Courses tagged with "Before 1300: Ancient and Medieval History" (6)

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Starts : 2006-02-01
7 votes
MIT OpenCourseWare (OCW) Free Computer Sciences Before 1300: Ancient and Medieval History Infor Information environments Information Theory Nutrition

This research-oriented course will focus on algebraic and computational techniques for optimization problems involving polynomial equations and inequalities with particular emphasis on the connections with semidefinite optimization. The course will develop in a parallel fashion several algebraic and numerical approaches to polynomial systems, with a view towards methods that simultaneously incorporate both elements. We will study both the complex and real cases, developing techniques of general applicability, and stressing convexity-based ideas, complexity results, and efficient implementations. Although we will use examples from several engineering areas, particular emphasis will be given to those arising from systems and control applications.

Starts : 2003-02-01
12 votes
MIT OpenCourseWare (OCW) Free Computer Sciences Before 1300: Ancient and Medieval History Infor Information environments Information Theory Nutrition

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.

Starts : 2009-09-01
18 votes
MIT OpenCourseWare (OCW) Free Computer Sciences Before 1300: Ancient and Medieval History Infor Information control Information Theory Nutrition

This course aims to give students the tools and training to recognize convex optimization problems that arise in scientific and engineering applications, presenting the basic theory, and concentrating on modeling aspects and results that are useful in applications. Topics include convex sets, convex functions, optimization problems, least-squares, linear and quadratic programs, semidefinite programming, optimality conditions, and duality theory. Applications to signal processing, control, machine learning, finance, digital and analog circuit design, computational geometry, statistics, and mechanical engineering are presented. Students complete hands-on exercises using high-level numerical software.

Acknowledgements

The course materials were developed jointly by Prof. Stephen Boyd (Stanford), who was a visiting professor at MIT when this course was taught, and Prof. Lieven Vanderberghe (UCLA).

Starts : 2009-09-01
11 votes
MIT OpenCourseWare (OCW) Free Computer Sciences Before 1300: Ancient and Medieval History Infor Information environments Information Theory Nutrition

This course is an introduction to linear optimization and its extensions emphasizing the underlying mathematical structures, geometrical ideas, algorithms and solutions of practical problems. The topics covered include: formulations, the geometry of linear optimization, duality theory, the simplex method, sensitivity analysis, robust optimization, large scale optimization network flows, solving problems with an exponential number of constraints and the ellipsoid method, interior point methods, semidefinite optimization, solving real world problems problems with computer software, discrete optimization formulations and algorithms.

Starts : 2010-09-01
14 votes
MIT OpenCourseWare (OCW) Free Computer Sciences Before 1300: Ancient and Medieval History Infor Information control Information Theory Nutrition

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.

Starts : 2015-02-01
10 votes
MIT OpenCourseWare (OCW) Free Computer Sciences Before 1300: Ancient and Medieval History Infor Information control Information Theory Nutrition

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.

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