Courses tagged with "Information Theory" (203)

This course begins with an introduction to the theory of computability, then proceeds to a detailed study of its most illustrious result: Kurt Gödel's theorem that, for any system of true arithmetical statements we might propose as an axiomatic basis for proving truths of arithmetic, there will be some arithmetical statements that we can recognize as true even though they don't follow from the system of axioms. In my opinion, which is widely shared, this is the most important single result in the entire history of logic, important not only on its own right but for the many applications of the technique by which it's proved. We'll discuss some of these applications, among them: Church's theorem that there is no algorithm for deciding when a formula is valid in the predicate calculus; Tarski's theorem that the set of true sentence of a language isn't definable within that language; and Gödel's second incompleteness theorem, which says that no consistent system of axioms can prove its own consistency.

6.867 is an introductory course on machine learning which gives an overview of many concepts, techniques, and algorithms in machine learning, beginning with topics such as classification and linear regression and ending up with more recent topics such as boosting, support vector machines, hidden Markov models, and Bayesian networks. The course will give the student the basic ideas and intuition behind modern machine learning methods as well as a bit more formal understanding of how, why, and when they work. The underlying theme in the course is statistical inference as it provides the foundation for most of the methods covered.

Machine Vision provides an intensive introduction to the process of generating a symbolic description of an environment from an image. Lectures describe the physics of image formation, motion vision, and recovering shapes from shading. Binary image processing and filtering are presented as preprocessing steps. Further topics include photogrammetry, object representation alignment, analog VLSI and computational vision. Applications to robotics and intelligent machine interaction are discussed.

This course covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

This subject offers an interactive introduction to discrete mathematics oriented toward computer science and engineering. The subject coverage divides roughly into thirds:

1. Fundamental concepts of mathematics: Definitions, proofs, sets, functions, relations.
2. Discrete structures: graphs, state machines, modular arithmetic, counting.
3. Discrete probability theory.

On completion of 6.042J, students will be able to explain and apply the basic methods of discrete (noncontinuous) mathematics in computer science. They will be able to use these methods in subsequent courses in the design and analysis of algorithms, computability theory, software engineering, and computer systems.

Interactive site components can be found on the Unit pages in the left-hand navigational bar, starting with Unit 1: Proofs.

This course introduces the fundamentals of machine tool and computer tool use. Students work with a variety of machine tools including the bandsaw, milling machine, and lathe. Instruction given on MATLAB®, MAPLE®, XESS™, and CAD. Emphasis is on problem solving, not programming or algorithmic development. Assignments are project-oriented relating to mechanical engineering topics. It is recommended that students take this subject in the first IAP after declaring the major in Mechanical Engineering.

This course was co-created by Prof. Douglas Hart and Dr. Kevin Otto.

This course introduces the theory and technology of micro/nano fabrication. Lectures and laboratory sessions focus on basic processing techniques such as diffusion, oxidation, photolithography, chemical vapor deposition, and more. Through team lab assignments, students are expected to gain an understanding of these processing techniques, and how they are applied in concert to device fabrication. Students enrolled in this course have a unique opportunity to fashion and test micro/nano-devices, using modern techniques and technology.

6.012 is the header course for the department's "Devices, Circuits and Systems" concentration. The topics covered include modeling of microelectronic devices, basic microelectronic circuit analysis and design, physical electronics of semiconductor junction and MOS devices, relation of electrical behavior to internal physical processes, development of circuit models, and understanding the uses and limitations of various models. The course uses incremental and large-signal techniques to analyze and design bipolar and field effect transistor circuits, with examples chosen from digital circuits, single-ended and differential linear amplifiers, and other integrated circuits.

MASLab (Mobile Autonomous System Laboratory), also known as 6.186, is a robotics contest. The contest takes place during MIT's Independent Activities Period and participants earn 6 units of P/F credit and 6 Engineering Design Points. Teams of three to four students have less than a month to build and program sophisticated robots which must explore an unknown playing field and perform a series of tasks.

