The MIT Course Catalog for the current year can be viewed online at http://web.mit.edu/catalog/. In addition to a description of courses for each academic year and program requirements, the catalogues may include: Early Catalogues
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3-0-9 units. Introduces topology, covering topics fundamental to modern analysis and geometry. Topological spaces and continuous functions, connectedness, compactness, separation axioms, covering spaces, and the fundamental group. Students in Course 18 must register for the undergraduate version, 18.901.
Humanities and Engineering (Course 21E) Humanities and Science (Course 21S) Linguistics and Philosophy (Course 24-2) Literature (Course 21L) Mathematical Economics (Course 14-2) Music (Course 21M-1) Philosophy (Course 24-1) Political Science (Course 17) Science, Technology, and Society/Second Major (STS)
Black Matters: Introduction to Black Studies. Editor's Pick. Ethics for Engineers: Artificial Intelligence. String Theory for Undergraduates. Educator. Principles of Chemical Science. New. Language Variation and Change. OCW makes the materials used in the teaching of MIT's subjects available on the Web.
The MIT Course Catalogue, also referred to as the MIT Bulletin and the MIT Course Catalog, is a rich source of information on the courses and programs that have made the Massachusetts Institute of Technology the major institution it is today.
The MIT Course Catalogue, also referred to as the MIT Bulletin and the MIT Course Catalog, is a rich source of information on the courses and programs that have made the Massachusetts Institute of Technology the major institution it is today.
Topics include point-counting, isogenies, pairings, and the theory of complex multiplication, with applications to integer factorization, primality proving, and elliptic curve cryptography. Includes a brief introduction to modular curves and the proof of Fermat's Last Theorem.
Prerequisites: one year of high-school calculus or the equivalent, with a score of 5 on the AB Calculus test (or the AB portion of the BC test, or an equivalent score on a standard international exam), or equivalent college transfer credit, or a passing grade on the first half of the 18.01 advanced standing exam.
Basic techniques for the efficient numerical solution of problems in science and engineering. Root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods in linear algebra. Knowledge of programming in a language such as MATLAB, Python, or Julia is helpful. In person not required.
Topics may include Wedderburn theory and structure of Artinian rings, Morita equivalence and elements of category theory, localization and Goldie's theorem, central simple algebras and the Brauer group, representations, polynomial identity rings, invariant theory growth of algebras, Gelfand-Kirillov dimension.
Differential forms, introduction to Lie groups, the DeRham theorem, Riemannian manifolds , curvature, the Hodge theory. 18.966 is a continuation of 18.965 and focuses more deeply on various aspects of the geometry of manifolds. Contents vary from year to year, and can range from Riemannian geometry (curvature, holonomy) to symplectic geometry, complex geometry and Hodge-Kahler theory, or smooth manifold topology. Prior exposure to calculus on manifolds, as in 18.952, recommended. In person not required.
Continuation of 18.965, focusing more deeply on various aspects of the geometry of manifolds. Contents vary from year to year, and can range from Riemannian geometry (curvature, holonomy) to symplectic geometry, complex geometry and Hodge-Kahler theory, or smooth manifold topology.
Introductory Latin subject for students with some prior knowledge of basic grammar and vocabulary. Intended to refresh and enrich ability to read ancient and/or medieval literary and historical texts. May be taken independently of Latin I with permission of instructor. Latin I and Latin II may be combined by petition (after completion of both) to count as a single HASS-H. Limited to 20.
In the first half of the term, students use short prose texts to study the basics of Old English grammar. They go on to read short poems, and conclude by tackling portions of the epic Beowulf in the last third of the term. Assessment based upon translation work, daily vocabulary quizzes, and three exams.
Students use data collected in 12.511 to develop written and oral reports of the results , with each student focusing on a different area. For example, students can develop the geophysical modeling or synthesis of the results into other studies in the area. The final written and oral reports are combined into a comprehensive report and presentation of the field camp and its results. Students taking graduate version complete additional assignments.
Introduces the basic tools needed for data analysis and interpretation in the Geosciences, as well as other sciences. Composed of four modules, targeted at introducing students to the basic concepts and applications in each module. MatLab: Principles and practice in its uses, script and function modules, basic approaches to solving problems. Statistics: Correlation, means, dispersion, precision, accuracy, distributions, central limit theorem, skewness, probability, Chi-Square, Gaussian and other common distributions used in hypothesis testing. Regression: Random and grid search methods, basic least squares and algorithms applicable to regression, inversion and parameter estimation. Signal Processing: Analog and digital signals, Z-transform, Fourier series, fast Fourier transforms, spectral analysis leakage and bias, digital filtering. Students taking the graduate version complete different assignments.
