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.

Earth contains a variety of plants to provide food, medicine and, most importantly, energy sources for humans. In this lesson, students will categorize plants by their components and shapes. Additionally, they will learn the mechanisms behind the making of medicines and bio-fuels. It is important that the students have prior knowledge of the plant cell structures and functions. The video duration is 21 minutes, during which the students will use skills such as classification and experimentation. The students must therefore be supplied with various samples of plants. In Arabic with English subtitles.

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

This lesson focuses on the process of pollination. The learning objectives include learning the anatomy and physiology of flowers, the ecology of pollination, and a focus on plants as essential players in the natural world. There are no prerequisites for the lesson. The lesson will take 1½ hours, or 2 class periods or more -- depending on the areas teachers want to spend more time on or how far in depth they want their students to go. Materials needed are colored modeling clay, 8 or more assorted fresh flowers or pictures of flowers, preferably native to the local ecosystem. Dissecting microscopes or magnifying glasses are great for examining the fresh flowers, but not necessary. Additionally, pictures of different subjects/objects amongst plants are needed for the last activity. Activities for the breaks include assessing student knowledge of flowers by model building, and examining flowers to determine and distinguish between the pollination anatomy of different flowers.

In this lesson, through various examples and activities, exponential growth and polynomial growth are compared to develop an insight about how quickly the number can grow or decay in exponentials. A basic knowledge of scientific notation, plotting graphs and finding intersection of two functions is assumed.

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.

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 video lesson presents a real world problem that can be solved by using the Pythagorean theorem. The problem faces a juice seller daily. He has equilateral barrels with equal heights and he always tries to empty the juice of two barrels into a third barrel that has a volume equal to the sum of the volumes of the two barrels. This juice seller wants to find a simple way to help him select the right barrel without wasting time, and without any calculations - since he is ignorant of Mathematics. The prerequisite for this lesson includes knowledge of the following: the Pythagorean theorem; calculation of a triangles area knowing the angle between its two sides; cosine rule; calculation of a circle's area; and calculation of the areas and volumes of solids with regular bases.

This lesson teaches students about the history of the Pythagorean theorem, along with proofs and applications. It is geared toward high school Geometry students that have completed a year of Algebra.

This lesson aims to help students with quadratic functions y = ax2 + bx + c. This is the next step after linear functions bx + c. The lesson begins with three quadratics and their graphs (three parabolas): y = x2 - 2x + (0 or 1 or 2). The prerequisite or co-requisite is some working experience with algebra, like factoring x2 -2x into x(x-2). The objective is to connect four things: the formula for y, the graph of y (a parabola), the roots of y and the minimum or maximum of y. The particular example y = x2 – 2x could be repeated by the teacher, for emphasis. The lesson will take more than one class period (and this is deserved!). The breaks allow time to consider parabolas starting with -x2 and opening downward. A physical path would be one (dangerous?) activity.

Video lecture on quadratic equations and their graphs. The video connects the equation, the graph, the roots, and the minimum or maximum of the quadratic function.

The topic of this video is energy in general, and specifically the ways we can quantify it. In order to make the concepts accessible to a broad audience, this video focuses on everyday things and events. How is it that energy plays a part in a child riding a scooter? How is the energy we consume in playing related to the energy on the food we eat? This video poses these questions to the class and challenges them to put a list of five such items into an ordering from most energy to least.

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.