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Mon, 03 Jun 2013 19:02:16 GMT
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Advanced Algorithms
https://www.merlot.org/merlot/viewMaterial.htm?id=681036
This course is a firstyear 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, wordlevel parallelism, bit scaling, dynamic programming, network flow, linear programming, fixedparameter 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 GMT
Prof. David R. Karger

Dynamic 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 GMT
Prof. Dimitri Bertsekas

Statistics 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 thirdyear students, the course also accepts fourthyear 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 GMT
Associate Prof. Kenichi Ishikawa

1.151 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 secondmoment analysis. System reliability is introduced. Other topics covered include Bayesian analysis and riskbased decision, estimation of distribution parameters, hypothesis testing, simple and multiple linear regressions, and Poisson and Markov processes. There is an emphasis placed on realworld applications to engineering problems.
Thu, 20 Oct 2011 20:57:39 GMT
Prof. Daniele Veneziano

6.041 / 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 GMT
Prof. Munther Dahleh

6.045J 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, contextfree languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NPcompleteness, probabilistic computation, and interactive proof systems.
Fri, 10 Aug 2012 22:05:53 GMT
Prof. Nancy Lynch

6.825 Techniques in Artificial Intelligence (SMA 5504)
https://www.merlot.org/merlot/viewMaterial.htm?id=681148
6.825 is a graduatelevel introduction to artificial intelligence. Topics covered include: representation and inference in firstorder logic, modern deterministic and decisiontheoretic planning techniques, basic supervised learning methods, and Bayesian network inference and learning. This course was also taught as part of the SingaporeMIT Alliance (SMA) programme as course number SMA 5504 (Techniques in Artificial Intelligence).
Fri, 10 Aug 2012 22:06:10 GMT
Prof. Leslie Kaelbling Prof. Tomás LozanoPérez(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 GMT
Prof. David R. Karger

6.895 Theory of Parallel Systems (SMA 5509)
https://www.merlot.org/merlot/viewMaterial.htm?id=681049
6.895 covers theoretical foundations of generalpurpose 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, messagerouting algorithms, and VLSI layout theory. The class will emphasize randomized algorithms and probabilistic analysis, including highprobability arguments. This course was also taught as part of the SingaporeMIT Alliance (SMA) programme as course number SMA 5509 (Theory of Parallel Systems).
Fri, 10 Aug 2012 22:05:31 GMT
Dr. Bradley Kuszmaul Prof. Charles Leiserson Prof. Hsu Wen Jing Prof. Michael Bender

6.972 Algebraic Techniques and Semidefinite Optimization
https://www.merlot.org/merlot/viewMaterial.htm?id=681100
This researchoriented 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 convexitybased 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 GMT
Prof. Pablo Parrilo

Introductory Statistics (formerly Collaborative Statistics)
https://www.merlot.org/merlot/viewMaterial.htm?id=764645
<p>'Introductory Statistics follows the scope and sequence of a onesemester, 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 TI83,83+,84+ Calculators, technology integration problems, and statistics labs.'</p>
Mon, 03 Jun 2013 19:02:16 GMT
Susan Dean; Barbara Illowsky De Anza College

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 VapnikChervonenkis theory, concentration inequalities in product spaces, and other elements of empirical process theory.
Thu, 20 Oct 2011 20:57:15 GMT
Prof. Dmitry Panchenko

Analysis I
https://www.merlot.org/merlot/viewMaterial.htm?id=591463
Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some pointset topology, including some work in Euclidean nspace. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on pointset topology and nspace, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2space (the plane) and its pointset topology. Option C (18.100C) is a 15unit variant of Option B, with further instruction and practice in written and oral communication.
Thu, 20 Oct 2011 20:57:30 GMT
Prof. Arthur Mattuck

Analysis I
https://www.merlot.org/merlot/viewMaterial.htm?id=591493
This course is meant as a first introduction to rigorous mathematics; understanding and writing of proofs will be emphasized. We will cover basic notions in real analysis: pointset topology, metric spaces, sequences and series, continuity, differentiability, and integration.
Thu, 20 Oct 2011 20:57:33 GMT
Dr. Dan Ciubotaru

Calculus Online Textbook
https://www.merlot.org/merlot/viewMaterial.htm?id=591417
Published in 1991 and still in print from WellesleyCambridge Press, the book is a useful resource for educators and selflearners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide. Prof. Strang has also developed a related series of videos, Highlights of Calculus, on the basic ideas of calculus.
Thu, 20 Oct 2011 20:57:25 GMT
Prof. Gilbert Strang

Digital Signal Processing
https://www.merlot.org/merlot/viewMaterial.htm?id=591576
The course treats: the discrete Fourier Transform (DFT), the Fast Fourier Transform (FFT), their application in OFDM and DSL; elements of estimation theory and their application in communications; linear prediction, parametric methods, the YuleWalker equations, the Levinson algorithm, the Schur algorithm; detection and estimation filters; nonparametric estimation; selective filtering, application to beamforming. Study Goals: You will have acquired insight in how signal processing mathematics is really applied in concrete engineering examples. You will know how to do a timefrequency analysis, how to apply the FFT in Digital Subscriber Lines (DSL), how to estimate, separate and filter signals..
Thu, 20 Oct 2011 20:57:41 GMT
Dewilde, P.M.

