The following topics are covered in the course: complex algebra and functions; analyticity; contour integration, Cauchy’s theorem; singularities, Taylor and Laurent series; residues, evaluation of integrals; multivalued functions, potential theory in two dimensions; Fourier analysis and Laplace transforms.

Complex analysis is a basic tool with a great many practical applications to the solution of physical problems. It revolves around complex analytic functions—functions that have a complex derivative. Unlike calculus using real variables, the mere existence of a complex derivative has strong implications for the properties of the function. Applications reviewed in this class include harmonic functions, two dimensional fluid flow, easy methods for computing (seemingly) hard integrals, Laplace transforms, and Fourier transforms with applications to engineering and physics.

In this interdisciplinary seminar, we explore a variety of visual and written tools for self exploration and self expression. Through discussion, written assignments, and directed exercises, students practice utilizing a variety of media to explore and express who they are.

This class explores composition and arrangement for the large jazz ensemble from 1920s foundations to current postmodern practice. Consideration given to a variety of styles and to the interaction of improvisation and composition. Study of works by Basie, Ellington, Evans, Gillespie, Golson, Mingus, Morris, Nelson, Williams, and others. Open rehearsals, workshops, and performances of student compositions by the MIT Festival Jazz Ensemble and the Aardvark Jazz Orchestra.

This class explores sound and what can be done with it. Sources are recorded from students’ surroundings - sampled and electronically generated (both analog and digital). Assignments include composing with the sampled sounds, feedback, and noise, using digital signal processing (DSP), convolution, algorithms, and simple mixing. The class focuses on sonic and compositional aspects rather than technology, math, or acoustics, though these are examined in varying detail. Students complete weekly composition and listening assignments; material for the latter is drawn from sound art, experimental electronica, conventional and non-conventional classical electronic works, popular music, and previous students’ compositions.

This course outlines the physics, modeling, application, and technology of compound semiconductors (primarily III-Vs) in electronic, optoelectronic, and photonic devices and integrated circuits. Topics include: properties, preparation, and processing of compound semiconductors; theory and practice of heterojunctions, quantum structures, and pseudomorphic strained layers; metal-semiconductor field effect transistors (MESFETs); heterojunction field effect transistors (HFETs) and bipolar transistors (HBTs); photodiodes, vertical-and in-plane-cavity laser diodes, and other optoelectronic devices.

The course begins with the basics of compressible fluid dynamics, including governing equations, thermodynamic context and characteristic parameters. The next large block of lectures covers quasi-one-dimensional flow, followed by a discussion of disturbances and unsteady flows. The second half of the course comprises gas dynamic discontinuities, including shock waves and detonations, and concludes with another large block dealing with two-dimensional flows, both linear and non-linear.

2.26 is a 6-unit Honors-level subject serving as the Mechanical Engineering department’s sole course in compressible fluid dynamics. The prerequisites for this course are undergraduate courses in thermodynamics, fluid dynamics, and heat transfer.
The goal of this course is to lay out the fundamental concepts and results for the compressible flow of gases. Topics to be covered include: appropriate conservation laws; propagation of disturbances; isentropic flows; normal shock wave relations, oblique shock waves, weak and strong shocks, and shock wave structure; compressible flows in ducts with area changes, friction, or heat addition; heat transfer to high speed flows; unsteady compressible flows, Riemann invariants, and piston and shock tube problems; steady 2D supersonic flow, Prandtl-Meyer function; and self-similar compressible flows. The emphasis will be on physical understanding of the phenomena and basic analytical techniques.

6.844 is a graduate introduction to programming theory, logic of programming, and computability, with the programming language Scheme used to crystallize computability constructions and as an object of study itself. Topics covered include: programming and computability theory based on a term-rewriting, “substitution” model of computation by Scheme programs with side-effects; computation as algebraic manipulation: Scheme evaluation as algebraic manipulation and term rewriting theory; paradoxes from self-application and introduction to formal programming semantics; undecidability of the Halting Problem for Scheme; properties of recursively enumerable sets, leading to Incompleteness Theorems for Scheme equivalences; logic for program specification and verification; and Hilbert’s Tenth Problem.

This course introduces architecture of digital systems, emphasizing structural principles common to a wide range of technologies. It covers the topics including multilevel implementation strategies, definition of new primitives (e.g., gates, instructions, procedures, processes) and their mechanization using lower-level elements. It also includes analysis of potential concurrency, precedence constraints and performance measures, pipelined and multidimensional systems, instruction set design issues and architectural support for contemporary software structures.

