Content varies from year to year. Introduces new and significant developments in algebraic topology with the focus on homotopy theory and related areas. Spring 2003: An introduction to higher algebraic K-theory.

Survey and special topics designed for graduate students in the brain and cognitive sciences. Emphasizes ethological studies of natural behavior patterns and their analysis in laboratory work, with contributions from field biology (mammology, primatology), sociobiology, and comparative psychology. Stresses human behavior but also includes major contributions from studies of other vertebrates and of invertebrates.

In this graduate-level course, we will be covering advanced topics in combinatorial optimization. We will start with non-bipartite matchings and cover many results extending the fundamental results of matchings, flows and matroids. The emphasis is on the derivation of purely combinatorial results, including min-max relations, and not so much on the corresponding algorithmic questions of how to find such objects. The intended audience consists of Ph.D. students interested in optimization, combinatorics, or combinatorial algorithms.

This is a seminar based on research literature. Papers covered are selected to illustrate important problems and approaches in the field of computational and systems biology, and provide students a framework from which to evaluate new developments. The MIT Initiative in Computational and Systems Biology (CSBi) is a campus-wide research and education program that links biology, engineering, and computer science in a multidisciplinary approach to the systematic analysis and modeling of complex biological phenomena. This course is one of a series of core subjects offered through the CSB Ph.D. program, for students with an interest in interdisciplinary training and research in the area of computational and systems biology.

The concept of globalization fosters the understanding of the interconnectedness of cultures and societies geographically wide apart; America, Europe, Asia, and Africa. Subject scans existing debates over globalization in four continents. Explores how globalization impacts everyday life in the First and Third World; how globalization leads to a common cosmopolitan culture; the emergence of a global youth culture; and religious, social, and political movements that challenge globalization. Materials examined include pop music, advertisements, film posters, and political cartoons. Topic for Spring 2003: Popular Culture in Japan. Taught in English.

Students carry out independent experimental study under the direction of a member of the Biology Department faculty. Subject allows students with a strong interest in independent research to fulfill the project laboratory requirement for the Biology Department Program in the context of a research laboratory at MIT. Written and oral presentation of the research results is required. The permission of the faculty supervisor and the Biology Undergraduate Office must be obtained in advance. Instruction and practice in written and oral communication provided.

This course is an advanced topics course on market and mechanism design. We will study existing or new market institutions, understand their properties, and think about whether they can be re-engineered or improved. Topics discussed include mechanism design, auction theory, one-sided matching in house allocation, two-sided matching, stochastic matching mechanisms, student assignment, and school choice.

This is an introductory (i.e. first year graduate students are welcome and expected) course in generalized geometry, with a special emphasis on Dirac geometry, as developed by Courant, Weinstein, and Severa, as well as generalized complex geometry, as introduced by Hitchin. Dirac geometry is based on the idea of unifying the geometry of a Poisson structure with that of a closed 2-form, whereas generalized complex geometry unifies complex and symplectic geometry. For this reason, the latter is intimately related to the ideas of mirror symmetry.

This course will focus on various aspects of mirror symmetry. It is aimed at students who already have some basic knowledge in symplectic and complex geometry (18.966, or equivalent). The geometric concepts needed to formulate various mathematical versions of mirror symmetry will be introduced along the way, in variable levels of detail and rigor.

Subject aims to provide an overview of Indian popular culture over the last two decades, through a variety of material such as popular fiction, music, television and Bombay cinema. Explores major themes and their representations in relation to current social and political issues. In particular, examines the elements of the formulaic "masala movie", music and melodrama, the ideas of nostalgia and incumbent change in youth culture, as well as shifting questions of gender and sexuality in popular fiction. Students review journalistic writing, advertising clips, and political cartoons to understand the relation between the popular culture and the social imagery of a nation. Taught in English.

This course will give a detailed introduction to the theory of tensor categories and review some of its connections to other subjects (with a focus on representation-theoretic applications). In particular, we will discuss categorifications of such notions from ring theory as: module, morphism of modules, Morita equivalence of rings, commutative ring, the center of a ring, the centralizer of a subring, the double centralizer property, graded ring, etc.

The goal of this course is to prepare you to engage in experimental investigations of questions related to linguistic theory, focusing on phonetics and phonology.

