Our goal with this textbook is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.
The textbook contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds.

This course is an introduction to linear optimization and its extensions emphasizing the underlying mathematical structures, geometrical ideas, algorithms and solutions of practical problems. The topics covered include: formulations, the geometry of linear optimization, duality theory, the simplex method, sensitivity analysis, robust optimization, large scale optimization network flows, solving problems with an exponential number of constraints and the ellipsoid method, interior point methods, semidefinite optimization, solving real world problems problems with computer software, discrete optimization formulations and algorithms.

This course provides a critical analysis of mass media in our culture. Various types of media such as books, films, video games, and online interactions will be discussed and reviewed. This course will also evaluate how information and ideas travel between people on a large scale.

This subject provides an introduction to modeling and simulation, covering continuum methods, atomistic and molecular simulation, and quantum mechanics. Hands-on training is provided in the fundamentals and applications of these methods to key engineering problems. The lectures provide exposure to areas of application based on the scientific exploitation of the power of computation. We use web based applets for simulations, thus extensive programming skills are not required.

Through a progressive series of composition projects, students investigate the sonic organization of musical works and performances, focusing on fundamental questions of unity and variety. Aesthetic issues are considered in the pragmatic context of the instructions that composers provide to achieve a desired musical result, whether these instructions are notated in prose, as graphic images, or in symbolic notation. No formal training is required. Weekly listening, reading, and composition assignments draw on a broad range of musical styles and intellectual traditions, from various cultures and historical periods.

Traditionally, progress in electronics has been driven by miniaturization. But as electronic devices approach the molecular scale, classical models for device behavior must be abandoned. To prepare for the next generation of electronic devices, this class teaches the theory of current, voltage and resistance from atoms up. To describe electrons at the nanoscale, we will begin with an introduction to the principles of quantum mechanics, including quantization, the wave-particle duality, wavefunctions and Schrĺ_dinger's equation. Then we will consider the electronic properties of molecules, carbon nanotubes and crystals, including energy band formation and the origin of metals, insulators and semiconductors. Electron conduction will be taught beginning with ballistic transport and concluding with a derivation of Ohm's law. We will then compare ballistic to bulk MOSFETs. The class will conclude with a discussion of possible fundamental limits to computation.

Organization of synaptic connectivity as the basis of neural computation and learning. Single and multilayer perceptrons. Dynamical theories of recurrent networks: amplifiers, attractors, and hybrid computation. Backpropagation and Hebbian learning. Models of perception, motor control, memory, and neural development. Alternate years.

This class will provide an introductory-level introduction to mammalian neuroanatomy. You will be taught through lectures (the introductory lecture focusing on structure, and the concluding lecture focusing on function), and through hands-on lab experience.

This course is an introduction to the mammalian nervous system, with emphasis on the structure and function of the human brain. Topics include the function of nerve cells, sensory systems, control of movement, learning and memory, and diseases of the brain.

This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods in linear algebra.

This course is offered to undergraduates and introduces students to the formulation, methodology, and techniques for numerical solution of engineering problems. Topics covered include: fundamental principles of digital computing and the implications for algorithm accuracy and stability, error propagation and stability, the solution of systems of linear equations, including direct and iterative techniques, roots of equations and systems of equations, numerical interpolation, differentiation and integration, fundamentals of finite-difference solutions to ordinary differential equations, and error and convergence analysis. The subject is taught the first half of the term. This class was originally listed in Course 13 (Ocean Engineering) as 13.002J.

An introduction to the results and techniques of observations of the ocean in the context of its physical properties and dynamical constraints. Emphasis on large-scale steady circulation and the time-dependent processes that contribute to it. Includes the physical setting of the ocean, atmospheric forcing, application of conservation laws, description of wind-driven and thermohaline circulation, eddy processes, and interpretive techniques.

This course is an introduction to the fundamental aspects of science and engineering necessary for exploring, observing, and utilizing the oceans. Hands-on projects focus on instrumentation in the marine environment and the design of ocean observatories for ocean monitoring and exploration. Topics include acoustics, sound speed and refraction, sounds generated by ships and marine animals, sonar systems and their principles of operation, hydrostatic behavior of floating and submerged bodies geared towards ocean vehicle design, stability of ocean vessels, and the application of instrumentation and electronics in the marine environment. Students work with sensor systems and deploy them in the field to gather and analyze real world data.

Introduction to Oceanography is a textbook appropriate to an introductory-level university course in oceanography. The book covers the fundamental geological, chemical, physical and biological processes in the ocean, with an emphasis on the North Atlantic region.

Planet Earth’s ocean covers over seventy percent of its surface, yet oceanographic research has only recently come to its full potential with the advent of new technologies. This course in Introductory Oceanography emphasizes the need to understand geologic, chemical, physical, and biologic processes or features that occur in ocean environments. It is designed to be thorough enough to prepare you for more advance work, while presenting the concepts to non-majors in a way that is meaningful and not overwhelming.Login: guest_oclPassword: ocl

This course provides students with concepts, techniques and tools to design, analyze, and improve core operational capabilities, and apply them to a broad range of application domains and industries. It emphasizes the effect of uncertainty in decision-making, as well as the interplay between high-level financial objectives and operational capabilities. Topics covered include production control, risk pooling, quality management, process design, and revenue management. Also included are case studies, guest lectures, and simulation games which demonstrate central concepts.

This course, which spans a third of a semester, provides students with experienceĺĘusing techniques employed in synthetic organic chemistry. It alsoĺĘintroduces them to the exciting research area of catalytic chiral catalysis. This class is part of the new laboratory curriculum in the MIT Department of Chemistry. Undergraduate Research-Inspired Experimental Chemistry Alternatives (URIECA) introduces students to cutting edge research topics in a modular format.

This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications.

Permaculture Design is a method of land planning that can be applied at scales from the home garden to city block to village to farm. It is an ethically based whole-systems design approach that uses concepts, principles, and methods derived from ecosystems, indigenous technologies, and other time-tested practices to create sustainable human settlements and institutions. Although rooted in horticulture and agriculture, Permaculture design is interdisciplinary, touching on a wide range of subjects including regional planning, ecology, animal husbandry, appropriate technology, architecture, social justice, and international development.

This open text book is derived from the content of the Massive Open Online Course “Intro to Permaculture”. The original course also included interactive mapping and design tools that accompanied this content. The course and book provide a general overview of the Permaculture design system. The book can be downloaded as a print version. However, there are many accompanying videos and content pages that are linked to throughout the text, so it is best viewed online where the links can be accessed.

We often make judgments about good and bad, right and wrong. Philosophical ethics is the critical examination of these and other concepts central to how we evaluate our own and each others’ behavior and choices.

This text examines some of the main threads of discussion on these topics that have developed over the last couple of millenia, mostly within the Western cultural tradition. It considers basic questions about moral and ethical judgment: Is there such a thing as something that is really right or really wrong independent of time, place and perspective? What is the relationship between religion and ethics? How can we reconcile self-interest and ethics? Is it ever acceptable to harm one person in order to help others? What do recent discussions in evolutionary biology or have to say about human moral systems? What is the relation between gender and ethics? The authors invite you to participate in their exploration of these and many other questions in philosophical ethics.

If you are adopting or adapting this book for a course, please let us know on our adoption form for the Introduction to Philosophy open textbook series: https://docs.google.com/forms/d/e/1FAIpQLSdwf2E7bRGvWefjhNZ07kgpgnNFxVxxp-iidPE5gfDBQNGBGg/viewform?usp=sf_link.