First term of a theoretical treatment of the physics of solids. Concept of elementary excitations. Symmetry: translational, rotational, and time-reversal invariances: theory of representations. Energy bands: APW, OPW, pseudopotential and LCAO schemes. Survey of electronic structure of metals, semimetals, semiconductors, and insulators. Excitons. Critical points. Response functions. Interactions in the electron gas.

This course is taught in four main parts. The first is a review of fundamental thermodynamic concepts (e.g. energy exchange in propulsion and power processes), and is followed by the second law (e.g. reversibility and irreversibility, lost work). Next are applications of thermodynamics to engineering systems (e.g. propulsion and power cycles, thermo chemistry), and the course concludes with fundamentals of heat transfer (e.g. heat exchange in aerospace devices)

Advanced topics emphasizing thermo-fluid dynamic phenomena and analysis methods. Single-heated channel-transient analysis. Multiple-heated channels connected at plena. Loop analysis including single and two-phase natural circulation. Kinematics and dynamics of two-phase flows with energy addition. Boiling, instabilities, and critical conditions. Subchannel analysis.

Advanced topics emphasizing thermo-fluid dynamic phenomena and analysis methods. Single-heated channel-transient analysis. Multiple-heated channels connected at plena. Loop analysis including single and two-phase natural circulation. Kinematics and dynamics of two-phase flows with energy addition. Boiling, instabilities, and critical conditions. Subchannel analysis.

This subject deals primarily with equilibrium properties of macroscopic systems, basic thermodynamics, chemical equilibrium of reactions in gas and solution phase, and rates of chemical reactions.

Laws of thermodynamics applied to materials and materials processes. Solution theory. Equilibrium diagrams. Overview of fluid transport processes. Kinetics of processes that occur in materials, including diffusion, phase transformations, and the development of microstructure.

Principles of thermodynamics are used to infer the physical conditions of formation and modification of igneous and metamorphic rocks. Includes phase equilibria of homogeneous and heterogeneous systems and thermodynamic modeling of non-ideal crystalline solutions. Surveys the processes that lead to the formation of metamorphic and igneous rocks in the major tectonic environments in the Earth's crust and mantle.

This subject deals primarily with equilibrium properties of macroscopic and microscopic systems, basic thermodynamics, chemical equilibrium of reactions in gas and solution phase, and macromolecular interactions.

Treatment of the laws of thermodynamics and their applications to equilibrium and the properties of materials. Provides a foundation to treat general phenomena in materials science and engineering, including chemical reactions, magnetism, polarizability, and elasticity. Develops relations pertaining to multiphase equilibria as determined by a treatment of solution thermodynamics. Develops graphical constructions that are essential for the interpretation of phase diagrams. Treatment includes electrochemical equilibria and surface thermodynamics. Introduces aspects of statistical thermodynamics as they relate to macroscopic equilibrium phenomena.

"This class will be constructed as a lecture-discussion, the purpose being to engage important theoretical issues while simultaneously studying their continuing historical significance. To enhance discussion, three debates will be held in class. Each student will be required to participate in one of these debates. Each student will also be required to write three short papers. Class participation is essential and will be factored into the final grade.The course will portray the history of theory neither as the history of architectural theory exclusively, nor as a series of prepackaged static pronouncements, but as part of a broader set of issues with an active history that must be continually probed and queried. The sequence of topics will not be absolutely predetermined, but some of the primary issues that will be addressed are: pedagogy, professionalism, nature, modernity and the Enlightenment. Classroom discussions and debates are intended to demonstrate differences of opinion and enhance awareness of the consequences that these differences had in specific historical contexts."

The course consists of a sampling of topics from algebraic combinatorics. The topics include the matrix-tree theorem and other applications of linear algebra, applications of commutative and exterior algebra to counting faces of simplicial complexes, and applications of algebra to tilings.

The main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible.

Topics vary from year to year. Fall Term: Numerical properties and vanish theorems for ample, nef, and big line bundles and vector bundles; multiplier ideals and their applications

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.

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 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."

" 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."

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.

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.