MERLOT Materials
https://www.merlot.org/
MERLOT MaterialsCopyright (C) 2018 MERLOT Some Rights ReservedMon, 03 Jun 2013 19:02:16 GMTMERLOThttps://www.merlot.org/merlot/images/merlot_column.png
https://www.merlot.org/
-1-11.151 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 20:57:39 GMTProf. Daniele Veneziano6.041 / 6.431 Probabilistic Systems Analysis and Applied Probability
https://www.merlot.org/merlot/viewMaterial.htm?id=681142
This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.Fri, 10 Aug 2012 22:06:08 GMTProf. Munther Dahleh6.045J Automata, Computability, and Complexity
https://www.merlot.org/merlot/viewMaterial.htm?id=681089
This course is offered to undergraduates and introduces basic mathematical models of computation and the finite representation of infinite objects. The course is slower paced than 6.840J/18.404J. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems.Fri, 10 Aug 2012 22:05:53 GMTProf. Nancy Lynch6.825 Techniques in Artificial Intelligence (SMA 5504)
https://www.merlot.org/merlot/viewMaterial.htm?id=681148
6.825 is a graduate-level introduction to artificial intelligence. Topics covered include: representation and inference in first-order logic, modern deterministic and decision-theoretic planning techniques, basic supervised learning methods, and Bayesian network inference and learning. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5504 (Techniques in Artificial Intelligence).Fri, 10 Aug 2012 22:06:10 GMTProf. Leslie Kaelbling Prof. Tomás Lozano-Pérez(Contributor)6.856J / 18.416J Randomized Algorithms
https://www.merlot.org/merlot/viewMaterial.htm?id=681135
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.Fri, 10 Aug 2012 22:06:06 GMTProf. David R. Karger6.895 Theory of Parallel Systems (SMA 5509)
https://www.merlot.org/merlot/viewMaterial.htm?id=681049
6.895 covers theoretical foundations of general-purpose parallel computing systems, from languages to architecture. The focus is on the algorithmic underpinnings of parallel systems. The topics for the class will vary depending on student interest, but will likely include multithreading, synchronization, race detection, load balancing, memory consistency, routing networks, message-routing algorithms, and VLSI layout theory. The class will emphasize randomized algorithms and probabilistic analysis, including high-probability arguments. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5509 (Theory of Parallel Systems).Fri, 10 Aug 2012 22:05:31 GMTDr. Bradley Kuszmaul Prof. Charles Leiserson Prof. Hsu Wen Jing Prof. Michael Bender6.972 Algebraic Techniques and Semidefinite Optimization
https://www.merlot.org/merlot/viewMaterial.htm?id=681100
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.Fri, 10 Aug 2012 22:05:56 GMTProf. Pablo ParriloAdvanced Algorithms
https://www.merlot.org/merlot/viewMaterial.htm?id=681036
This course is a first-year graduate course in algorithms. Emphasis is placed on fundamental algorithms and advanced methods of algorithmic design, analysis, and implementation. Techniques to be covered include amortization, randomization, fingerprinting, word-level parallelism, bit scaling, dynamic programming, network flow, linear programming, fixed-parameter algorithms, and approximation algorithms. Domains include string algorithms, network optimization, parallel algorithms, computational geometry, online algorithms, external memory, cache, and streaming algorithms, and data structures.Fri, 10 Aug 2012 22:05:27 GMTProf. David R. KargerDynamic Programming and Stochastic Control
https://www.merlot.org/merlot/viewMaterial.htm?id=681092
This course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We will consider optimal control of a dynamical system over both a finite and an infinite number of stages (finite and infinite horizon). We will also discuss some approximation methods for problems involving large state spaces. Applications of dynamic programming in a variety of fields will be covered in recitations.Fri, 10 Aug 2012 22:05:53 GMTProf. Dimitri BertsekasStatistics Mathematical Principles
https://www.merlot.org/merlot/viewMaterial.htm?id=681024
Course Highlights<br/>This course aims to facilitate students understanding of the basics of probability and statistics, stochastic processes, and signal processing through drills and processes, and in putting them into practice without difficulty. Despite mainly targeting third-year students, the course also accepts fourth-year students to participate. Through this course, students may learn subjects such as combination and probability, random variables and probability distributions, random walk, Brownian motion, Langevin equation, autocorrelation, noise, error, Fourier transformation, power spectrum, digital signal processing, etc. With regard to signal processing, the course will provide drills and practices by computer using the SPICE3 program.Fri, 10 Aug 2012 22:05:23 GMTAssociate Prof. Kenichi Ishikawa 18.465 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 20:57:15 GMTProf. Dmitry PanchenkoIntroductory Statistics (formerly Collaborative Statistics)
https://www.merlot.org/merlot/viewMaterial.htm?id=764645
<p>'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.'</p>Mon, 03 Jun 2013 19:02:16 GMTSusan Dean; Barbara Illowsky De Anza College1.010 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 20:57:49 GMTProf. Daniele Veneziano10.34 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 20:57:51 GMTProf. Kenneth Beers16.920J / 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 20:57:39 GMTProf. Boo Cheong Khoo Prof. Jacob White Prof. Jaime Peraire Prof. Anthony Patera18.01 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 20:57:47 GMTProf. David Jerison18.014 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 20:57:23 GMTProf. James Munkres Dr. Anna Lachowska18.02 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 20:57:19 GMTProf. David Jerison Prof. Arthur Mattuck18.02 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 20:57:16 GMTProf. Denis Auroux18.022 Calculus
https://www.merlot.org/merlot/viewMaterial.htm?id=591710
This is an undergraduate course on calculus of several variables. It covers all of the topics covered in Calculus II (18.02), but presents them in greater depth. These topics are vector algebra in 3-space, determinants, matrices, vector-valued functions of one variable, space motion, scalar functions of several variables, partial differentiation, gradient, optimization techniques, double integrals, line integrals in the plane, exact differentials, conservative fields, Green's theorem, triple integrals, line and surface integrals in space, the divergence theorem, and Stokes' theorem. Additional topics covered in 18.022 are geometry, vector fields, and linear algebra.Thu, 20 Oct 2011 20:57:55 GMTProf. Hartley Rogers18.04 Complex Variables with Applications
https://www.merlot.org/merlot/viewMaterial.htm?id=591297
The following topics are covered in the course: complex algebra and functions; analyticity; contour integration, Cauchy's theorem; singularities, Taylor and Laurent series; residues, evaluation of integrals; multivalued functions, potential theory in two dimensions; Fourier analysis and Laplace transforms.Thu, 20 Oct 2011 20:57:12 GMTProf. R. Rosales18.04 Complex Variables with Applications
https://www.merlot.org/merlot/viewMaterial.htm?id=591412
This course explored topics such as complex algebra and functions, analyticity, contour integration, Cauchy's theorem, singularities, Taylor and Laurent series, residues, evaluation of integrals, multivalued functions, potential theory in two dimensions, Fourier analysis and Laplace transforms.Thu, 20 Oct 2011 20:57:24 GMTProf. Alar Toomre18.06 Linear Algebra
https://www.merlot.org/merlot/viewMaterial.htm?id=591386
This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.Thu, 20 Oct 2011 20:57:22 GMTProf. Gilbert Strang18.06CI Linear Algebra - Communications Intensive
https://www.merlot.org/merlot/viewMaterial.htm?id=591458
This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing. The course starts with the standard linear algebra syllabus and eventually develops the techniques to approach a more advanced topic: abstract root systems in a Euclidean space.Thu, 20 Oct 2011 20:57:29 GMTAndrew Brooke-Taylor(Teaching Assistant) Dr. Anna Lachowska