Topics in surface modeling: b-splines, non-uniform rational b-splines, physically based deformable surfaces, sweeps and generalized cylinders, offsets, blending and filleting surfaces. Non-linear solvers and intersection problems. Solid modeling: constructive solid geometry, boundary representation, non-manifold and mixed-dimension boundary representation models, octrees. Robustness of geometric computations. Interval methods. Finite and boundary element discretization methods for continuum mechanics problems. Scientific visualization. Variational geometry. Tolerances. Inspection methods. Feature representation and recognition. Shape interrogation for design, analysis, and manufacturing. Involves analytical and programming assignments.

16.225 is a graduate level course on Computational Mechanics of Materials. The primary focus of this course is on the teaching of state-of-the-art numerical methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered in this course will include: linear and finite deformation elasticity, inelasticity and dynamics. Numerical formulation and algorithms will include: Variational formulation and variational constitutive updates, finite element discretization, error estimation, constrained problems, time integration algorithms and convergence analysis. There will be a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. At the beginning of the course, the students will be given the source of a base code with all the elements of a finite element program which constitute overhead and do not contribute to the learning objectives of this course (assembly and equation-solving methods, etc.). Each assignment will consist of formulating and implementing on this basic platform, the increasingly complex algorithms resulting from the theory given in class, as well as in using the code to numerically solve specific problems. The application to real engineering applications and problems in engineering science will be stressed throughout.

This course is a graduate level introduction to automatic discourse processing. The emphasis will be on methods and models that have applicability to natural language and speech processing. The class will cover the following topics: discourse structure, models of coherence and cohesion, plan recognition algorithms, and text segmentation. We will study symbolic as well as machine learning methods for discourse analysis. We will also discuss the use of these methods in a variety of applications ranging from dialogue systems to automatic essay writing. This subject qualifies as an Artificial Intelligence and Applications concentration subject.

Wave equations for fluid and visco-elastic media. Wave-theory formulations of acoustic source radiation and seismo-acoustic propagation in stratified ocean waveguides. Wavenumber Integration and Normal Mode methods for propagation in plane-stratified media. Seismo-Acoustic modeling of seabeds and ice covers. Seismic interface and surface waves in a stratified seabed. Parabolic Equation and Coupled Mode approaches to propagation in range-dependent ocean waveguides. Numerical modeling of target scattering and reverberation clutter in ocean waveguides. Ocean ambient noise modeling. Students develop propagation models using all the numerical approaches relevant to state-of-the-art acoustic research.

This course covers the analytical, graphical, and numerical methods supporting the analysis and design of integrated biological systems. Topics include modularity and abstraction in biological systems, mathematical encoding of detailed physical problems, numerical methods for solving the dynamics of continuous and discrete chemical systems, statistics and probability in dynamic systems, applied local and global optimization, simple feedback and control analysis, statistics and probability in pattern recognition.

Introduction to computer graphics hardware, algorithms, and software. Topics include: line generators, affine transformations, line and polygon clipping, splines, interactive techniques, perspective projection, solid modeling, hidden surface algorithms, lighting models, shading, and animation. Substantial programming experience required. 6.837 offers an introduction to computer graphics hardware, algorithms, and software. Topics include: line generators, affine transformations, line and polygon clipping, splines, interactive techniques, perspective projection, solid modeling, hidden surface algorithms, lighting models, shading, and animation. Substantial programming experience is required.

Topics on the engineering and analysis of network protocols and architecture, including: architectural principles for designing heterogeneous networks; congestion control; unicast and multicast routing; wireless and mobile networking; network quality of service; router design; network security; streaming and multicast applications; naming; content distribution; and peer-to-peer networking. Readings from original research papers, industry white papers, and Internet RFCs. Semester-long project and paper.

Emphasizes the relationship among technology, hardware organization, and programming systems in the evolution of computer architecture. Pipelined, out-of-order, and speculative execution. Superscaler, VLIW, vector, and multithreaded processors. Addressing structures and virtual memory, and exception handling. I/O and memory systems. Parallel computers; message passing and shared memory systems. Memory models, synchronization, and cache coherence protocols. Vector supercomputers. Assumes an undergraduate knowledge of computer systems.

