Focus on theoretical work for studying operations planning and control problems. Topics vary from year to year, and include inventory theory, sequencing theory, aggregate production planning, production scheduling, multistage production/distribution systems, performance evaluation, and flexible manufacturing systems.

6.895 covers theoretical foundations of general-purpose parallel computing systems, from languages to architecture. The focus is on the algorithmic underpinnings of parallel systems. The topics for the class will vary depending on student interest, but will likely include multithreading, synchronization, race detection, load balancing, memory consistency, routing networks, message-routing algorithms, and VLSI layout theory. The class will emphasize randomized algorithms and probabilistic analysis, including high-probability arguments.

This course covers topics such as sums of independent random variables, central limit phenomena, infinitely divisible laws, Levy processes, Brownian motion, conditioning, and martingales.

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 is the second term of a theoretical treatment of the physics of solids. Topics covered include linear response theory; the physics of disorder; superconductivity; the local moment and itinerant magnetism; the Kondo problem and Fermi liquid theory.

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)

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.

Students writing a thesis in Political Science develop their research topics, review relevant research and scholarship, frame their research questions and arguments, choose an appropriate methodology for analysis, and draft the introductory and methodology sections of their theses. Includes substantial instruction and practice in writing with revision and oral presentations.

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 provides a survey of the theory and application of time series methods in econometrics. Topics covered will include univariate stationary and non-stationary models, vector autoregressions, frequency domain methods, models for estimation and inference in persistent time series, and structural breaks.

We will cover different methods of estimation and inferences of modern dynamic stochastic general equilibrium models (DSGE): simulated method of moments, Maximum likelihood and Bayesian approach. The empirical applications in the course will be drawn primarily from macroeconomics.

The course provides a survey of the theory and application of time series methods in econometrics.

The course provides a survey of the theory and application of time series methods in econometrics.

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

This course provides an introduction to algebraic number theory. Topics covered include dedekind domains, unique factorization of prime ideals, number fields, splitting of primes, class group, lattice methods, finiteness of the class number, Dirichlet's units theorem, local fields, ramification, discriminants.