6.004 offers an introduction to the engineering of digital systems. Starting with MOS transistors, the course develops a series of building blocks — logic gates, combinational and sequential circuits, finite-state machines, computers and finally complete systems. Both hardware and software mechanisms are explored through a series of design examples.
6.004 is required material for any EECS undergraduate who wants to understand (and ultimately design) digital systems. A good grasp of the material is essential for later courses in digital design, computer architecture and systems. The problem sets and lab exercises are intended to give students “hands-on” experience in designing digital systems; each student completes a gate-level design for a reduced instruction set computer (RISC) processor during the semester.

This course covers the algorithmic and machine learning foundations of computational biology combining theory with practice. We cover both foundational topics in computational biology, and current research frontiers. We study fundamental techniques, recent advances in the field, and work directly with current large-scale biological datasets.

A computational camera attempts to digitally capture the essence of visual information by exploiting the synergistic combination of task-specific optics, illumination, sensors and processing. In this course we will study this emerging multi-disciplinary field at the intersection of signal processing, applied optics, computer graphics and vision, electronics, art, and online sharing through social networks. If novel cameras can be designed to sample light in radically new ways, then rich and useful forms of visual information may be recorded — beyond those present in traditional photographs. Furthermore, if computational process can be made aware of these novel imaging models, them the scene can be analyzed in higher dimensions and novel aesthetic renderings of the visual information can be synthesized.
We will discuss and play with thermal cameras, multi-spectral cameras, high-speed, and 3D range-sensing cameras and camera arrays. We will learn about opportunities in scientific and medical imaging, mobile-phone based photography, camera for HCI and sensors mimicking animal eyes. We will learn about the complete camera pipeline. In several hands-on projects we will build physical imaging prototypes and understand how each stage of the imaging process can be manipulated.

This course is an introduction to computational theories of human cognition. Drawing on formal models from classic and contemporary artificial intelligence, students will explore fundamental issues in human knowledge representation, inductive learning and reasoning. What are the forms that our knowledge of the world takes? What are the inductive principles that allow us to acquire new knowledge from the interaction of prior knowledge with observed data? What kinds of data must be available to human learners, and what kinds of innate knowledge (if any) must they have?

An introduction to computational theories of human cognition. Emphasizes questions of inductive learning and inference, and the representation of knowledge. Project required for graduate credit. This class is suitable for intermediate to advanced undergraduates or graduate students specializing in cognitive science, artificial intelligence, and related fields.

This class introduces design as a computational enterprise in which rules are developed to compose and describe architectural and other designs. The class covers topics such as shapes, shape arithmetic, symmetry, spatial relations, shape computations, and shape grammars. It focuses on the application of shape grammars in creative design, and teaches shape grammar fundamentals through in-class, hands-on exercises with abstract shape grammars. The class discusses issues related to practical applications of shape grammars.

Why has it been easier to develop a vaccine to eliminate polio than to control influenza or AIDS? Has there been natural selection for a ’language gene’? Why are there no animals with wheels? When does ‘maximizing fitness’ lead to evolutionary extinction? How are sex and parasites related? Why don’t snakes eat grass? Why don’t we have eyes in the back of our heads? How does modern genomics illustrate and challenge the field?
This course analyzes evolution from a computational, modeling, and engineering perspective. The course has extensive hands-on laboratory exercises in model-building and analyzing evolutionary data.

The course focuses on casting contemporary problems in systems biology and functional genomics in computational terms and providing appropriate tools and methods to solve them. Topics include genome structure and function, transcriptional regulation, and stem cell biology in particular; measurement technologies such as microarrays (expression, protein-DNA interactions, chromatin structure); statistical data analysis, predictive and causal inference, and experiment design. The emphasis is on coupling problem structures (biological questions) with appropriate computational approaches.

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.
This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.472J. In 2005, ocean engineering subjects became part of Course 2 (Department of Mechanical Engineering), and this course was renumbered 2.158J.

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 includes: linear and finite deformation elasticity, inelasticity and dynamics. Numerical formulation and algorithms include: variational formulation and variational constitutive updates, finite element discretization, error estimation, constrained problems, time integration algorithms and convergence analysis. There is a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. The application to real engineering applications and problems in engineering science is stressed throughout the course.