Online courses directory (2511)

Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations.

This course provides an introduction to algebraic number theory. Topics covered include dedekind domains, unique factorization of prime ideals, number fields, splitting of primes, class group, lattice methods, finiteness of the class number, Dirichlet's units theorem, local fields, ramification, discriminants.

In this course we shall develop theoretical methods suitable for the description of the many-body phenomena, such as Hamiltonian second-quantized operator formalism, Greens functions, path integral, functional integral, and the quantum kinetic equation. The concepts to be introduced include, but are not limited to, the random phase approximation, the mean field theory (aka saddle-point, or semiclassical approximation), the tunneling dynamics in imaginary time, instantons, Berry phase, coherent state path integral, renormalization group.

This subject introduces the history of science from antiquity to the present. Students consider the impact of philosophy, art, magic, social structure, and folk knowledge on the development of what has come to be called "science" in the Western tradition, including those fields today designated as physics, biology, chemistry, medicine, astronomy and the mind sciences. Topics include concepts of matter, nature, motion, body, heavens, and mind as these have been shaped over the course of history. Students read original works by Aristotle, Vesalius, Newton, Lavoisier, Darwin, Freud, and Einstein, among others.

D-Lab: Energy offers a hands-on, project-based approach that engages students in understanding and addressing the applications of small-scale, sustainable energy technology in developing countries where compact, robust, low-cost systems for generating power are required. Projects may include micro-hydro, solar, or wind turbine generators along with theoretical analysis, design, prototype construction, evaluation and implementation. Students will have the opportunity both to travel to Nicaragua during spring break to identify and implement projects.

D-Lab: Energy is part of MIT's D-Lab program, which fosters the development of appropriate technologies and sustainable solutions within the framework of international development.

This course is an elective subject in MIT’s undergraduate Energy Studies Minor. This Institute-wide program complements the deep expertise obtained in any major with a broad understanding of the interlinked realms of science, technology, and social sciences as they relate to energy and associated environmental challenges.

This course provides the opportunity for students-as readers, viewers, writers and speakers-to engage with social and ethical issues they care deeply about. Over the course of the semester, through discussing the writing of classic and contemporary authors, we will explore different perspectives on a range of social issues such as free speech, poverty and homelessness, mental illness, capital punishment and racial and gender inequality. In addition, we will analyze selected documentary and feature films and photographs that represent or dramatize social problems or issues. In assigned essays, students will have the opportunity to write about social and ethical issues of their own choice. This course aims to help students to grow significantly in their ability to understand and grapple with arguments, to integrate secondary print and visual sources and to craft well-reasoned and elegant essays. Students will also keep a reading journal and give oral presentations. In class we will discuss assigned texts, explore strategies for successful academic writing, freewrite and respond to one another's essays.

In this course, you will be exposed to the work of many great documentary photographers and photojournalists, as well as to writing about the documentary tradition. Further, throughout the term, you will hone your photographic skills and 'eye,' and you will work on a photo documentary project of your own, attempting to reduce a tiny area of the moving world to a set of still images that convey what the viewer needs to know about what you saw—without hearing the sounds, smelling the odors, experiencing what was happening outside the viewfinder, and without seeing the motion.

The major focus of 16.13 is on boundary layers, and boundary layer theory subject to various flow assumptions, such as compressibility, turbulence, dimensionality, and heat transfer. Parameters influencing aerodynamic flows and transition and influence of boundary layers on outer potential flow are presented, along with associated stall and drag mechanisms. Numerical solution techniques and exercises are included.

This course covers the principles of materials science and cell biology underlying the design of medical implants, artificial organs, and matrices for tissue engineering. Methods for biomaterials surface characterization and analysis of protein adsorption on biomaterials. Molecular and cellular interactions with biomaterials are analyzed in terms of unit cell processes, such as matrix synthesis, degradation, and contraction. Mechanisms underlying wound healing and tissue remodeling following implantation in various organs. Tissue and organ regeneration. Design of implants and prostheses based on control of biomaterials-tissue interactions. Comparative analysis of intact, biodegradable, and bioreplaceable implants by reference to case studies. Criteria for restoration of physiological function for tissues and organs.

This course analyzes cooperative processes that shape the natural environment, now and in the geologic past. It emphasizes the development of theoretical models that relate the physical and biological worlds, the comparison of theory to observational data, and associated mathematical methods. Topics include carbon cycle dynamics; ecosystem structure, stability and complexity; mass extinctions; biosphere-geosphere coevolution; and climate change. Employs techniques such as stability analysis; scaling; null model construction; time series and network analysis.

