This is an advanced subject in computer modeling and CAD CAM fabrication, with a focus on building large-scale prototypes and digital mock-ups within a classroom setting. Prototypes and mock-ups are developed with the aid of outside designers, consultants, and fabricators. Field trips and in-depth relationships with building fabricators demonstrate new methods for building design. The class analyzes complex shapes, shape relationships, and curved surfaces fabrication at a macro scale leading to new architectural languages, based on methods of construction.

" This course introduces principles and technologies for converting heat into electricity via solid-state devices. The first part of the course discusses thermoelectric energy conversion and thermoelectric materials, thermionic energy conversion, and photovoltaics. The second part of the course discusses solar thermal technologies. Various solar heat collection systems will be reviewed, followed by an introduction to the principles of solar thermophotovoltaics and solar thermoelectrics. Spectral control techniques, which are critical for solar thermal systems, will be discussed."

Enzymes, nature's catalysts, are remarkable biomolecules capable of extraordinary specificity and selectivity. Directed evolution has been used to produce enzymes with many unique properties, including altered substrate specificity, thermal stability, organic solvent resistance, and enantioselectivity--selectivity of one stereoisomer over another. The technique of directed evolution comprises two essential steps: mutagenesis of the gene encoding the enzyme to produce a library of variants, and selection of a particular variant based on its desirable catalytic properties. In this course we will examine what kinds of enzymes are worth evolving and the strategies used for library generation and enzyme selection. We will focus on those enzymes that are used in the synthesis of drugs and in biotechnological applications. This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literature to discuss and learn about current biological research in a highly interactive setting. Many instructors of the Advanced Undergraduate Seminars are postdoctoral scientists with a strong interest in teaching.

Representation, analysis, and design of discrete time signals and systems. Review of Z-transforms, discrete-time Fourier transforms, and difference equations. Discrete-time processing of continuous-time signals. Decimation, interpolation, and sampling rate conversion. Flowgraph structures for DT systems. Time-and frequency-domain design techniques for recursive (IIR) and non-recursive (FIR) filters. Linear prediction. Discrete Fourier transform, FFT algorithm. Short-time Fourier analysis and filter banks. Multirate techniques. Hilbert transforms, Cepstral analysis, various applications.

Design and analysis of concurrent algorithms, emphasizing those suitable for use in distributed networks. Process synchronization, allocation of computational resources, distributed consensus, distributed graph algorithms, election of a leader in a network, distributed termination, deadlock detection, concurrency control, communication, and clock synchronization. Special consideration given to issues of efficiency and fault tolerance. Formal models and proof methods for distributed computation. Course Description 6.852J / 18.437J intends to: (1) provide a rigorous introduction to the most important research results in the area of distributed algorithms, and (2) prepare interested students to carry out independent research in distributed algorithms. Topics covered include: design and analysis of concurrent algorithms, emphasizing those suitable for use in distributed networks, process synchronization, allocation of computational resources, distributed consensus, distributed graph algorithms, election of a leader in a network, distributed termination, deadlock detection, concurrency control, communication, and clock synchronization. Special consideration is given to issues of efficiency and fault tolerance. Formal models and proof methods for distributed computation are also discussed.

This course intends to provide a rigorous introduction to the most important research results in the area of distributed algorithms, and prepare interested students to carry out independent research in distributed algorithms. Topics covered include: design and analysis of concurrent algorithms, emphasizing those suitable for use in distributed networks, process synchronization, allocation of computational resources, distributed consensus, distributed graph algorithms, election of a leader in a network, distributed termination, deadlock detection, concurrency control, communication, and clock synchronization. Special consideration is given to issues of efficiency and fault tolerance. Formal models and proof methods for distributed computation are also discussed.

" Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems."

Seminar on a selected topic from Renaissance architecture. Requires original research and presentation of a report. The aim of this course is to highlight some technical aspects of the classical tradition in architecture that have so far received only sporadic attention. It is well known that quantification has always been an essential component of classical design: proportional systems in particular have been keenly investigated. But the actual technical tools whereby quantitative precision was conceived, represented, transmitted, and implemented in pre-modern architecture remain mostly unexplored. By showing that a dialectical relationship between architectural theory and data-processing technologies was as crucial in the past as it is today, this course hopes to promote a more historically aware understanding of the current computer-induced transformations in architectural design.

The course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We will consider optimal control of a dynamical system over both a finite and an infinite number of stages. This includes systems with finite or infinite state spaces, as well as perfectly or imperfectly observed systems. We will also discuss approximation methods for problems involving large state spaces. Applications of dynamic programming in a variety of fields will be covered in recitations.

Momentum principles and energy principles. Lagrange's equations, Hamilton's principle. Applications to mechanical systems including gyroscopic effects. Study of steady motions and nature of small deviations therefrom. Natural modes and natural frequencies for continuous and lumped parameter systems. Forced vibrations. Dynamic stability theory. Causes of instability. This course reviews momentum and energy principles, and then covers the following topics: Hamilton's principle and Lagrange's equations; three-dimensional kinematics and dynamics of rigid bodies; steady motions and small deviations therefrom, gyroscopic effects, and causes of instability; free and forced vibrations of lumped-parameter and continuous systems; nonlinear oscillations and the phase plane; nonholonomic systems; and an introduction to wave propagation in continuous systems. This course was originally developed by Professor T. Akylas.

