This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods in linear algebra.

This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications.

The goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.

This course is a self-contained introduction to statistics with economic applications. Elements of probability theory, sampling theory, statistical estimation, regression analysis, and hypothesis testing. It uses elementary econometrics and other applications of statistical tools to economic data. It also provides a solid foundation in probability and statistics for economists and other social scientists.

This course will provide a solid foundation in probability and statistics for economists and other social scientists. We will emphasize topics needed for further study of econometrics and provide basic preparation for 14.32. Topics include elements of probability theory, sampling theory, statistical estimation, and hypothesis testing.

Introduces topology, covering topics fundamental to modern analysis and geometry. Topological spaces and continuous functions, connectedness, compactness, separation axioms, and selected further topics such as function spaces, metrization theorems, embedding theorems, the Tychonoff theorem.

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.

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering.

This class is a global survey of the great transformation in history known as the "Industrial Revolution." Topics include origins of mechanized production, the factory system, steam propulsion, electrification, mass communications, mass production and automation. Emphasis on the transfer of technology and its many adaptations around the world. Countries treated include Great Britain, France, Germany, the US, Sweden, Russia, Japan, China, and India. Includes brief reflection papers and a final paper.

This course provides techniques of effective presentation of mathematical material. Each section of this course is associated with a regular mathematics subject, and uses the material of that subject as a basis for written and oral presentations. The section presented here is on chaotic dynamical systems.

This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis. Users may find additional or updated materials at Professor Carter's 3.016 course Web site.

Lebesgue's integration theory with applications to analysis, including an introduction to convolution and the Fourier transform.

Hitherto it had gone by the original Indian name Manna-hatta, or as some still have it, 'The Manhattoes'; but this was now decried as savage and heathenish... At length, when the council was almost in despair, a burgher, remarkable for the size and squareness of his head, proposed that they should call it New-Amsterdam. The proposition took every body by surprise; it was so striking, so apposite, so ingenious. The name was adopted by acclamation, and New-Amsterdam the metropolis was thenceforth called. --Washington Irving, 1808 In less tongue-in-cheek style, this course examines the evolution of New York City from 1607 to the present. The readings focus on the city's social and physical histories, and the class discussions compare New York's development to patterns in other cities.

This course surveys the history of the Middle East, from the end of the 19th century to the present. It examines major political, social, intellectual and cultural issues and practices. It also focuses on important events, movements, and ideas that prevailed during the last century and affect its current realities.

First of two-term sequence on modeling, analysis and control of dynamic systems. Mechanical translation, uniaxial rotation, electrical circuits and their coupling via levers, gears and electro-mechanical devices. Analytical and computational solution of linear differential equations and state-determined systems. Laplace transforms, transfer functions. Frequency response, Bode plots. Vibrations, modal analysis. Open- and closed-loop control, instability. Time-domain controller design, introduction to frequency-domain control design techniques. Case studies of engineering applications.

In this class, students use data and systems knowledge to build models of complex socio-technical systems for improved system design and decision-making. Students will enhance their model-building skills, through review and extension of functions of random variables, Poisson processes, and Markov processes; move from applied probability to statistics via Chi-squared t and f tests, derived as functions of random variables; and review classical statistics, hypothesis tests, regression, correlation and causation, simple data mining techniques, and Bayesian vs. classical statistics. A class project is required.

This undergraduate course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics.

Selective survey of Latin American history from the wars of independence at the start of the nineteenth century to the present. Issues studied include: independence and its aftermath, slavery and its abolition, Latin America in the global economy, relations between Latin America and the US, dictatorships and democracies in the twentieth century, and revolution in Mexico, Cuba, and Central America.

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

This course is a continuation of 18.014. It covers the same material as 18.02 (Multivariable Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.