A two-semester course on statistical mechanics. Basic principles are examined in 8.333: the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Postulates of classical statistical mechanics, microcanonical, canonical, and grand canonical distributions; applications to lattice vibrations, ideal gas, photon gas. Quantum statistical mechanics; Fermi and Bose systems. Interacting systems: cluster expansions, van der Waal's gas, and mean-field theory. Topics from modern statistical mechanics are explored in 8.334: the hydrodynamic limit and classical field theories. Phase transitions and broken symmetries: universality, correlation functions, and scaling theory. The renormalization approach to collective phenomena. Dynamic critical behavior. Random systems.

Statistical Mechanics is a probabilistic approach to equilibrium properties of large numbers of degrees of freedom. In this two-semester course, basic principles are examined. Topics include: thermodynamics, probability theory, kinetic theory, classical statistical mechanics, interacting systems, quantum statistical mechanics, and identical particles.

Statistical Physics in Biology is a survey of problems at the interface of statistical physics and modern biology. Topics include: bioinformatic methods for extracting information content of DNA; gene finding, sequence comparison, and phylogenetic trees; physical interactions responsible for structure of biopolymers; DNA double helix, secondary structure of RNA, and elements of protein folding; considerations of force, motion, and packaging; protein motors, membranes. We also look at collective behavior of biological elements, cellular networks, neural networks, and evolution.

This course provides an introduction to the physical chemistry of biological systems. Topics include: connection of macroscopic thermodynamic properties to microscopic molecular properties using statistical mechanics, chemical potentials, equilibrium states, binding cooperativity, behavior of macromolecules in solution and at interfaces, and solvation. Example problems include protein structure, genomic analysis, single molecule biomechanics, and biomaterials.

This course explores the theory of self-assembly in surfactant-water (micellar) and surfactant-water-oil (micro-emulsion) systems. It also introduces the theory of polymer solutions, as well as scattering techniques, light, x-ray, and neutron scattering applied to studies of the structure and dynamics of complex liquids, and modern theory of the liquid state relevant to structured (supramolecular) liquids.

This course is a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, correlation, decision theory, and Bayesian statistics.

Fundamentals of detection and estimation for signal processing, communications, and control. Vector spaces of random variables. Bayesian and Neyman-Pearson hypothesis testing. Bayesian and nonrandom parameter estimation. Minimum-variance unbiased estimators and the Cramer-Rao bounds. Representations for stochastic processes; shaping and whitening filters; Karhunen-Loeve expansions. Detection and estimation from waveform observations. Advanced topics: linear prediction and spectral estimation; Wiener and Kalman filters.

12.103 explores the role of scientific knowledge, discovery, method, and argument in environmental policymaking from both idealistic and realistic perspectives. The course will use case studies of science-intensive environmental controversies to study how science was used and abused in the policymaking process. Case studies include: global warming, biodiversity loss, and nuclear waste disposal siting. Subject includes intensive practice in the writing and presentation of "position statements" on environmental science issues.

" This is a one-semester class about gauge/gravity duality (often called AdS/CFT) and its applications."

Introduction to the main concepts of string theory to undergraduates. Since string theory is quantum mechanics of a relativistic string, the foundations of the subject can be explained to students exposed to both special relativity (8.033) and basic quantum mechanics (8.05). Subject develops the aspects of string theory and makes it accessible to students familiar with basic electromagnetism (8.02) and statistical mechanics (8.044). This includes the study of D-branes and string thermodynamics. This course introduces string theory to undergraduate and is based upon Prof. Zwiebach's textbook entitled A First Course in String Theory. Since string theory is quantum mechanics of a relativistic string, the foundations of the subject can be explained to students exposed to both special relativity and basic quantum mechanics. This course develops the aspects of string theory and makes it accessible to students familiar with basic electromagnetism and statistical mechanics.

The strong force which bind quarks together is described by a relativistic quantum field theory called quantum chromodynamics (QCD). Subject surveys: The QCD Langrangian, asymptotic freedom and deep inelastic scattering, jets, the QCD vacuum, instantons and the U(1) problem, lattice guage theory, and other phases of QCD.

The strong force which bind quarks together is described by a relativistic quantum field theory called quantum chromodynamics (QCD). Subject surveys: The QCD Langrangian, asymptotic freedom and deep inelastic scattering, jets, the QCD vacuum, instantons and the U(1) problem, lattice guage theory, and other phases of QCD. Strong Interactions is a course in the construction and application of effective field theories, which are a modern tool of choice in making predictions based on the Standard Model. Concepts such as matching, renormalization, the operator product expansion, power counting, and running with the renormalization group will be discussed. Topics will be taken from heavy quark decays and CP violation, factorization in hard processes (deep inelastic scattering and exclusive processes), non-relativistic bound states in field theory (QED and QCD), chiral perturbation theory, few-nucleon systems, and possibly other Standard Model subjects.