Topics include the origin of the solar system and the early Earth atmosphere; the origin and evolution of life and its influence on climate up through and including the modern age and the problem of global warming; the global carbon cycle; and astrobiology. T. Bosak, G. Fournier.
Overview of basic topics in solid-earth geophysics, such as the Earth's rotation, gravity and magnetic field, seismology, and thermal structure. Formulation of physical principles presented in three one-hour lectures per week. Current applications discussed in an additional one-hour tutorial each week. Students taking graduate version complete different assignments.
Introduction to the physics of remote sensing with applications to the study of the Earth, Moon, planets and other solar system bodies, as well as to emerging fields, such as autonomous navigation. Includes the principles of optical, thermal, radar and lidar remote sensing. Covers fundamental properties of electromagnetic waves; principles of electromagnetic scattering from real and idealized materials, including various types of surfaces and vegetation; interaction of electromagnetic radiation with the atmosphere; and thermal and microwave emission from various media. Discusses past, present, and future remote sensing platforms along with the fundamentals of orbital mechanics and data processing tools and methods. Assignments require students to write simple computer programs and plot mathematical functions. Students taking graduate version complete different assignments.
Presenting scientific research geared toward a scientific audience. Each student gives one 30-minute talk, one AGU-style 15-minute talk, and one poster presentation. Students present their ongoing research and use the class as a forum to practice for upcoming talks in more formal settings. Abstracts are prepared for each presentation and discussed in class. Students provide comments, questions, encouragement, critiques, etc. on their peers' presentations.
Numerical modeling in oceanography and environmental fluid mechanics. Focuses on the building of computational models that describe processes such as transport (advection, diffusion), reaction (ecosystems), and boundary forcing, of relevance in the ocean. Models are developed in a hierarchical manner, starting from the simple (zero-dimensional in space), and incrementally advancing toward more complex, time-evolving systems in one-, two- (shallow water) and three-dimensions (Primitive equations). Students build their own models using the finite volume approach with an appreciation and understanding of the working of general circulation models
The Music subjects described below are grouped within seven areas: Introductory, Samplings, History/Culture, Composition/Theory, Performance, Advanced/Special Subjects, and Music and Media. Although most students start with introductory subjects, those who have vocal or instrumental training or extensive exposure to music are encouraged to begin at a higher starting level.
Multidisciplinary, term-long, independent study geared toward the development of significant artistic and technical projects in performance and design . Students pursue projects in an array of fields and are invited to propose artistic and research projects as actors, directors, designers, dramaturges, and/or technical designers. Often in conjunction with Theater Arts-produced productions, proposals for intensives must be vetted and supervised by a member of the Theater Arts faculty with whom the student will work over the course of term.
Explores the relationship between music and the supernatural, focusing on the social history and context of supernatural beliefs as reflected in key literary and musical works from 1600 to the present. Provides an understanding of the place of ambiguity and the role of interpretation in culture, science and art.
HASS-A. Covers major approaches to computational music theory and musicology in the symbolic (score-based) domain. Covers corpus studies, algorithms for music theory, musical search and similarity, encoding, feature extraction and machine learning, music generation, and computational music perception.
Interdisciplinary studio merges the disciplines of the performer, designer, cinematographer, director, playwright and technician, and examines the deep integration of live theatrical and cinematic idioms. Studio exercises, readings, field trips and in-class presentations provide the opportunity to study the history and theory surrounding the development of genre, and to engage the practice from both sides of the camera. Includes guest artists, lectures, and master classes. Students regularly test what they develop in studio on the stage. Each class focuses on a particular dramatist, theme, or artistic genre and culminates in a full-length collaboration that will be presented in the final week of class for an invited audience. Students taking graduate version complete additional assignments. Enrollment Limited.
Provides directed practice in the disciplines of performance practice, including design, acting, directing, technical theater, management, dramaturgy and other creative fields. Students test and refine their skills by participating in the creation of produced plays, intensive workshops, installations and other design or performance projects in dance, film, music theater, opera, and other performing arts events. Students work closely with faculty, peers and guest artists. Students seeking to design individual performance and design workshops must be supervised by a theater arts faculty member, and obtain his or her written approval.