Courses tagged with "Information Theory" (203)

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 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 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 students to the fundamentals of nonlinear optimization theory and methods. Topics include unconstrained and constrained optimization, linear and quadratic programming, Lagrange and conic duality theory, interior-point algorithms and theory, Lagrangian relaxation, generalized programming, and semi-definite programming. Algorithmic methods used in the class include steepest descent, Newton's method, conditional gradient and subgradient optimization, interior-point methods and penalty and barrier methods.

This course introduces students to the fundamentals of nonlinear optimization theory and methods. Topics include unconstrained and constrained optimization, linear and quadratic programming, Lagrange and conic duality theory, interior-point algorithms and theory, Lagrangian relaxation, generalized programming, and semi-definite programming. Algorithmic methods used in the class include steepest descent, Newton's method, conditional gradient and subgradient optimization, interior-point methods and penalty and barrier methods.

This short course provides an introduction to reactor dynamics including subcritical multiplication, critical operation in absence of thermal feedback effects and effects of Xenon, fuel and moderator temperature, etc. Topics include the derivation of point kinetics and dynamic period equations; techniques for reactor control including signal validation, supervisory algorithms, model-based trajectory tracking, and rule-based control; and an overview of light-water reactor startup. Lectures and demonstrations employ computer simulation and the use of the MIT Research Reactor.

This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

This course introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Emphasis is on methodology and the underlying mathematical structures. Topics include the simplex method, network flow methods, branch and bound and cutting plane methods for discrete optimization, optimality conditions for nonlinear optimization, interior point methods for convex optimization, Newton's method, heuristic methods, and dynamic programming and optimal control methods.

This course introduces students to the theory, algorithms, and applications of optimization. The optimization methodologies include linear programming, network optimization, integer programming, and decision trees. Applications to logistics, manufacturing, transportation, marketing, project management, and finance. Includes a team project in which students select and solve a problem in practice.

Modern computing platforms provide unprecedented amounts of raw computational power. But significant complexity comes along with this power, to the point that making useful computations exploit even a fraction of the potential of the computing platform is a substantial challenge. Indeed, obtaining good performance requires a comprehensive understanding of all layers of the underlying platform, deep insight into the computation at hand, and the ingenuity and creativity required to obtain an effective mapping of the computation onto the machine. The reward for mastering these sophisticated and challenging topics is the ability to make computations that can process large amount of data orders of magnitude more quickly and efficiently and to obtain results that are unavailable with standard practice.

This class is a hands-on, project-based introduction to building scalable and high-performance software systems. Topics include performance analysis, algorithmic techniques for high performance, instruction-level optimizations, cache and memory hierarchy optimization, parallel programming, and building scalable distributed systems.

The course also includes design reviews with industry mentors, as described in this MIT News article.

Principles of Applied Mathematics is a study of illustrative topics in discrete applied mathematics including sorting algorithms, information theory, coding theory, secret codes, generating functions, linear programming, game theory. There is an emphasis on topics that have direct application in the real world.

This course was recently revised to meet the MIT Undergraduate Communication Requirement (CR). It covers the same content as 18.310, but assignments are structured with an additional focus on writing.

This course surveys a variety of reasoning, optimization and decision making methodologies for creating highly autonomous systems and decision support aids. The focus is on principles, algorithms, and their application, taken from the disciplines of artificial intelligence and operations research.

Reasoning paradigms include logic and deduction, heuristic and constraint-based search, model-based reasoning, planning and execution, and machine learning. Optimization paradigms include linear programming, integer programming, and dynamic programming. Decision-making paradigms include decision theoretic planning, and Markov decision processes.

6.826 provides an introduction to the basic principles of computer systems, with emphasis on the use of rigorous techniques as an aid to understanding and building modern computing systems. Particular attention is paid to concurrent and distributed systems. Topics covered include: specification and verification, concurrent algorithms, synchronization, naming, networking, replication techniques (including distributed cache management), and principles and algorithms for achieving reliability.

The course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451 Principles of Digital Communication II, is offered in the spring.

Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM modulation, signal constellations, finite-energy waveform spaces, detection, and modeling and system design for wireless communication.

This course is the second of a two-term sequence with 6.450. The focus is on coding techniques for approaching the Shannon limit of additive white Gaussian noise (AWGN) channels, their performance analysis, and design principles. After a review of 6.450 and the Shannon limit for AWGN channels, the course begins by discussing small signal constellations, performance analysis and coding gain, and hard-decision and soft-decision decoding. It continues with binary linear block codes, Reed-Muller codes, finite fields, Reed-Solomon and BCH codes, binary linear convolutional codes, and the Viterbi algorithm.

More advanced topics include trellis representations of binary linear block codes and trellis-based decoding; codes on graphs; the sum-product and min-sum algorithms; the BCJR algorithm; turbo codes, LDPC codes and RA codes; and performance of LDPC codes with iterative decoding. Finally, the course addresses coding for the bandwidth-limited regime, including lattice codes, trellis-coded modulation, multilevel coding and shaping. If time permits, it covers equalization of linear Gaussian channels.

This course studies basic optimization and the principles of optimal control. It considers deterministic and stochastic problems for both discrete and continuous systems. The course covers solution methods including numerical search algorithms, model predictive control, dynamic programming, variational calculus, and approaches based on Pontryagin's maximum principle, and it includes many examples and applications of the theory.

This course is an introduction to the design, analysis, and fundamental limits of wireless transmission systems. Topics to be covered include: wireless channel and system models; fading and diversity; resource management and power control; multiple-antenna and MIMO systems; space-time codes and decoding algorithms; multiple-access techniques and multiuser detection; broadcast codes and precoding; cellular and ad-hoc network topologies; OFDM and ultrawideband systems; and architectural issues.

This course examines how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Topics covered include: randomized computation; data structures (hash tables, skip lists); graph algorithms (minimum spanning trees, shortest paths, minimum cuts); geometric algorithms (convex hulls, linear programming in fixed or arbitrary dimension); approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms.

In keeping with the tradition of the last twenty-some years, the Readings in Optimization seminar will focus on an advanced topic of interest to a portion of the MIT optimization community: randomized methods for deterministic optimization. In contrast to conventional optimization algorithms whose iterates are computed and analyzed deterministically, randomized methods rely on stochastic processes and random number/vector generation as part of the algorithm and/or its analysis. In the seminar, we will study some very recent papers on this topic, many by MIT faculty, as well as some older papers from the existing literature that are only now receiving attention.

With the growing availability and lowering costs of genotyping and personal genome sequencing, the focus has shifted from the ability to obtain the sequence to the ability to make sense of the resulting information. This course is aimed at exploring the computational challenges associated with interpreting how sequence differences between individuals lead to phenotypic differences in gene expression, disease predisposition, or response to treatment.

This course is a broad introduction to a host of sensor technologies, illustrated by applications drawn from human-computer interfaces and ubiquitous computing. After extensively reviewing electronics for sensor signal conditioning, the lectures cover the principles and operation of a variety of sensor architectures and modalities, including pressure, strain, displacement, proximity, thermal, electric and magnetic field, optical, acoustic, RF, inertial, and bioelectric. Simple sensor processing algorithms and wired and wireless network standards are also discussed. Students are required to complete written assignments, a set of laboratories, and a final project.