The unifying theme of this course is best captured by the title of our main reference book: "Recursive Methods in Economic Dynamics". We start by covering deterministic and stochastic dynamic optimization using dynamic programming analysis. We then study the properties of the resulting dynamic systems. Finally, we will go over a recursive method for repeated games that has proven useful in contract theory and macroeconomics. We shall stress applications and examples of all these techniques throughout the course.

6.012 is the header course for the department's "Devices, Circuits and Systems" concentration. The topics covered include modeling of microelectronic devices, basic microelectronic circuit analysis and design, physical electronics of semiconductor junction and MOS devices, relation of electrical behavior to internal physical processes, development of circuit models, and understanding the uses and limitations of various models. The course uses incremental and large-signal techniques to analyze and design bipolar and field effect transistor circuits, with examples chosen from digital circuits, single-ended and differential linear amplifiers, and other integrated circuits.

This course focuses on the fundamentals of structure, energetics, and bonding that underpin materials science. It is the introductory lecture class for sophomore students in Materials Science and Engineering, taken with 3.014 and 3.016 to create a unified introduction to the subject. Topics include: an introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to atomistic and molecular models of materials; the role of electronic bonding in determining the energy, structure, and stability of materials; quantum mechanical descriptions of interacting electrons and atoms; materials phenomena, such as heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism; symmetry properties of molecules and solids; structure of complex, disordered, and amorphous materials; tensors and constraints on physical properties imposed by symmetry; and determination of structure through diffraction. Real-world applications include engineered alloys, electronic and magnetic materials, ionic and network solids, polymers, and biomaterials.

This course is a core subject in MIT's undergraduate Energy Studies Minor. This Institute-wide program complements the deep expertise obtained in any major with a broad understanding of the interlinked realms of science, technology, and social sciences as they relate to energy and associated environmental challenges.

Hands-on introduction to NMR presenting background in classical theory and instrumentation. Each lecture is followed by lab experiments to demonstrate ideas presented during the lecture and to familiarize students with state-of-the-art NMR instrumentation. Experiments cover topics ranging from spin dynamics to spectroscopy, and include imaging.

This practicum subject integrates theory and practice through the design, implementation, and evaluation of a comprehensive community information infrastructure that promotes democratic involvement and informs community development projects. Students work with Lawrence Community Works, Inc. to involve constituents and generate solutions to an important planning problem in the City of Lawrence, Massachusetts. Final project presentations take place in a public forum, and serve to inform future development of the information infrastructure. Subject begins with an overview of the digital divide, e-government, public participation GIS, and neighborhood information systems. Subject includes a reflection component and a deliberate investigation of race, class, and gender dynamics.

The Experimental Project Lab in the Department of Aeronautics and Astronautics is a two-semester course sequence: 16.621 Experimental Projects I and 16.622 Experimental Projects II (this course). Students in 16.622 gain practical insight and improved understanding of engineering experimentation through design and execution of "project" experiments. Building upon work in course 16.621, students construct and test equipment, make systematic experimental measurements of phenomena, analyze data, and compare theoretical predictions with results. Deliverables comprise a written final project report and formal oral presentations. Instructions on oral presentations and multi-section reporting are given. Experimental Projects I and II provide a valuable link between theory (16.621) and practice (16.622).

This class is an applications-oriented course covering the modeling of large-scale systems in decision-making domains and the optimization of such systems using state-of-the-art optimization tools. Application domains include: transportation and logistics planning, pattern classification and image processing, data mining, design of structures, scheduling in large systems, supply-chain management, financial engineering, and telecommunications systems planning. Modeling tools and techniques include linear, network, discrete and nonlinear optimization, heuristic methods, sensitivity and post-optimality analysis, decomposition methods for large-scale systems, and stochastic optimization.

This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5223 (System Optimisation: Models and Computation).

15.762J Supply Chain Planning focuses on effective supply chain strategies for companies that operate globally, with an emphasis on how to plan and integrate supply chain components into a coordinated system. Students are exposed to concepts and models important in supply chain planning with emphasis on key tradeoffs and phenomena. The course introduces and utilizes key tactics such as risk pooling and inventory placement, integrated planning and collaboration, and information sharing. Lectures, computer exercises, and case discussions introduce various models and methods for supply chain analysis and optimization.

This course is a survey of modern macroeconomics at a quite advanced level. Topics include the neoclassical growth model, overlapping generations, endogenous growth models, business cycles, incomplete nominal adjustment, incomplete financial markets, fiscal and monetary policy, consumption and savings, and unemployment. The course is also an introduction to the mathematical tools used in modern macroeconomics, including dynamic systems, optimal control, and dynamic programming.

This course gives a historical perspective on financial panics. Topics include the growth of the industrial world, the Great Depression and surrounding events, and more recent topics such as the first oil crisis, Japanese stagnation, and conditions following the financial crisis of 2008.