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443418.465 Topics in Statistics: Statistical Learning Theory
https://www.merlot.org/merlot/viewMaterial.htm?id=591322
The main goal of this course is to study the generalization ability of a number of popular machine learning algorithms such as boosting, support vector machines and neural networks. Topics include Vapnik-Chervonenkis theory, concentration inequalities in product spaces, and other elements of empirical process theory.Thu, 20 Oct 2011 13:57:15 -0700Introductory Statistics (formerly Collaborative Statistics)
https://www.merlot.org/merlot/viewMaterial.htm?id=764645
'Introductory Statistics follows the scope and sequence of a one-semester, introduction to statistics course and is geared toward students majoring in fields other than math or engineering. This text assumes students have been exposed to intermediate algebra, and it focuses on the applications of statistical knowledge rather than the theory behind it. The foundation of this textbook is Collaborative Statistics, by Barbara Illowsky and Susan Dean, which has been widely adopted. Introductory Statistics includes innovations in art, terminology, and practical applications, all with a goal of increasing relevance and accessibility for students. We strove to make the discipline meaningful and memorable, so that students can draw a working knowledge from it that will enrich their future studies and help them make sense of the world around them. The text also includes Collaborative Exercises, integration with TI-83,83+,84+ Calculators, technology integration problems, and statistics labs.'Mon, 3 Jun 2013 12:02:16 -07001.010 Uncertainty in Engineering
https://www.merlot.org/merlot/viewMaterial.htm?id=591651
This course gives an introduction to probability and statistics, with emphasis on engineering applications. Course topics include events and their probability, the total probability and Bayes' theorems, discrete and continuous random variables and vectors, uncertainty propagation and conditional analysis. Second-moment representation of uncertainty, random sampling, estimation of distribution parameters (method of moments, maximum likelihood, Bayesian estimation), and simple and multiple linear regression. Concepts illustrated with examples from various areas of engineering and everyday life.Thu, 20 Oct 2011 13:57:49 -07001.151 Probability and Statistics in Engineering
https://www.merlot.org/merlot/viewMaterial.htm?id=591557
This class covers quantitative analysis of uncertainty and risk for engineering applications. Fundamentals of probability, random processes, statistics, and decision analysis are covered, along with random variables and vectors, uncertainty propagation, conditional distributions, and second-moment analysis. System reliability is introduced. Other topics covered include Bayesian analysis and risk-based decision, estimation of distribution parameters, hypothesis testing, simple and multiple linear regressions, and Poisson and Markov processes. There is an emphasis placed on real-world applications to engineering problems.Thu, 20 Oct 2011 13:57:39 -070010.34 Numerical Methods Applied to Chemical Engineering
https://www.merlot.org/merlot/viewMaterial.htm?id=591672
This course focuses on the use of modern computational and mathematical techniques in chemical engineering. Starting from a discussion of linear systems as the basic computational unit in scientific computing, methods for solving sets of nonlinear algebraic equations, ordinary differential equations, and differential-algebraic (DAE) systems are presented. Probability theory and its use in physical modeling is covered, as is the statistical analysis of data and parameter estimation. The finite difference and finite element techniques are presented for converting the partial differential equations obtained from transport phenomena to DAE systems. The use of these techniques will be demonstrated throughout the course in the MATLABÃ‚Â® computing environment.Thu, 20 Oct 2011 13:57:51 -070016.920J / 2.097J / 6.339J Numerical Methods for Partial Differential Equations (SMA 5212)
https://www.merlot.org/merlot/viewMaterial.htm?id=591550
A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields. Topics include: Mathematical Formulations; Finite Difference and Finite Volume Discretizations; Finite Element Discretizations; Boundary Element Discretizations; Direct and Iterative Solution Methods.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5212 (Numerical Methods for Partial Differential Equations).Thu, 20 Oct 2011 13:57:39 -070018.01 Single Variable Calculus
https://www.merlot.org/merlot/viewMaterial.htm?id=591626
This introductory calculus course covers differentiation and integration of functions of one variable, with applications.Thu, 20 Oct 2011 13:57:47 -070018.014 Calculus with Theory I
https://www.merlot.org/merlot/viewMaterial.htm?id=591403
18.014, Calculus with Theory, covers the same material as 18.01 (Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus. Topics: Axioms for the real numbers; the Riemann integral; limits, theorems on continuous functions; derivatives of functions of one variable; the fundamental theorems of calculus; Taylor's theorem; infinite series, power series, rigorous treatment of the elementary functions. Dr. Lachowska wishes to acknowledge Andrew Brooke-Taylor, Natasha Bershadsky, andÃ‚Â Alex Retakh for their help with this course web site.Thu, 20 Oct 2011 13:57:23 -070018.02 Multivariable Calculus
https://www.merlot.org/merlot/viewMaterial.htm?id=591337
This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. MIT OpenCourseWare offers another version of 18.02, from the Spring 2006 term. Both versions cover the same material, although they are taught by different faculty and rely on different textbooks. Multivariable Calculus (18.02) is taught during the Fall and Spring terms at MIT, and is a required subject for all MIT undergraduates.Thu, 20 Oct 2011 13:57:16 -070018.02 Multivariable Calculus
https://www.merlot.org/merlot/viewMaterial.htm?id=591363
This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include Vectors and Matrices, Partial Derivatives, Double and Triple Integrals, and Vector Calculus in 2 and 3-space.Thu, 20 Oct 2011 13:57:19 -0700