ES.2H3 Ancient Philosophy and Mathematics
https://www.merlot.org/merlot/viewMaterial.htm?id=591441
Western philosophy and theoretical mathematics were born together, and the crossfertilization of ideas in the two disciplines was continuously acknowledged throughout antiquity. In this course, we read works of ancient Greek philosophy and mathematics, and investigate the way in which ideas of definition, reason, argument and proof, rationality and irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry.
Thu, 20 Oct 2011 20:57:27 GMT
Dr. Lee Perlman

Fourier Analysis
https://www.merlot.org/merlot/viewMaterial.htm?id=591707
18.103 picks up where 18.100B (Analysis I) left off. Topics covered include the theory of the Lebesgue integral with applications to probability, Fourier series, and Fourier integrals.
Thu, 20 Oct 2011 20:57:55 GMT
Prof. Richard Melrose

Introduction to Partial Differential Equations
https://www.merlot.org/merlot/viewMaterial.htm?id=591320
This course analyzes initial and boundary value problems for ordinary differential equations and the wave and heat equation in one space dimension. It also covers the SturmLiouville theory and eigenfunction expansions, as well as the Dirichlet problem for Laplace's operator and potential theory.
Thu, 20 Oct 2011 20:57:15 GMT
Prof. Gigliola Staffilani Prof. Andras Vasy

Introduction to Probability and Statistics
https://www.merlot.org/merlot/viewMaterial.htm?id=591374
This course provides an elementary introduction to probability and statistics with applications. Topics include: basic probability models; combinatorics; random variables; discrete and continuous probability distributions; statistical estimation and testing; confidence intervals; and an introduction to linear regression.
Thu, 20 Oct 2011 20:57:20 GMT
Prof. Dmitry Panchenko

Introduction to Teaching and Learning Mathematics and Science
https://www.merlot.org/merlot/viewMaterial.htm?id=591635
This course provides an introduction to teaching and learning in a variety of K12 settings. Through visits to schools, classroom discussions, selected readings, and handson activities, we explore the challenges and opportunities of teaching. Topics of study include educational technology, design and experimentation, student learning, and careers in education.
Thu, 20 Oct 2011 20:57:47 GMT
Prof. Eric Klopfer

MatemÃƒÂ¡ticas (PreparaciÃƒÂ³n para la Universidad)
https://www.merlot.org/merlot/viewMaterial.htm?id=591433
En la asignatura se realiza una revisiÃƒÂ³n de los conceptos matemÃƒÂ¡ticos bÃƒÂ¡sicos que se requieren en la UPM para iniciar los estudios en cualquiera de las titulaciones de Arquitectura o IngenierÃƒÂa, con la preparaciÃƒÂ³n suficiente en esta materia. EstÃƒÂ¡ estructurada en cinco bloques temÃƒÂ¡ticos: AritmÃƒÂ©tica y Ãƒ?lgebra; TrigonometrÃƒÂa y NÃƒÂºmeros Complejos; GeometrÃƒÂa; CÃƒÂ¡lculo y Probabilidad que, a su vez, se dividen en lecciones. Se presentan en todas ellas cuestionarios de autoevaluaciÃƒÂ³n y material de estudio, en su mayor parte interactivo, que se puede revisar de forma independiente, sin seguir una secuencia predeterminada. De esta forma, cada estudiante puede realizar una prueba diagnÃƒÂ³stica previa, repasar los conocimientos que precise y, finalmente, resolver algunos ejercicios para asimilar y fijar lo aprendido.
Thu, 20 Oct 2011 20:57:26 GMT

MATH 140  Calculus I, Summer 2007
https://www.merlot.org/merlot/viewMaterial.htm?id=591375
This course is an introduction to differential and integral calculus. It begins with a short review of basic concepts surrounding the notion of a function. Then it introduces the important concept of the limit of a function, and use it to study continuity and the tangent problem. The solution to the tangent problem leads to the study of derivatives and their applications. Then it considers the area problem and its solution, the definite integral. The course concludes with the calculus of elementary transcendental functions.
Thu, 20 Oct 2011 20:57:20 GMT
Catalin Zara

MATH 141  Calculus II, Spring 2006
https://www.merlot.org/merlot/viewMaterial.htm?id=591434
Continuation of MATH 140. Topics include transcendental functions, techniques of integration, applications of the integral, improper integrals, l'Hospital's rule, sequences, and series.
Thu, 20 Oct 2011 20:57:27 GMT
Catalin Zara, Ph.D.