MASLab provides a significantly more difficult robotics problem than many other university-level robotics contests. Although students know the general size, shape, and color of the floors and walls, the students do not know the exact layout of the playing field. In addition, MASLab robots are completely autonomous, or in other words, the robots operate, calculate, and plan without human intervention. Finally, MASLab is one of the few robotics contests in the country to use a vision based robotics problem.

6.161 offers an introduction to laboratory optics, optical principles, and optical devices and systems. This course covers a wide range of topics, including: polarization properties of light, reflection and refraction, coherence and interference, Fraunhofer and Fresnel diffraction, holography, imaging and transforming properties of lenses, spatial filtering, two-lens coherent optical processor, optical properties of materials, lasers, electro-optic, acousto-optic and liquid-crystal light modulators, optical detectors, optical waveguides and fiber-optic communication systems. Students engage in extensive oral and written communication exercises. There are 12 engineering design points associated with this subject.

The topics covered in this course include:

• Languages and compilers to exploit multithreaded parallelism
• Implicit parallel programming using functional languages and their extensions
• Higher-order functions, non-strictness, and polymorphism
• Explicit parallel programming and nondeterminism
• The lambda calculus and its variants
• Term rewriting and operational semantics
• Compiling multithreaded code for symmetric multiprocessors and clusters
• Static analysis and compiler optimizations

This course is worth 4 Engineering Design Points.

This course uses computer-aided design methodologies for synthesis of multivariable feedback control systems. Topics covered include: performance and robustness trade-offs; model-based compensators; Q-parameterization; ill-posed optimization problems; dynamic augmentation; linear-quadratic optimization of controllers; H-infinity controller design; Mu-synthesis; model and compensator simplification; and nonlinear effects. The assignments for the course comprise of computer-aided (MATLAB®) design problems.

6.863 is a laboratory-oriented course on the theory and practice of building computer systems for human language processing, with an emphasis on the linguistic, cognitive, and engineering foundations for understanding their design.

6.857 Network and Computer Security is an upper-level undergraduate, first-year graduate course on network and computer security. It fits within the Computer Systems and Architecture Engineering concentration.

Can you make a cellphone change the world?

NextLab is a hands-on year-long design course in which students research, develop and deploy mobile technologies for the next billion mobile users in developing countries. Guided by real-world needs as observed by local partners, students work in multidisciplinary teams on term-long projects, closely collaborating with NGOs and communities at the local level, field practitioners, and experts in relevant fields.

Students are expected to leverage technical ingenuity in both mobile and internet technologies together with social insight in order to address social challenges in areas such as health, microfinance, entrepreneurship, education, and civic activism. Students with technically and socially viable prototypes may obtain funding for travel to their target communities, in order to obtain the first-hand feedback necessary to prepare their technologies for full fledged deployment into the real world (subject to guidelines and limitations).

Can you make a cellphone change the world?

NextLab is a hands-on year-long design course in which students research, develop and deploy mobile technologies for the next billion mobile users in developing countries. Guided by real-world needs as observed by local partners, students work in multidisciplinary teams on term-long projects, closely collaborating with NGOs and communities at the local level, field practitioners, and experts in relevant fields.

Students are expected to leverage technical ingenuity in both mobile and internet technologies together with social insight in order to address social challenges in areas such as health, microfinance, entrepreneurship, education, and civic activism. Students with technically and socially viable prototypes may obtain funding for travel to their target communities, in order to obtain the first-hand feedback necessary to prepare their technologies for full fledged deployment into the real world (subject to guidelines and limitations).

Can you make a cellphone change the world?

NextLab is a hands-on year-long design course in which students research, develop and deploy mobile technologies for the next billion mobile users in developing countries. Guided by real-world needs as observed by local partners, students work in multidisciplinary teams on term-long projects, closely collaborating with NGOs and communities at the local level, field practitioners, and experts in relevant fields.

Students are expected to leverage technical ingenuity in both mobile and internet technologies together with social insight in order to address social challenges in areas such as health, microfinance, entrepreneurship, education, and civic activism. Students with technically and socially viable prototypes may obtain funding for travel to their target communities, in order to obtain the first-hand feedback necessary to prepare their technologies for full fledged deployment into the real world (subject to guidelines and limitations).