In this class we will come to understand the vast changes in Spanish life that have taken place since Franco's death in 1975. We will focus on the new freedom from censorship, the re-emergence of movements for regional autonomy, the new cinema, reforms in education and changes in daily life: Sex roles, work, and family that have occurred in the last decade. In so doing, we will examine myths that are often considered commonplaces when describing Spain and its people.

This class introduces elementary programming concepts including variable types, data structures, and flow control. After an introduction to linear algebra and probability, it covers numerical methods relevant to mechanical engineering, including approximation (interpolation, least squares and statistical regression), integration, solution of linear and nonlinear equations, ordinary differential equations, and deterministic and probabilistic approaches. Examples are drawn from mechanical engineering disciplines, in particular from robotics, dynamics, and structural analysis. Assignments require MATLAB programming.

Introduction to numerical methods: interpolation, differentiation, integration, systems of linear equations. Solution of differential equations by numerical integration, partial differential equations of inviscid hydrodynamics: finite difference methods, panel methods. Fast Fourier Transforms. Numerical representation of sea waves. Computation of the motions of ships in waves. Integral boundary layer equations and numerical solutions.

This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.

Fundamentals of characterizing and recognizing patterns and features of interest in numerical data. Basic tools and theory for signal understanding problems with applications to user modeling, affect recognition, speech recognition and understanding, computer vision, physiological analysis, and more. Decision theory, statistical classification, maximum likelihood and Bayesian estimation, non-parametric methods, unsupervised learning and clustering. Additional topics on machine and human learning from active research.

Examines the history of the United States as a "nation of immigrants" within a broader global context. Considers migration from the mid-19th century to the present through case studies of such places as New York's Lower East Side, South Texas, Florida, and San Francisco's Chinatown. Examines the role of memory, media, and popular culture in shaping ideas about migration. Includes optional field trip to New York City.

This course takes a broad-based look at poker theory and applications of poker analytics to investment management and trading.

Prediction is at the heart of almost every scientific discipline, and the study of generalization (that is, prediction) from data is the central topic of machine learning and statistics, and more generally, data mining. Machine learning and statistical methods are used throughout the scientific world for their use in handling the "information overload" that characterizes our current digital age. Machine learning developed from the artificial intelligence community, mainly within the last 30 years, at the same time that statistics has made major advances due to the availability of modern computing. However, parts of these two fields aim at the same goal, that is, of prediction from data. This course provides a selection of the most important topics from both of these subjects.

Welcome to 6.041/6.431, a subject on the modeling and analysis of random phenomena and processes, including the basics of statistical inference. Nowadays, there is broad consensus that the ability to think probabilistically is a fundamental component of scientific literacy. For example: The concept of statistical significance (to be touched upon at the end of this course) is considered by the Financial Times as one of "The Ten Things Everyone Should Know About Science". A recent Scientific American article argues that statistical literacy is crucial in making health-related decisions. Finally, an article in the New York Times identifies statistical data analysis as an upcoming profession, valuable everywhere, from Google and Netflix to the Office of Management and Budget. The aim of this class is to introduce the relevant models, skills, and tools, by combining mathematics with conceptual understanding and intuition.

Interpretations of the concept of probability. Basic probability rules; random variables and distribution functions; functions of random variables. Applications to quality control and the reliability assessment of mechanical/electrical components, as well as simple structures and redundant systems. Elements of statistics. Bayesian methods in engineering. Methods for reliability and risk assessment of complex systems, (event-tree and fault-tree analysis, common-cause failures, human reliability models). Uncertainty propagation in complex systems (Monte Carlo methods, Latin Hypercube Sampling). Introduction to Markov models. Examples and applications from nuclear and chemical-process plants, waste repositories, and mechanical systems. Open to qualified undergraduates.

This course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.

Quantitative analysis of uncertainty and risk for engineering applications. Fundamentals of probability, random processes, statistics, and decision analysis. Random variables and vectors, uncertainty propagation, conditional distributions, and second-moment analysis. Introduction to system reliability. Bayesian analysis and risk-based decision. Estimation of distribution parameters, hypothesis testing, and simple and multiple linear regressions. Poisson and Markov processes. Emphasis on application to engineering problems.

Production of Educational Videos is an introduction to technical communication that is situated in the production of educational videos; the assignments are all focused on the production of videos that teach some aspect of MIT's first-year core curriculum. The objective of these assignments is improvement in both communication ability and communication habits; these improvements are effected by providing participants with instruction, practice, feedback, and the opportunity for reflection. In addition to improvements in communication skills, improvement is expected in students' attitude towards writing, oral presentations, and collaboration; as the semester progresses, students should feel confident of their ability to write, present, and collaborate.

This course develops logical, empirically based arguments using statistical techniques and analytic methods. Elementary statistics, probability, and other types of quantitative reasoning useful for description, estimation, comparison, and explanation are covered. Emphasis is on the use and limitations of analytical techniques in planning practice.

A two-semester subject on quantum theory, stressing principles: uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of measurement, transformation theory, equations of motion, and constants of motion. Symmetry in quantum mechanics, representations of symmetry groups. Variational and perturbation approximations. Systems of identical particles and applications. Time-dependent perturbation theory. Scattering theory: phase shifts, Born approximation. The quantum theory of radiation. Second quantization and many-body theory. Relativistic quantum mechanics of one electron. This is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

Studies how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Models of randomized computation. Data structures: hash tables, and skip lists. Graph algorithms: minimum spanning trees, shortest paths, and 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.

Aims to develop a teaching knowledge of the field through extensive reading and discussion of major works. The reading covers a broad range of topics -- political, economic, social, and cultural -- and represents a variety of historical methods. Students make frequent oral presentations and prepare a 20-page review essay.

This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. MIT students may choose to take one of three versions of Real Analysis; this version offers three additional units of credit for instruction and practice in written and oral presentation.The three options for 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 point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology.Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication. This fulfills the MIT CI requirement.  

This course uses readings and discussions to focus on a series of short-term events that shed light on American politics, culture, and social organization. It emphasizes finding ways to make sense of these complicated, highly traumatic events, and on using them to understand larger processes of change in American history. The class also gives students experience with primary documentation research through a term paper assignment.

This subject introduces the history of science from antiquity to the present. Students consider the impact of philosophy, art, magic, social structure, and folk knowledge on the development of what has come to be called "science" in the Western tradition, including those fields today designated as physics, biology, chemistry, medicine, astronomy and the mind sciences. Topics include concepts of matter, nature, motion, body, heavens, and mind as these have been shaped over the course of history. Students read original works by Aristotle, Vesalius, Newton, Lavoisier, Darwin, Freud, and Einstein, among others.