In this lesson, we learn how insects can fly in the rain. The objective is to calculate the impact forces of raindrops on flying mosquitoes. Students will gain experience with using Newton's laws, gathering data from videos and graphs, and most importantly, the utility of making approximations. No calculus will be used in this lesson, but familiarity with torque and force balances is suggested. No calculators will be needed, but students should have pencil and paper to make estimations and, if possible, copies of the graphs provided with the lesson. Between lessons, students are recommended to discuss the assignments with their neighbors.

Subject studies how and why machines work, how they are conceived, how they are developed (drawn), and how they are utilized. Students learn from the hands-on experiences of taking things apart mentally and physically, drawing (sketching, 3D CAD) what they envision and observe, taking occasional field trips, and completing an individual term project (concept, creation, and presentation). Emphasis on understanding the physics and history of machines.

This lesson is about the estimation of the value of Pi. Based on previous knowledge, the students try to estimate Pi value using different methods, such as: direct physical measurements; a geometric probability model; and computer technology. This lesson is designed to stimulate the learning interests of students, to enrich their experience of solving practical problems, and to develop their critical thinking ability. To understand this lesson, students should have some mathematic knowledge about circles, coordinate systems, and geometric probability. They may also need to know something about Excel. To estimate Pi value by direct physical measurements, the students can use any round or cylindrical shaped objects around them, such as round cups or water bottles. When estimating Pi value by a geometric probability model, a dartboard and darts should be prepared before the class. You can also use other games to substitute the dart throwing game. For example, you can throw marbles to the target drawn on the floor. This lesson is about 45-50 minutes. If the students know little about Excel, the teacher may need one more lesson to explain and demonstrate how to use the computer to estimate Pi value. Downloadable from the website is a video demonstration about how to use Excel for estimating Pi.

This course is an introduction to data cleaning, analysis and visualization. We will teach the basics of data analysis through concrete examples. You will learn how to take raw data, extract meaningful information, use statistical tools, and make visualizations. This was offered as a non-credit course during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

Selection of material from the following topics: calculus of variations (the first variation and the second variation); integral equations (Volterra equations; Fredholm equations, the Hilbert-Schmidt theorem); the Hilbert Problem and singular integral equations of Cauchy type; Wiener-Hopf Method and partial differential equations; Wiener-Hopf Method and integral equations; group theory.

This course is intended to assist undergraduates with learning the basics of programming in general and programming MATLAB in particular.

Analysis I 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 point-set topology, including some work in Euclidean n-space. 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 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 course provides an overview of Asian American history and its relevance for contemporary issues. It covers the first wave of Asian immigration in the 19th century, the rise of anti-Asian movements, the experiences of Asian Americans during WWII, the emergence of the Asian American movement in the 1960s, and the new wave of post–1965 Asian immigration. The class examines the role these experiences played in the formation of Asian American ethnicity. The course addresses key societal issues such as racial stereotyping, media racism, affirmative action, the glass ceiling, the "model minority" syndrome, and anti-Asian harassment or violence. The course is taught in English.

This course samples the wide variety of bioengineering options for students who plan to major in one of the undergraduate Engineering degree programs. The beginning lectures describe the science basis for bioengineering with particular emphasis on molecular cell biology and systems biology.

This is a fast-paced introductory course to the C++ programming language. It is intended for those with little programming background, though prior programming experience will make it easier, and those with previous experience will still learn C++-specific constructs and concepts.

This is a fast-paced introductory course to the C++ programming language. It is intended for those with little programming background, though prior programming experience will make it easier, and those with previous experience will still learn C++-specific constructs and concepts. This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

This course investigates the uses and boundaries of fiction in a range of novels and narrative styles--traditional and innovative, western and nonwestern--and raises questions about the pleasures and meanings of verbal texts in different cultures, times, and forms. Toward the end of the term, we will be particularly concerned with the relationship between art and war in a diverse selection of works.

This is a undergraduate course. It will cover normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators; Lebesgue measure, measurable functions, integrability, completeness of L-p spaces; Hilbert space; compact, Hilbert-Schmidt and trace class operators; as well as spectral theorem.

A general introduction to manifolds and Lie groups. The role of Lie groups in mathematics and physics. The exponential mapping. Correspondence with Lie algebras. Homogeneous spaces and transformation groups. Adjoint representation. Covering groups. Automorphism groups. Invariant differential forms and cohomology of Lie groups and homogeneous spaces. 18.101 recommended but not required. DThis course is devoted to the theory of Lie Groups with emphasis on its connections with Differential Geometry. The text for this class is Differential Geometry, Lie Groups and Symmetric Spaces by Sigurdur Helgason (American Mathematical Society, 2001). Much of the course material is based on Chapter I (first half) and Chapter II of the text. The text however develops basic Riemannian Geometry, Complex Manifolds, as well as a detailed theory of Semisimple Lie Groups and Symmetric Spaces.

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.

This course is an introduction to software engineering, using the Java™ programming language. It covers concepts useful to 6.005. Students will learn the fundamentals of Java. The focus is on developing high quality, working software that solves real problems.

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.

Introduction to Solid State Chemistry is a first-year single-semester college course on the principles of chemistry. This unique and popular course satisfies MIT's general chemistry degree requirement, with an emphasis on solid-state materials and their application to engineering systems.

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.