# Online courses directory (10)

This course covers concepts and techniques for the design and implementation of large software systems that can be adapted to uses not anticipated by the designer. Applications include compilers, computer-algebra systems, deductive systems, and some artificial intelligence applications. Topics include combinators, generic operations, pattern matching, pattern-directed invocation, rule systems, backtracking, dependencies, indeterminacy, memoization, constraint propagation, and incremental refinement. Substantial weekly programming assignments are an integral part of the subject.

There will be extensive programming assignments, using MIT/GNU Scheme. Students should have significant programming experience in Scheme, Common Lisp, Haskell, CAML or some other "functional" language.

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.

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.

Looking to get started with computer science while learning to program in Python?

This computer science course provides an introduction to computer science that’s both challenging and fun. It takes a broad look at the field of computer science through a variety of demonstrations and projects. We’ll cover both low- and high-level concepts, from how the circuits inside a computer represent data to how to design algorithms, as well as how all of this information affects the technology we use today. Additionally, we’ll teach the basics of Python programming, giving us a a way to put our new CS knowledge into practice.

No need to know any programming before starting the course; we’ll teach everything you need to know along the way. All you need to start is a good grasp of algebra, and you can fall in love with both the concepts and the practice of computer science.

This course relies on primary readings from the database community to introduce graduate students to the foundations of database systems, focusing on basics such as the relational algebra and data model, schema normalization, query optimization, and transactions. It is designed for students who have taken 6.033 (or equivalent); no prior database experience is assumed, though students who have taken an undergraduate course in databases are encouraged to attend.

The course is a comprehensive introduction to the theory, algorithms and applications of integer optimization and is organized in four parts: formulations and relaxations, algebra and geometry of integer optimization, algorithms for integer optimization, and extensions of integer optimization.

This course offers an advanced introduction to numerical linear algebra. Topics include direct and iterative methods for linear systems, eigenvalue decompositions and QR/SVD factorizations, stability and accuracy of numerical algorithms, the IEEE floating point standard, sparse and structured matrices, preconditioning, linear algebra software. Problem sets require some knowledge of MATLAB®.

This class presents the fundamental probability and statistical concepts used in elementary data analysis. It will be taught at an introductory level for students with junior or senior college-level mathematical training including a working knowledge of calculus. A small amount of linear algebra and programming are useful for the class, but not required.

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