers: spectrum of factors affecting pharmaceutical effects on physiology, including drug formulation, mode of dosing and dosing rate, metabolism and metabolic cascades, storage in fatty tissues, and diffusional limitations.
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Instructor:
Sakul Ratanalert
Info - 3 points
Quantum Optimization and Machine Learnin
QUANTUM OPT & ML
An introduction to the recent development in quantum optimization and quantum machine learning using gate-based Noisy Intermediate Scale Quantum (NISQ) computers. IBM’s quantum programming framework Qiskit is utilized. Qbits, quantum gates and quantum measurements, quantum algorithms (Grover’s search, Simon’s algorithm, quantum Fourier transform, quantum phase estimation) quantum optimization (quantum annealing, QAOA, variational quantum eigensolver), quantum machine learning (quantum support vector machine, quantum neural networks).
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Instructor:
Xiaodong Wang
CULPA: 15 Info - 3 points
COMPUT METHODS IN FINANCE
MS IEOR students only. Application of various computational methods/techniques in quantitative/computational finance. Transform techniques: fast Fourier transform for data de-noising and pricing, finite difference methods for partial differential equations (PDE), partial integro-differential equations (PIDE), Monte-Carlo simulation techniques in finance, and calibration techniques, filtering and parameter estimation techniques. Computational platform will be C++/Java/Python/Matlab/R.
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Instructor:
Alireza Javaheri
Info - 3 points
RANDOM SIGNALS & NOISE
Characterization of stochastic processes as models of signals and noise; stationarity, ergodicity, correlation functions, and power spectra. Gaussian processes as models of noise in linear and nonlinear systems; linear and nonlinear transformations of random processes; orthogonal series representations. Applications to circuits and devices, to communication, control, filtering, and prediction.
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Instructor:
Irving Kalet
CULPA: 3
h-index: 12
Info
- 3 points
DIGITAL IMAGE PROCESSING
Introduction to the mathematical tools and algorithmic implementation for representation and processing of digital pictures, videos, and visual sensory data. Image representation, filtering, transform, quality enhancement, restoration, feature extraction, object segmentation, motion analysis, classification, and coding for data compression. A series of programming assignments reinforces material from the lectures.
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Instructor:
Christine P Hendon
Wikipedia h-index: 21 Info - 3 points
ATOMISTIC SIMULATIONS FOR SCIENCE AND EN
Many materials properties and chemical processes are governed by atomic-scale phenomena such as phase transformations, atomic/ionic transport, and chemical reactions. Thanks to progress in computer technology and methodological development, now there exist atomistic simulation approaches for the realistic modeling and quantitative prediction of such properties. Atomistic simulations are therefore becoming increasingly important as a complement for experimental characterization, to provide parameters for meso- and macroscale models, and for the in-silico discovery of entirely new materials. This course aims at providing a comprehensive overview of cutting-edge atomistic modeling techniques that are frequently used both in academic and industrial research and engineering. Participants will develop the ability to interpret results from atomistic simulations and to judge whether a problem can be reliably addressed with simulations. The students will also obtain basic working knowledge in standard simulation software.
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Instructor:
Alexander Urban
h-index: 24 Info - 3 points
TPC NEUROSCI & DEEP LEARN
Comp. w. Brain Cir of MO
Selected advanced topics in neuroscience and deep learning. Content varies from year to year, and different topics rotate through the course numbers 6070 to 6079.
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Instructor:
Aurel A Lazar
h-index: 53 Info - 3 points
PLASMA PHYSICS II
Magnetic coordinates. Equilibrium, stability, and transport of torodial plasmas. Ballooning and tearing instabilities. Kinetic theory, including Vlasov equation, Fokker-Planck equation, Landau damping, kinetic transport theory. Drift instabilities.
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Instructor:
Carlos Paz Soldan
h-index: 28 Info - 3 points
TOPICS IN SOFTWARE ENGINEERING
Topics in Software engineering arranged as the need and availability arises. Topics are usually offered on a one-time basis. Since the content of this course changes, it may be repeated for credit with advisor approval. Consult the department for section assignment.
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Instructor:
Gail E Kaiser
CULPA: 10 Info - 3 points
Human-Computer Interaction
Human–computer interaction (HCI) studies (1) what computers are used for, (2) how people interact with computers, and (3) how either of those should change in the future. Topics include ubiquitous computing, mobile health, interaction techniques, social computing, mixed reality, accessibility, and ethics. Activities include readings, presentations, and discussions of research papers. Substantial HCI research project required.
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Instructor:
Brian A Smith
CULPA: 2 h-index: 5 Info - 3 points
Future Energy: Economics, Systems, Polic
Holistic understanding of the science and socioeconomic modelling of climate change, the properties of renewable energy sources, their economic and engineering
implications, and the policy decisions in the transition to future energy. Fundamentals of systems needed to support deep penetration of renewable energy, including grid stability, transmission and storage systems, and the design and operations of carbonaware datacenters.
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Instructor:
Debasis Mitra
Wikipedia h-index: 61 Info - 3 points
Mathematics of Machine Learning, Signals
Math of ML, Signals, & Co
Advanced Linear Algebra, Complex Variable Theory, Integral Transforms, Measure Theory and Probability Theory, Advanced Information Theory, Differential and Difference Equations, Calculus of Variations, Nonlinear Optimization, State-Space Modeling, Advanced Signal Processing and Recognition: non-Stationary Signal Recognition, Spectral and Cepstral Analysis, Supervised and Unsupervised Clustering, Decision Theory, Math of modern NN architectures.
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Instructor:
Homayoon Beigi
Info - 3 points
Advanced Spoken Language Processing
ADV SPOKEN LANG PROC
Applications of spoken language processing, including text-to-speech and dialogue systems. Analysis of speech and text, including entrainment, empathy, personality, emotion, humor, sarcasm, deception, trust, radicalization, and charisma.
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Instructor:
Julia Hirschberg
CULPA: 8
h-index: 77
Info
- 3 points
Quantum Sensing Theory
QUANTUM SENSING THEORY
Introduction to quantum detection and estimation theory and its applications to quantum communications, quantum radar, quantum metrology, and quantum tomography. Background on quantum mechanics, quantum detection, composite quantum systems, Gaussian states, and quantum estimation.
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Instructor:
Xiaodong Wang
CULPA: 15 Info - 3 points
TOPICS-INFORMATION PROCESSING
Reinforcement Learning
Advanced topics spanning electrical engineering and computer science such as speech processing and recognition, image and multimedia content analysis, and other areas drawing on signal processing, information theory, machine learning, pattern recognition, and related topics. Content varies from year to year, and different topics rotate through the course numbers 6890 to 6899.
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Instructor:
Javad Ghaderi
h-index: 17 Info - 3 points
TOPICS-INFORMATION PROCESSING
TPC: Adv Big Data & AI
Advanced topics spanning Electrical Engineering and Computer Science such as speech processing and recognition, image and multimedia content analysis, and other areas drawing on signal processing, information theory, machine learning, pattern recognition, and related topics. Content varies from year to year, and different topics rotate through the course numbers 6890 to 6899. Topic: Advanced Big Data Analytics.
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Instructor:
Ching-Yung Lin
h-index: None Info - 3 points
TOPICS IN COMPUTER SCIENCE
HIGH PERF MACH LEARNING
Selected topics in computer science (advanced level). Content and prerequisites vary between sections and semesters. May be repeated for credit. Check “topics course” webpage on the department website for more information on each section.
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Instructor:
Kaoutar El Maghraoui
Info - 3 points