Introduction to discrete and computational geometry. Topics covered: planar graphs, geometric graphs, the theory of crossings, extremal graph theory, arrangements of curves and points in the plane (mainly pseudolines and pseudocircles), problems involving distances, Gallai-Sylvester-type problems, Davenport-Schinzel sequences. Emphasis on teaching methods in combinatorial geometry. Many results presented are recent, and include open problems.

Geometry is concerned with the various aspects of size, shape and space. In this unit, you will explore the concepts of angles, shapes, symmetry, area and volume through interactive activities.

A rigorous introduction designed for mathematicians into perturbative quantum field theory, using the language of functional integrals. Basics of classical field theory. Free quantum theories. Feynman diagrams. Renormalization theory. Local operators. Operator product expansion. Renormalization group equation. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and string theory.

This is a second-semester graduate course on the geometry of manifolds. The main emphasis is on the geometry of symplectic manifolds, but the material also includes long digressions into complex geometry and the geometry of 4-manifolds, with special emphasis on topological considerations.

Fundamental principles of biochemistry. Analysis of the mode of action and structure of regulatory, binding, and catalytic proteins. The tools and analytical methods that biochemists use to dissect biological problems. Analysis of the mode of action and structure of regulatory, binding, and catalytic proteins.

This course provides a challenging introduction to some of the central ideas of theoretical computer science. It attempts to present a vision of "computer science beyond computers": that is, CS as a set of mathematical tools for understanding complex systems such as universes and minds. Beginning in antiquity--with Euclid's algorithm and other ancient examples of computational thinking--the course will progress rapidly through propositional logic, Turing machines and computability, finite automata, GĚŚdel's theorems, efficient algorithms and reducibility, NP-completeness, the P versus NP problem, decision trees and other concrete computational models, the power of randomness, cryptography and one-way functions, computational theories of learning, interactive proofs, and quantum computing and the physical limits of computation. Class participation is essential, as the class will include discussion and debate about the implications of many of these ideas.

Background for and techniques of visual observation, electronic imaging, and spectroscopy of the Moon, planets, satellites, stars, and brighter deep-space objects. Weekly outdoor observing sessions using 8-inch diameter telescopes when weather permits. Indoor sessions introduce needed skills. Introduction to contemporary observational astronomy including astronomical computing, image and data processing, and how astronomers work. Student must maintain a careful and complete written log which is graded. In this seminar we explore the background and techniques of visual observation and imaging of the Moon, planets, and brighter deep-space objects using 8-inch telescopes. (Some sample images appear in our "photo album".) Telescope work begins with visual observing, then we advance to CCD (charge-coupled device) cameras. Each class observing session meets one evening a week. Whenever weather conditions permit us to observe outdoors we do so! In cloudy weather we'll try some astronomical computing and image processing indoors instead. Either way, virtually all the work for the seminar is done during the evening sessions, so students must attend section every week in order to pass. Past experience has been that if you're really enthusiastic about hands-on out-under-the-sky astronomy, enough to be willing to deal with dressing warmly, tinkering with equipment, and committing one evening a week, 12.409 is great fun! One student wrote, "Unlike most seminars, you will earn your units and, unlike most other MIT courses, you will look forward to doing it!" But we'll be direct: 12.409 is not for everyone, and in past years many whose interest was merely casual found themselves unwilling to devote one entire evening every week to the class. If your interest is only casual then consider whether a more typical astronomy survey subject might be a better choice, since it'll have more outside preparation time that you can rearrange at your discretion and less in-class time that you can't.

This course introduces students to both passive and active electronic components (op-amps, 555 timers, TTL digital circuits). Basic analog and digital circuits and theory of operation are covered. The labs allow the students to master the use of electronic instruments and construct and/or solder several circuits. The labs also reinforce the concepts discussed in class with a hands-on approach and allow the students to gain significant experience with electrical instruments such as function generators, digital multimeters, oscilloscopes, logic analyzers and power supplies. In the last lab, the students build an electronic circuit that they can keep. The course is geared to freshmen and others who want an introduction to electronics circuits. This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

Introduces the study of aging, its implications for individuals, families, and society, and the background for health policy related to older persons. Presents an overview on aging from different perspectives: demography, biology, epidemiology of diseases, physical and mental disorders, functional capacity and disability, health services, federal and state health policies, social aspects of aging, and ethical issues in the care of older individuals.

6.776 covers circuit and system level design issues of high speed communication systems, with primary focus being placed on wireless and broadband data link applications. Specific circuit topics include transmission lines, high speed and low noise amplifiers, VCO's, and high speed digital circuits. Specific system topics include frequency synthesizers, clock and data recovery circuits, and GMSK transceivers. In addition to learning analysis skills for the above items, students will gain a significant amount of experience in simulating circuits in SPICE and systems in CppSim (a custom C++ simulator).

6.976 covers system level issues of high speed communication systems and their impact on circuit requirements, with primary focus being placed on wireless and broadband data link applications. Course topics include: transistor level design techniques for high speed amplifiers, mixers, VCO's, registers and gates, and phase locked loops, and the impact of transmission line effects on circuit designs for narrowband and broadband systems. Finally, behavioral level simulation techniques are presented for phase locked loops and other communication circuits.

This class examines the history and theory of historic preservation, focusing on the United States, but with reference to traditions and practices in other countries. The class is designed to examine the largely untold history of the historic preservation movement in this country, and explore what laws, public policies and cultural attitudes shape how we preserve or do not preserve the built environment. The class will give students a grounding in the history, theory and practice of historic preservation, but is not an applied, technical course.

