This course provides an overview of the distinctive features which distinguish sound categories of languages of the world. Theories which relate these categories to their acoustic and articulatory correlates, both universally and in particular languages, are covered. Models of word recognition by listeners, features, and phonological structure are also discussed. In addition, the course offers a variety of perspectives on these issues, drawn from Electrical Engineering, Linguistics and Cognitive Science.

This course examines theories and principles that underlie the concept of free speech in the United States, the historical context in which the values of free speech and toleration emerged, and the philosophical arguments that were and are made for and against them. Students analyze a variety of contexts and communicative practices, including new media technologies, to debate how “speech” can be described and when it should be appropriately regulated. The course also considers current disputes over free speech on college campuses.

This course explores the history of the ideal of personal freedom with an eye towards contemporary debates over the pros and cons of the regulatory state. The first part of the course surveys the sociological and theological sources of the concepts of freedom and civil society, and introduces liberty’s leading relatives or competitors: property, equality, community, and republicanism. The second part consists of a series of case studies in the rise of modern liberty and libertarianism: the abolition of slavery, the struggle for religious freedom, and the twentieth-century American civil liberties movement. In the last part of the course, we take up debates over the role of libertarianism vs. the regulatory state in a variety of contexts: counter-terrorism, health care, the financial markets, and the Internet.

This course is the first half of the year-long introductory graduate sequence 18.745/18.755 on Lie groups and Lie algebras. Topics include foundations of the theory of Lie groups and Lie algebras; theorems of Engel and Lie; the universal enveloping algebra, the Poincare-Birkhoff-Witt theorem; free Lie algebras; the Campbell-Hausdorff formula; classification and structure of finite dimensional complex simple Lie algebras; their finite dimensional representations; and the Weyl character formula.

This course is the second half of the year-long introductory graduate sequence Lie Groups and Lie Algebras I & Lie Groups and Lie Algebras II. Topics include classical groups, Haar measure on locally compact groups, the representation-theoretic understanding of the hydrogen atom, representations of compact (in particular, finite) groups, the Peter-Weyl theorem with proof, maximal tori, Cartan and Iwasawa decompositions, classification of real reductive Lie groups, topology of Lie groups, proof of the third fundamental theorem of Lie theory, Levi decomposition, Ado’s theorem, Borel subgroups, and flag manifolds.

This class explores the artistry of Lighting Design. Students gain an overall technical working knowledge of the tools of the trade, and learn how, and where to apply them to a final design. However essential technical expertise is, the class stresses the artistic, conceptual, collaborative side of the craft. The class format is a “hands on” approach, with a good portion of class time spent in a theatre.

This course offers a rigorous treatment of linear algebra, including vector spaces, systems of linear equations, bases, linear independence, matrices, determinants, eigenvalues, inner products, quadratic forms, and canonical forms of matrices. Compared with 18.06 Linear Algebra, more emphasis is placed on theory and proofs.

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. It parallels the combination of theory and applications in Professor Strang’s textbook Introduction to Linear Algebra.
Course Format
This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:

A complete set of Lecture Videos by Professor Gilbert Strang.
Summary Notes for all videos along with suggested readings in Prof. Strang’s textbook Linear Algebra.
Problem Solving Videos on every topic taught by an experienced MIT Recitation Instructor.
Problem Sets to do on your own with Solutions to check your answers against when you’re done.
A selection of Java® Demonstrations to illustrate key concepts.
A full set of Exams with Solutions, including review material to help you prepare.

This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing. The course starts with the standard linear algebra syllabus and eventually develops the techniques to approach a more advanced topic: abstract root systems in a Euclidean space.

This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. It also includes methods and tools for solving these PDEs, such as separation of variables, Fourier series and transforms, eigenvalue problems, and Green’s functions.

This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat / diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems. The Julia Language (a free, open-source environment) is introduced and used in homework for simple examples.

This course is about the study of speech sounds; how we produce and perceive them and their acoustic properties. Topics include the influence of the production and perception systems on phonological patterns and sound change, students learn acoustic analysis and experimental techniques. Students taking the graduate version complete different assignments.

This course studies the development of bilingualism in human history (from Australopithecus to present day). It focuses on linguistic aspects of bilingualism; models of bilingualism and language acquisition; competence versus performance; effects of bilingualism on other domains of human cognition; brain imaging studies; early versus late bilingualism; opportunities to observe and conduct original research; and implications for educational policies among others. The course is taught in English.

This course is a detailed examination of the grammar of Japanese and its structure which is significantly different from English, with special emphasis on problems of interest in the study of linguistic universals. Data from a broad group of languages is studied for comparison with Japanese. This course assumes familiarity with linguistic theory.

Linguists take it for granted that all languages, including languages in the Global South, are worthy of study. Yet some 40% of children in the world are prevented from studying in and valorizing their home languages—including some of the very languages that linguists study with such fondness. So much research in linguistics and the benefits thereof remain inaccessible to the bulk of the very speech communities whose languages linguists study. This seminar examines efforts by linguists and educators to make their research more inclusive, accessible, and hospitable, and to reduce linguistic-discrimination practices in various communities world-wide.

This seminar explored the idea that the study of linguistics can be a means to develop young people’s understanding of scientific inquiry as well as their understanding of the nature of language. The challenge of this seminar was to create pedagogical materials and methods that will motivate learners of all ages to be inquisitive about their native language and about language in general. Seminar participants worked with one another and in partnership with K–12 teachers to accomplish this goal.

This course is designed for high-intermediate ESL students who need to develop better listening comprehension and oral skills, which will primarily be achieved by detailed instructions on pronunciation. Our focus will be on (1) producing accurate and intelligible English, (2) becoming more comfortable listening to rapidly spoken English, and (3) learning common expressions, gambits, and idioms used in both formal and informal contexts.

The 15.821 and 15.822 Sequence
Marketing research may be divided into methods that emphasize understanding “the customer” and methods that emphasize understanding “the market.” This course (15.821) deals with the customer and emphasizes qualitative methods (interviews, focus groups, Voice of the Customer, composing questions for a survey). The companion course (15.822) deals with the market and emphasizes quantitative methods (sampling, survey execution, quantitative data interpretation, conjoint analysis, factor analysis).
The methods covered in 15.821 are often used in the “front-end” of market research project, whose second-stage is a quantitative survey. The quality of information gathered in the second-stage is greatly enhanced in this way.
15.821 is designed for the nonspecialist, e.g., someone planning a career in general management, product or project management, R&D, advertising, or entrepreneurship. 15.822 teaches analytical techniques that are standard in consulting or marketing research, and is ideally suited for students planning careers in those fields.

In this seminar we’ll read individual poems closely within a set of questions about the moral and political position of poetry – and of intellectuals – in different cultural contexts. Of course, part of the divergence in the social positions of poetry [and of ’the aesthetic’] depends on the dominant paradigm of the social, political and literary culture; part of the divergence derives from the momentum of literary development in the culture [how did the culture experience modernism?, for instance], and part depends on the different attitudes toward traditional form. We read poets from North America (Whitman, Williams, Lowell, Plath, Bishop), from South America (Neruda), from Western Europe (Yeats), and Eastern Europe (Akhmatova, Szymborska); we conclude with a month dedicated to the work of the Polish poet Czeslaw Milosz, who won the Nobel Prize for literature (the first to win from a position of exile) in 1980.