Study of condensed matter systems where interactions between electrons play an important role. Topics vary depending on lecturer but may include low-dimension magnetic and electronic systems, disorder and quantum transport, magnetic impurities (the Kondo problem), quantum spin systems, the Hubbard model and high temperature superconductors. Topics are chosen to illustrate the application of diagrammatic techniques, field theory approaches, and renormalization group methods in condensed matter physics. In this course we shall develop theoretical methods suitable for the description of the many-body phenomena, such as Hamiltonian second-quantized operator formalism, Greens functions, path integral, functional integral, and the quantum kinetic equation. The concepts to be introduced include, but are not limited to, the random phase approximation, the mean field theory (aka saddle-point, or semiclassical approximation), the tunneling dynamics in imaginary time, instantons, Berry phase, coherent state path integral, renormalization group.

Introduces mechanics of rock deformation. Discusses recognition, interpretation, and mechanics of faults, folds, structural features of igneous and metamorphic rocks, and superposed deformations. Introduces regional structural geology and tectonics. Laboratory includes techniques of structural analysis, recognition and interpretation of structures on geologic maps, and construction of interpretive cross sections. Structural geology is the study of processes and products of rock deformation. This course introduces the techniques of structural geology through a survey of the mechanics of rock deformation, a survey of the features and geometries of faults and folds, and techniques of strain analysis. Regional structural geology and tectonics are introduced. Class lectures are supplemented by lab exercises and demonstrations as well as field trips to local outcrops.

This course covers the fundamental concepts of structural mechanics with applications to marine, civil, and mechanical structures. Topics include analysis of small deflections of beams, moderately large deflections of beams, columns, cables, and shafts; elastic and plastic buckling of columns, thin walled sections and plates; exact and approximate methods; energy methods; principle of virtual work; introduction to failure analysis of structures. We will include examples from civil, mechanical, offshore, and ship structures such as the collision and grounding of ships.

Structural components in nuclear power plant systems, their functional purposes, operating conditions, and mechanical-structural design requirements. Combines mechanics techniques with models of material behavior to determine adequacy of component design. Considerations include mechanical loading, brittle fracture, inelastic behavior, elevated temperatures, neutron irradiation, and seismic effects.

Lectures plus guided readings and discussion with project reports, covering major CNS structures, with emphasis on systems being used as models for experimental studies of development and plasticity. Topics include: basic patterns of connections in CNS; review of lab techniques (anatomy, tissue culture); embryogenesis; PNS anatomy and development; process outgrowth and synaptogenesis; growth factors and cell survival; spinal and hindbrain anatomy; development of regional specificity with introduction to comparative anatomy and CNS evolution; trigeminal system; retinotectal system development, plasticity, regeneration; neocortex anatomy and development; olfactory system; corpus striatum; brain transplants; limbic system and hippocampal anatomy and plasticity.

The Core Mantle Boundary (CMB) represents one of the most important physical and chemical discontinuities of the deep Earth as it separates the solid state, convective lower mantle from the liquid outer core. In this seminar course, we will examine our current understanding of the CMB region from integrated seismological, mineral physics and geodynamical perspectives. Instructors will introduce state-of-the-art methodologies that are employed to characterize the CMB region and relevant papers will be discussed in class. Topics will include CMB detection and topography, D'' anisotropy, seismic velocity anomalies (e.g., ultra-low velocity zones), temperature, chemical reactions, phase relations, and mineral fabrications at the core-mantle boundary. These results will be integrated to address the CMB's fundamental role in both mantle and core dynamics.

Provides a comprehensive introduction to crystalline structure, crystal chemistry, and bonding in rock-forming minerals. Introduces the theory relating crystal structure and crystal symmetry to physical properties such as refractive index, elastic modulus, and seismic velocity. Surveys the distribution of silicate, oxide, and metallic minerals in the interiors and on the surfaces of planets, and discusses the processes that led to their formation.

Provides an integrated approach to understanding the practice of engineering in the real world. Students research the life cycle of a major engineering project, new technology, or startup company from multiple perspectives: technical, economic, political, cultural. Emphasis on analyzing engineering artifacts, understanding documentation, framing logical arguments, communicating effectively, and working in teams.