A first-year graduate course in algorithms. Emphasizes fundamental algorithms and advanced methods of algorithmic design, analysis, and implementation. Data structures. Network flows. Linear programming. Computational geometry. Approximation algorithms. Alternate years.

This course is a first-year graduate course in algorithms. Emphasis is placed on fundamental algorithms and advanced methods of algorithmic design, analysis, and implementation. Techniques to be covered include amortization, randomization, fingerprinting, word-level parallelism, bit scaling, dynamic programming, network flow, linear programming, fixed-parameter algorithms, and approximation algorithms. Domains include string algorithms, network optimization, parallel algorithms, computational geometry, online algorithms, external memory, cache, and streaming algorithms, and data structures.

Following a brief classroom discussion of relevant principles, each student completes the paper design of several advanced circuits such as multiplexers, sample-and-holds, gain-controlled amplifiers, analog multipliers, digital-to-analog or analog-to-digital converters, and power amplifiers. One of each student's designs is presented to the class, and one may be built and evaluated. Associated laboratory emphasizing the use of modern analog building blocks. Alternate years.

Current research topics in computational complexity theory. Nondeterministic, alternating, probabilistic, and parallel computation models. Boolean circuits. Complexity classes and complete sets. The polynomial-time hierarchy. Interactive proof systems. Relativization. Definitions of randomness. Pseudo-randomness and derandomizations. Interactive proof systems and probabilistically checkable proofs. The topics for this course cover various aspects of complexity theory, such as the basic time and space classes, the polynomial-time hierarchy and the randomized classes. This is a pure theory class, so no applications were involved.

Materials covered include: special relativity, electrodynamics of moving media, waves in dispersive media, microstrip integrated circuits, quantum optics, remote sensing, radiative transfer theory, scattering by rough surfaces, effective permittivities, and random media.

This course is a graduate introduction to natural language processing - the study of human language from a computational perspective. It covers syntactic, semantic and discourse processing models, emphasizing machine learning or corpus-based methods and algorithms. It also covers applications of these methods and models in syntactic parsing, information extraction, statistical machine translation, dialogue systems, and summarization. The subject qualifies as an Artificial Intelligence and Applications concentration subject.

A comprehensive treatment of the theory of partial differential equations (pde) from an applied mathematics perspective. Equilibrium, propagation, diffusion, and other phenomena. Initial and boundary value problems. Transform methods, eigenvalue and eigenfunction expansions, Green's functions. Theory of characteristics and shocks. Boundary layers and other singular perturbation phenomena. Elementary concepts for the numerical solution of pde's. Illustrative examples from fluid dynamics, nonlinear waves, geometrical optics, and other applications.

Recent results in cryptography and interactive proofs. Lectures by instructor, invited speakers, and students. Alternate years. The topics covered in this course include interactive proofs, zero-knowledge proofs, zero-knowledge proofs of knowledge, non-interactive zero-knowledge proofs, secure protocols, two-party secure computation, multiparty secure computation, and chosen-ciphertext security.

This course is offered to undergraduates and addresses several algorithmic challenges in computational biology. The principles of algorithmic design for biological datasets are studied and existing algorithms analyzed for application to real datasets. Topics covered include: biological sequence analysis, gene identification, regulatory motif discovery, genome assembly, genome duplication and rearrangements, evolutionary theory, clustering algorithms, and scale-free networks.

In-depth study of an active research topic in computer graphics. Topics change each term. Readings from the literature, student presentations, short assignments, and a programming project. Animation is a compelling and effective form of expression; it engages viewers and makes difficult concepts easier to grasp. Today's animation industry creates films, special effects, and games with stunning visual detail and quality. This graduate class will investigate the algorithms that make these animations possible: keyframing, inverse kinematics, physical simulation, optimization, optimal control, motion capture, and data-driven methods. Our study will also reveal the shortcomings of these sophisticated tools. The students will propose improvements and explore new methods for computer animation in semester-long research projects. The course should appeal to both students with general interest in computer graphics and students interested in new applications of machine learning, robotics, biomechanics, physics, applied mathematics and scientific computing.

Device and circuit level optimization of digital building blocks. MOS and bipolar device models and second order effects. Circuit design styles and arithmetic structures. Estimation and minimization of energy consumption. Interconnect models and parasitics; driver design; timing issues (clock skew, self-timed circuits, etc.). Memory architectures, circuits (sense amplifiers) and devices. Testing of integrated circuits. Extensive use of circuit layout and SPICE in design projects and software labs.

Advanced interdisciplinary introduction to modern scientific computing on parallel supercomputers. Numerical topics include dense and sparse linear algebra, N-body problems, and Fourier transforms. Geometrical topics include partitioning and mesh generation. Other topics include architectures and software systems with hands-on emphasis on understanding the realities and myths of what is possible on the world's fastest machines.

Elementary quantum mechanics and statistical physics. Introduces applied quantum physics. Emphasizes experimental basis for quantum mechanics. Applies Schrodinger's equation to the free particle, tunneling, the harmonic oscillator, and hydrogen atom. Variational methods. Elementary statistical physics; Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions. Simple models for metals, semiconductors, and devices such as electron microscopes, scanning tunneling microscope, thermonic emitters, atomic force microscope, and more.

Phenomenological approach to superconductivity, with emphasis on superconducting electronics. Electrodynamics of superconductors, London's model, and flux quantization. Josephson Junctions and superconducting quantum devices, equivalent circuits, and high-speed superconducting electronics. Quantized circuits for quantum computing. Overview of type II superconductors, critical magnetic fields, pinning, the critical state model, superconducting materials, and microscopic theory of superconductivity. Alternate years.

This module introduces approximation and projections in Hilbert space.

This course introduces students to the basic knowledge representation, problem solving, and learning methods of artificial intelligence. Upon completion of 6.034, students should be able to develop intelligent systems by assembling solutions to concrete computational problems, understand the role of knowledge representation, problem solving, and learning in intelligent-system engineering, and appreciate the role of problem solving, vision, and language in understanding human intelligence from a computational perspective.

Introduces representations, techniques, and architectures used to build applied systems and to account for intelligence from a computational point of view. Applications of rule chaining, heuristic search, constraint propagation, constrained search, inheritance, and other problem-solving paradigms. Applications of identification trees, neural nets, genetic algorithms, and other learning paradigms. Speculations on the contributions of human vision and language systems to human intelligence.

This course provides a challenging introduction to some of the central ideas of theoretical computer science. Beginning in antiquity, the course will progress through finite automata, circuits and decision trees, Turing machines and computability, efficient algorithms and reducibility, the P versus NP problem, NP-completeness, the power of randomness, cryptography and one-way functions, computational learning theory, and quantum computing. It examines the classes of problems that can and cannot be solved by various kinds of machines. It tries to explain the key differences between computational models that affect their power.

Graduate-level introduction to automatic speech recognition. Provides relevant background in acoustic theory of speech production, properties of speech sounds, signal representation, acoustic modeling, pattern classification, search algorithms, stochastic modeling techniques (including hidden Markov modeling), and language modeling. Examines approaches of state-of-the-art speech recognition systems. Introduces students to the rapidly developing field of automatic speech recognition. Its content is divided into three parts. Part I deals with background material in the acoustic theory of speech production, acoustic-phonetics, and signal representation. Part II describes algorithmic aspects of speech recognition systems including pattern classification, search algorithms, stochastic modelling, and language modelling techniques. Part III compares and contrasts the various approaches to speech recognition, and describes advanced techniques used for acoustic-phonetic modelling, robust speech recognition, speaker adaptation, processing paralinguistic information, speech understanding, and multimodal processing.