This class is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics include kinematics; force-momentum formulation for systems of particles and rigid bodies in planar motion; work-energy concepts; virtual displacements and virtual work; Lagrange's equations for systems of particles and rigid bodies in planar motion; linearization of equations of motion; linear stability analysis of mechanical systems; free and forced vibration of linear multi-degree of freedom models of mechanical systems; and matrix eigenvalue problems. The class includes an introduction to numerical methods and using MATLABĺ¨ to solve dynamics and vibrations problems.

Upon successful completion of this course, students will be able to: * Create lumped parameter models (expressed as ODEs) of simple dynamic systems in the electrical and mechanical energy domains * Make quantitative estimates of model parameters from experimental measurements * Obtain the time-domain response of linear systems to initial conditions and/or common forcing functions (specifically; impulse, step and ramp input) by both analytical and computational methods * Obtain the frequency-domain response of linear systems to sinusoidal inputs * Compensate the transient response of dynamic systems using feedback techniques * Design, implement and test an active control system to achieve a desired performance measureMastery of these topics will be assessed via homework, quizzes/exams, and lab assignments.

Introduction to dynamics and vibration of lumped-parameter models of mechanical systems. Three-dimensional particle kinematics. Force-momentum formulation for systems of particles and for rigid bodies (direct method). Newton-Euler equations. Work-enery (variational) formulation for systems particles and for rigid bodies (indirect method). Virtual displacements and work. Lagrange's equations for systems of particles and for rigid bodies. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear damped lumped parameter multi-degree of freedom models of mechanical systems. Application to the design of ocean and civil engineering structures such as tension leg platforms.

An introduction to theoretical studies of systems of many interacting components, the individual dynamics of which may be simple, but the collective dynamics of which are often nonlinear and analytically intractable. Topics vary from year to year. Format includes both pedagogical lectures and round-table reviews of current literature. Subjects of interest include: problems in natural science (e.g., geology, ecology, and biology) where quantitative theory is still in development; problems in physics, such as turbulence, that demonstrate powerful concepts such as scaling and universality; and modern computational methods for the simulation and study of such problems. Discussions in context of contemporary experimental or observational data.

An introduction to theoretical studies of systems of many interacting components, the individual dynamics of which may be simple, but the collective dynamics of which are often nonlinear and analytically intractable. Topics vary from year to year. Format includes both pedagogical lectures and round-table reviews of current literature. Subjects of interest include: problems in natural science (e.g., geology, ecology, and biology) where quantitative theory is still in development; problems in physics, such as turbulence, that demonstrate powerful concepts such as scaling and universality; and modern computational methods for the simulation and study of such problems. Discussions in context of contemporary experimental or observational data.

An introduction to theoretical studies of systems of many interacting components, the individual dynamics of which may be simple, but the collective dynamics of which are often nonlinear and analytically intractable. Topics vary from year to year. Format includes both pedagogical lectures and round-table reviews of current literature. Subjects of interest include: problems in natural science (e.g., geology, ecology, and biology) where quantitative theory is still in development; problems in physics, such as turbulence, that demonstrate powerful concepts such as scaling and universality; and modern computational methods for the simulation and study of such problems. Discussions in context of contemporary experimental or observational data.

Introduction to nonlinear deterministic dynamical systems. Nonlinear ordinary differential equations. Planar autonomous systems. Fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma. Stability of equilibria by Lyapunov's first and second methods. Feedback linearization. Application to nonlinear circuits and control systems. Alternate years. Description from course website: This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems.

This course begins with a study of the role of dynamics in the general physics of the atmosphere, the consideration of the differences between modeling and approximation, and the observed large-scale phenomenology of the atmosphere. Only then are the basic equations derived in rigorous manner. The equations are then applied to important problems and methodologies in meteorology and climate, with discussions of the history of the topics where appropriate. Problems include the Hadley circulation and its role in the general circulation, atmospheric waves including gravity and Rossby waves and their interaction with the mean flow, with specific applications to the stratospheric quasi-biennial oscillation, tides, the super-rotation of Venus' atmosphere, the generation of atmospheric turbulence, and stationary waves among other problems. The quasi-geostrophic approximation is derived, and the resulting equations are used to examine the hydrodynamic stability of the circulation with applications ranging from convective adjustment to climate.

The Early Universe provides an introduction to modern cosmology. The first part of the course deals with the classical cosmology, and later part with modern particle physics and its recent impact on cosmology.

Ecologies of Construction examines the resource requirements for the making and maintenance of the contemporary built environment. This course introduces the field of industrial ecology as a primary source of concepts and methods in the mapping of material and energy expenditures dedicated to construction activities.