This class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.

Building on Complex Adaptive Systems theory and basic Agent Based Modeling knowledge presented in SPM4530, the Advanced course will focus on the model development process. The students are expected to conceptualize, develop and verify a model during the course, individually or in a group. The modeling tasks will be, as much as possible, based on real life research problems, formulated by various research groups from within and outside the faculty.
Study Goals The main goal of the course is to learn how to form a modeling question, perform a system decomposition, conceptualize and formalize the system elements, implement and verify the simulation and validate an Agent Based Model of a socio-technical system.

Explores how organizations can use system dynamics to achieve important goals. Student teams work with client managers to tackle the clients' most pressing issues. Students discuss experiences with their clients, and learn modeling and consulting skills they need to be effective. Focus on gaining practical insight from the system dynamics process. Projects are sponsored by diverse organizations from a range of industries and sizes from start-ups to the Fortune 500.

This is the second undergraduate architecture design studio, which introduces design logic and skills that enable design thinking, representation, and development. Through the lens of nano-scale machines, technologies, and phenomena, students are asked to explore techniques for describing form, space, and architecture. Exercises encourage various connotations of the "machine" and challenge students to translate conceptual strategies into more integrated design propositions through both digital and analog means.

This textbook is based on a different paradigm for organizing an engineering science core --- a systems, accounting and modeling approach --- that emphasizes the common, underlying concepts of engineering science. Although this approach is not new, as most graduate students have been struck by this idea sometime during their graduate education, its use as the organizing principle for an undergraduate curriculum is new. By focusing on the underlying concepts and stressing the similarities between subjects that are often perceived by students (and taught by faculty) as unconnected topics, this approach provides engineering students a foundational framework for recognizing and building connections as they travel through their education.

Starting from atoms, see how many molecules you can build. Collect your molecules and see them in 3D!

Build an atom out of protons, neutrons, and electrons, and see how the element, charge, and mass change. Then play a game to test your ideas!

Physics, modeling, application, and technology of compound semiconductors (primarily III-Vs) in electronic, optoelectronic, and photonic devices and integrated circuits. Topics: properties, preparation, and processing of compound semiconductors; theory and practice of heterojunctions, quantum structures, and pseudomorphic strained layers; metal-semiconductor field effect transistors (MESFETs); heterojunction field effect transistors (HFETs) and bipolar transistors (HBTs); and optoelectronic devices.

16.225 is a graduate level course on Computational Mechanics of Materials. The primary focus of this course is on the teaching of state-of-the-art numerical methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered in this course will include: linear and finite deformation elasticity, inelasticity and dynamics. Numerical formulation and algorithms will include: Variational formulation and variational constitutive updates, finite element discretization, error estimation, constrained problems, time integration algorithms and convergence analysis. There will be a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. At the beginning of the course, the students will be given the source of a base code with all the elements of a finite element program which constitute overhead and do not contribute to the learning objectives of this course (assembly and equation-solving methods, etc.). Each assignment will consist of formulating and implementing on this basic platform, the increasingly complex algorithms resulting from the theory given in class, as well as in using the code to numerically solve specific problems. The application to real engineering applications and problems in engineering science will be stressed throughout.

This course explores natural and electric lighting that integrates occupant comfort, energy efficiency and daylight availability in an architectural context. Students are asked to evaluate daylighting in real space and simulations, and also high dynamic range photography and physical model building.

" This course will guide graduate students through the process of using rapid prototyping and CAD/CAM devices in a studio environment. The class has a theoretical focus on machine use within the process of design. Each student is expected to have completed one graduate level of design computing with a full understanding of solid modeling in CAD. Students are also expected to have completed at least one graduate design studio."

This course provides a review of physical, chemical, ecological, and economic principles used to examine interactions between humans and the natural environment. Mass balance concepts are applied to ecology, chemical kinetics, hydrology, and transportation; energy balance concepts are applied to building design, ecology, and climate change; and economic and life cycle concepts are applied to resource evaluation and engineering design. Numerical models are used to integrate concepts and to assess environmental impacts of human activities. Problem sets involve development of MATLABĺ¨ models for particular engineering applications. Some experience with computer programming is helpful but not essential.

" This intensive micro-subject provides the necessary skills in Microsoftĺ¨ Excel spreadsheet modeling for ESD.71 Engineering Systems Analysis for Design. Its purpose is to bring entering students up to speed on some of the advanced techniques that we routinely use in analysis. It is motivated by our experience that many students only have an introductory knowledge of Excel, and thus waste a lot of time thrashing about unproductively. Many people think they know Excel, but overlook many efficient tools, such as Data Table and Goal Seek. It is also useful for a variety of other subjects."

Explore fractions while you help yourself to 1/3 of a chocolate cake and wash it down with 1/2 a glass of orange juice! Create your own fractions using fun interactive objects. Match shapes and numbers to earn stars in the fractions games. Challenge yourself on any level you like. Try to collect lots of stars!

This course will focus on understanding aspects of modern technology displaying exponential growth curves and the impact on global quality of life through a weekly updated class project integrating knowledge and providing practical tools for political and business decision-making concerning new aspects of bioengineering, personalized medicine, genetically modified organisms, and stem cells. Interplays of economic, ethical, ecological, and biophysical modeling will be explored through multi-disciplinary teams of students, and individual brief reports.

This site teaches High Schoolers how to Interpret Categorical and Quantitative Data through a series of 45 questions and interactive activities aligned to 2 Common Core mathematics skills.

During this course, we will be exploring basic questions of architecture through several short design exercises. Working with many different media, students will discover the interrelationship of architecture and its related disciplines, such as structures, sustainability, architectural history and the visual arts. Each problem will focus on one of these disciplines and one exploration and presentation technique.

First of two-term sequence on modeling, analysis and control of dynamic systems. Mechanical translation, uniaxial rotation, electrical circuits and their coupling via levers, gears and electro-mechanical devices. Analytical and computational solution of linear differential equations and state-determined systems. Laplace transforms, transfer functions. Frequency response, Bode plots. Vibrations, modal analysis. Open- and closed-loop control, instability. Time-domain controller design, introduction to frequency-domain control design techniques. Case studies of engineering applications.

The application of electronics to energy conversion and control; phase-controlled rectifier/inverter circuits, dc/dc converters, high-frequency inverters, and motion control systems. Characteristics of power semiconductor devices: diodes, bipolar and field effect transistors, IGBTS, and thyristors. Modeling, analysis, and control techniques. Magnetic circuits. Numerous application examples.

This class deals with the modeling and analysis of queueing systems, with applications in communications, manufacturing, computers, call centers, service industries and transportation. Topics include birth-death processes and simple Markovian queues, networks of queues and product form networks, single and multi-server queues, multi-class queueing networks, fluid models, adversarial queueing networks, heavy-traffic theory and diffusion approximations. The course will cover state of the art results which lead to research opportunities.