This course is the first subject in the Environmental Policy and Planning sequence. It reviews philosophical debates including growth vs. deep ecology, command-and-control" vs. market-oriented approaches to regulation, and the importance of expertise vs. indigenous knowledge. Its emphasis is placed on environmental planning techniques and strategies. Related topics include the management of sustainability, the politics of ecosystem management, environmental governance and the changing role of civil society, ecological economics, integrated assessment (combining environmental impact assessment (EIA) and risk assessment), joint fact finding in science-intensive policy disputes, environmental justice in poor communities of color, and environmental dispute resolution."

I realize that "Modes of Assertion" is a rather cryptic title for the course. What we will explore are ways of modulating the force of an assertion. This will engage us in formal semantics and pragmatics, the theory of speech acts and performative utterances, and quite a bit of empirical work on a not-too-well understood complex of data. It is obvious that he made a big mistake. If you're like me you didn't feel much of a difference. But now see what happens when you embed the two sentences: We have to fire him, because he obviously made a big mistake. We have to fire him, because it is obvious that he made a big mistake. One of the two examples is unremarkable, the other suggests that the reason he needs to be fired is not that he made a big mistake but the fact that it is obvious that he did. We will try to understand what is going on here and look at related constructions not just in English but also German (with its famous discourse particles like ja ) and Quechua and Tibetan (with their systems of evidentiality-marking, as recently studied in dissertations from Stanford and UCLA).

This multidisciplinary lecture / workshop engages students in a variety of approaches to the study and practice of performance as an area of aesthetic and social interaction. Special attention is paid to the use of diverse media in performance. Interdisciplinary approaches to study encourage students to seek out material histories of performance and practice.

This course focuses on financing tools and program models to support local economic development. It includes an overview of private capital markets and financing sources to understand capital market imperfections that constrain economic development; business accounting; financial statement analysis; federal economic development programs; and public finance tools. Program models covered include revolving loan funds, guarantee programs, venture capital funds, bank holding companies, community development loan funds and credit unions, micro enterprise funds, and the use of the Community Reinvestment Act to leverage bank financing.

Geometry of pseudoconvex domains, the Monge-Ampere equation, Hodge theory on Kaehler manifolds, the theory of toric varieties and (time permitting) some applications to combinatorics.

The Empire Strikes back refers to the theoretical framework introduced to study texts and their recurrent themes. Theory explores the ways in which post-colonial texts have a problematic relationship with the colonizer's language. Explores strategies used to subvert and appropriate the pre-existing discourse of the Empire in order to give rise to a new form. Introduction to post-colonial literature from South Asia, as well as from the South Asian diaspora. Through study of novels by Rushdie, Ghosh, Seth, Roy, Desai, Ontaatdje, Suleri, Sidhwa, and Lahiri, students explore the phenomenon of the post-colonial writer's encounter with modernity. Examines how authors articulate recurrent themes of the post-colonial condition: migration and history, memory and desire, and rootlessness and hybridity. Taught in English. This subject aims to provide an overview of contemporary texts in regional languages in South Asian Literature and Cinema. We will cover major authors and film makers, writing from Bangladesh, India, Nepal, Pakistan and Sri Lanka. Within India, we will look at authors and directors working in different regional languages and as we examine their different socio-cultural, political and historical contexts we will attempt to understand what it means to study them under the all-unifying category of "South Asian Literature and Culture". Some of the major issues we shall explore include caste, gender, globalization and social change. We will end with exploring some of the newer, younger writers and directors and try to analyze some of the thematic and formal shifts in their work. Authors include Ashapurna Devi, Manto, Vijayan, Premchand, Mohanty, and Nasreen and film makers will include Adoor Gopalakrishnan, Satyajit Ray, Shyam Benegal, Aparna Sen and Rituporno Ghosh.

This graduate-level course focuses on one-dimensional nonparametric statistics developed mainly from around 1945 and deals with order statistics and ranks, allowing very general distributions. For multidimensional nonparametric statistics, an early approach was to choose a fixed coordinate system and work with order statistics and ranks in each coordinate. A more modern method, to be followed in this course, is to look for rotationally or affine invariant procedures. These can be based on empirical processes as in computer learning theory. Robustness, which developed mainly from around 1964, provides methods that are resistant to errors or outliers in the data, which can be arbitrarily large. Nonparametric methods tend to be robust.