Courses tagged with "OpenCourseWare" (118)

Sort by: Name, Rating, Price
Start time: Any, Upcoming, Recent started, New, Always Open
Price: Any, Free, Paid
Starts : 2004-09-01
13 votes
MIT OpenCourseWare (OCW) Free Mathematics Graduate MIT OpenCourseWare

Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced methods of applied mathematics. It was designed to strengthen the mathematical abilities of graduate students and train them to think on their own.

Starts : 2004-09-01
10 votes
MIT OpenCourseWare (OCW) Free Mathematics Graduate MIT OpenCourseWare

This course analyzes the functions of a complex variable and the calculus of residues. It also covers subjects such as ordinary differential equations, partial differential equations, Bessel and Legendre functions, and the Sturm-Liouville theory.

Starts : 2016-02-01
8 votes
MIT OpenCourseWare (OCW) Free Mathematics Graduate MIT OpenCourseWare

This graduate-level course focuses on current research topics in computational complexity theory. Topics include: 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.

Starts : 2009-09-01
16 votes
MIT OpenCourseWare (OCW) Free Computer Sciences Graduate Mathematics MIT OpenCourseWare

The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc.

Starts : 2005-09-01
16 votes
MIT OpenCourseWare (OCW) Free Closed [?] Business Graduate MIT OpenCourseWare Sloan School of Management Stochastic Processes

The class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.

Starts : 2013-09-01
No votes
MIT OpenCourseWare (OCW) Free Mathematics Graduate MIT OpenCourseWare Sloan School of Management

This class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.

Starts : 2010-09-01
12 votes
MIT OpenCourseWare (OCW) Free Mathematics MIT OpenCourseWare Undergraduate

This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups.

Starts : 2011-02-01
15 votes
MIT OpenCourseWare (OCW) Free Mathematics MIT OpenCourseWare Undergraduate

This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.

Starts : 2009-02-01
9 votes
MIT OpenCourseWare (OCW) Free Mathematics MIT OpenCourseWare Undergraduate

This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected.

Starts : 2015-09-01
13 votes
MIT OpenCourseWare (OCW) Free Mathematics Graduate MIT OpenCourseWare

This is the first semester of a two-semester sequence on Algebraic Geometry. The goal of the course is to introduce the basic notions and techniques of modern algebraic geometry. It covers fundamental notions and results about algebraic varieties over an algebraically closed field; relations between complex algebraic varieties and complex analytic varieties; and examples with emphasis on algebraic curves and surfaces. This course is an introduction to the language of schemes and properties of morphisms.

Starts : 2009-02-01
11 votes
MIT OpenCourseWare (OCW) Free Mathematics Graduate MIT OpenCourseWare

This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry.

Starts : 2006-02-01
7 votes
MIT OpenCourseWare (OCW) Free Computer Sciences Electrical Engineering and Computer Science Graduate MIT OpenCourseWare

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 : 2006-09-01
9 votes
MIT OpenCourseWare (OCW) Free Mathematics Graduate MIT OpenCourseWare

This course is a first course in algebraic topology. The emphasis is on homology and cohomology theory, including cup products, Kunneth formulas, intersection pairings, and the Lefschetz fixed point theorem.

Starts : 2006-02-01
15 votes
MIT OpenCourseWare (OCW) Free Mathematics Graduate MIT OpenCourseWare

In this second term of Algebraic Topology, the topics covered include fibrations, homotopy groups, the Hurewicz theorem, vector bundles, characteristic classes, cobordism, and possible further topics at the discretion of the instructor.

Starts : 2015-02-01
14 votes
MIT OpenCourseWare (OCW) Free Computer Sciences Graduate Mathematics MIT OpenCourseWare

This course is organized around algorithmic issues that arise in machine learning. Modern machine learning systems are often built on top of algorithms that do not have provable guarantees, and it is the subject of debate when and why they work. In this class, we focus on designing algorithms whose performance we can rigorously analyze for fundamental machine learning problems.

Starts : 2010-09-01
12 votes
MIT OpenCourseWare (OCW) Free Mathematics MIT OpenCourseWare Undergraduate

Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations.

Starts : 2005-09-01
8 votes
MIT OpenCourseWare (OCW) Free Mathematics MIT OpenCourseWare Undergraduate

This course continues from Analysis I (18.100B), in the direction of manifolds and global analysis. The first half of the course covers multivariable calculus. The rest of the course covers the theory of differential forms in n-dimensional vector spaces and manifolds.

Starts : 2006-02-01
9 votes
MIT OpenCourseWare (OCW) Free Mathematics Graduate MIT OpenCourseWare Physics

This course provides a graduate-level introduction to stellar astrophysics. It covers a variety of topics, ranging from stellar structure and evolution to galactic dynamics and dark matter.

Starts : 2010-09-01
10 votes
MIT OpenCourseWare (OCW) Free Mathematics MIT OpenCourseWare Undergraduate

This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts.

Acknowledgement

Prof. McKernan would like to acknowledge the contributions of Lars Hesselholt to the development of this course.

Starts : 2005-02-01
10 votes
MIT OpenCourseWare (OCW) Free Mathematics MIT OpenCourseWare Undergraduate

This is an undergraduate course on differential calculus in one and several dimensions. It is intended as a one and a half term course in calculus for students who have studied calculus in high school. The format allows it to be entirely self contained, so that it is possible to follow it without any background in calculus.