Introduces abstraction as an important mechanism for problem decomposition and solution formulation in the biomedical domain, and examines computer representation, storage, retrieval, and manipulation of biomedical data. Examines effect of programming paradigm choice on problem-solving approaches, introduces data structures and algorithms. Presents knowledge representation schemes for capturing biomedical domain complexity. Teaches principles of data modeling for efficient storage and retrieval. The final project involves building a medical information system that encompasses the different concepts taught in the subject.

Used for students receiving Advanced Placement credit and transfer credit. Program of study or research to be arranged with a Department faculty member. Written report required. Permission of Department required.

Describes how economic theory is linked to economic evaluation techniques like cost-benefit and cost-effectiveness analysis and to introduce students to many concepts that are specific to economic evaluation. Introduces students to the many varieties of economic evaluation to establish a common terminology. Discusses cost-benefit with a demonstration of how this type of evaluation is most clearly linked to economic theory. Explores other theories and concepts, including cost measurement, benefit valuation, and incremental decision-making. Finally, explores recommendations on performing economic evaluations that are made in the United States with a focus on how these are related to underlying economic theory and other concepts.

Critical review of works, theories, and polemics in architecture in the aftermath of WWII. Aim is a historical understanding of the period and the development of a meaningful framework to assess contemporary issues in architecture. Special attention paid to historiographic questions of how architects construe the terms of their "present." Required of M.Arch. students.

Thermal backgrounds in space. Cosmological principle and its consequences: Newtonian cosmology and types of "universes"; survey of relativistic cosmology; horizons. Overview of evolution in cosmology; radiation and element synthesis; physical models of the "early stages." Formation of large-scale structure to variability of physical laws. First and last states. Some knowledge of relativity expected. 8.962 recommended though not required. This course provides an overview of astrophysical cosmology with emphasis on the Cosmic Microwave Background (CMB) radiation, galaxies and related phenomena at high redshift, and cosmic structure formation. Additional topics include cosmic inflation, nucleosynthesis and baryosynthesis, quasar (QSO) absorption lines, and gamma-ray bursts. Some background in general relativity is assumed.

A series of presentations on an advanced topic in the field of geology by the visiting William Otis Crosby lecturer. The Crosby lectureship is awarded to a distinguished international scientist each year to introduce new scientific perspectives to the MIT community. Subject content and structure vary from year to year.

This course features a rigorous introduction to modern cryptography, with an emphasis on the fundamental cryptographic primitives of public-key encryption, digital signatures, pseudo-random number generation, and basic protocols and their computational complexity requirements.

" This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases."

" This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules."

The subject of this course is the historical process by which the meaning of "technology" has been constructed. Although the word itself is traceable to the ancient Greek root teckhne (meaning art), it did not enter the English language until the 17th century, and did not acquire its current meaning until after World War I. The aim of the course, then, is to explore various sectors of industrializing 19th and 20th century Western society and culture with a view to explaining and assessing the emergence of technology as a pivotal word (and concept) in contemporary (especially Anglo-American) thought and expression.

This course examines computers anthropologically, as artifacts revealing the social orders and cultural practices that create them. Students read classic texts in computer science along with cultural analyses of computing history and contemporary configurations. It explores the history of automata, automation and capitalist manufacturing; cybernetics and WWII operations research; artificial intelligence and gendered subjectivity; robots, cyborgs, and artificial life; creation and commoditization of the personal computer; the growth of the Internet as a military, academic, and commercial project; hackers and gamers; technobodies and virtual sociality. Emphasis is placed on how ideas about gender and other social differences shape labor practices, models of cognition, hacking culture, and social media.

This course focuses on Third World development using case studies and team collaboration. Students draw lessons from success stories and identify challenges, unintended consequences and failures in implementing technologies, projects and policies. Students acquire skills in the building of partnerships and learn how to pilot, implement, and scale-up a selected innovation for the common good. Teams develop an idea, project or business plan that is ready to roll by semester's end.