Examines the development of computing techniques and technology in the nineteenth and twentieth centuries, particularly critical evaluation of how the very idea of "computer" changes and evolves over time. Emphasis is on technical innovation, industrial development, social context, and the role of government. Topics include Babbage, Hollerith, differential analyzers, control systems, ENIAC, radar, operations research, computers as scientific instruments, the rise of "computer science," artificial intelligence, personal computers, and networks. Includes class visits by members of the MIT community who have made important historical contributions. This course focuses on one particular aspect of the history of computing: the use of the computer as a scientific instrument. The electronic digital computer was invented to do science, and its applications range from physics to mathematics to biology to the humanities. What has been the impact of computing on the practice of science? Is the computer different from other scientific instruments? Is computer simulation a valid form of scientific experiment? Can computer models be viewed as surrogate theories? How does the computer change the way scientists approach the notions of proof, expertise, and discovery? No comprehensive history of scientific computing has yet been written. This seminar examines scientific articles, participants' memoirs, and works by historians, sociologists, and anthropologists of science to provide multiple perspectives on the use of computers in diverse fields of physical, biological, and social sciences and the humanities. We explore how the computer transformed scientific practice, and how the culture of computing was influenced, in turn, by scientific applications.

A laboratory-based exploration of the principles, techniques, and applications of holography as a 3-D imaging communication medium. Begins with interference and diffraction, and proceeds through laser off-axis holography to white-light "rainbow" and reflection holography. Term project required, with oral presentation and written report. MAS.450 is a laboratory course about holography and holographic imaging. This course teaches holography from a scientific and analytical point of view, moving from interference and diffraction to imaging of single points to the display of three-dimensional images. Using a "hands-on" approach, students explore the underlying physical phenomena that make holograms work, as well as designing laboratory setups to make their own images. The course also teaches mathematical techniques that allow the behavior of holography to be understood, predicted, and harnessed. Holography today brings together the fields of optics, chemistry, computer science, electrical engineering, visualization, three-dimensional display, and human perception in a unique and comprehensive way. As such, MAS.450 offers interesting and useful exposure to a wide range of principles and ideas. As a course satisfying the Institute Laboratory Requirement, MAS.450 teaches about science, scientific research, and the scientific method through observation and exploration, hinting at the excitement that inventors feel before they put their final equations to paper.

"This course covers the same material as Differential Equations (18.03) with more emphasis on theory. In addition, it treats mathematical aspects of ordinary differential equations such as existence theorems."

Subject studies how and why machines work, how they are conceived, how they are developed (drawn), and how they are utilized. Students learn from the hands-on experiences of taking things apart mentally and physically, drawing (sketching, 3D CAD) what they envision and observe, taking occasional field trips, and completing an individual term project (concept, creation, and presentation). Emphasis on understanding the physics and history of machines.

Provides a hands-on introduction to the resources for designing and fabricating smart systems, including CAD/CAM/CAE; NC machining, 3-D printing, injection molding, laser cutting; PCB layout and fabrication; sensors and actuators; analog instrumentation; embedded digital processing; wired and wireless communications. Emphasis on learning how to use the tools as well as understand how they work.

Lectures and clinical case discussions designed to provide the student with a clear understanding of the physiology, endocrinology, and pathology of human reproduction. Emphasis is on the role of technology in reproductive science. Suggestions for future research contributions in the field are probed. Students become involved in the wider aspects of reproduction, such as prenatal diagnosis, in vitro fertilization, abortion, menopause, contraception and ethics relation to reproductive science. This course is designed to give the student a clear understanding of the pathophysiology of the menstrual cycle, fertilization, implantation, ovum growth development, differentiation and associated abnormalities. Disorders of fetal development including the principles of teratology and the mechanism of normal and abnormal parturition will be covered as well as the pathophysiology of the breast and disorders of lactation. Fetal asphyxia and its consequences will be reviewed with emphasis on the technology currently available for its detection. In addition the conclusion of the reproductive cycle, menopause, and the use of hormonal replacement will be covered.

Principles of supervisory control and telerobotics. Different levels of automation are discussed, as well as the allocation of roles and authority between humans and machines. Human-vehicle interface design in highly automated systems. Decision aiding. Tradeoffs between human control and human monitoring. Automated alerting systems and human intervention in automatic operation. Enhanced human interface technologies such as virtual presence. Performance, optimization, and social implications of the human-automation system. Examples from aerospace, ground, and undersea vehicles, robotics, and industrial systems. Human Supervisory Control of Automated Systems discusses elements of the interactions between humans and machines. These elements include: assignment of roles and authority; tradeoffs between human control and human monitoring; and human intervention in automatic processes. Further topics comprise: performance, optimization and social implications of the system; enhanced human interfaces; decision aiding; and automated alterting systems. Topics refer to applications in aerospace, industrial and transportation systems.

This course covers the development of the fundamental equations of fluid mechanics and their simplifications for several areas of marine hydrodynamics and the application of these principles to the solution of engineering problems. Topics include the principles of conservation of mass, momentum and energy, lift and drag forces, laminar and turbulent flows, dimensional analysis, added mass, and linear surface waves, including wave velocities, propagation phenomena, and descriptions of real sea waves. Wave forces on structures are treated in the context of design and basic seakeeping analysis of ships and offshore platforms. Geophysical fluid dynamics will also be addressed including distributions of salinity, temperature, and density; heat balance in the ocean; major ocean circulations and geostrophic flows; and the influence of wind stress. Experimental projects conducted in ocean engineering laboratories illustrating concepts taught in class, including ship resistance and model testing, lift and drag forces on submerged bodies, and vehicle propulsion.