This 15-minute video lesson looks at the Standard Error of the Mean (a.k.a. the standard deviation of the sampling distribution of the sample mean!). [Statistics playlist: Lesson 38 of 85]

This 12-minute video lesson looks at the T-Statistic Confidence Interval (for small sample sizes). [Statistics playlist: Lesson 52 of 85]

A whirl-wind tour of the statistics used in behavioral science research, covering topics including: data visualization, building your own null-hypothesis distribution through permutation, useful parametric distributions, the generalized linear model, and model-based analyses more generally. Familiarity with MATLABA, Octave, or R will be useful, prior experience with statistics will be helpful but is not essential. This course is intended to be a ground-up sketch of a coherent, alternative perspective to the "null-hypothesis significance testing" method for behavioral research (but don't worry if you don't know what this means).

This course is a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, correlation, decision theory, and Bayesian statistics.

While the French had kept their end of the bargain by completing the statue itself, the Americans had still not fulfilled their commitment to erect a pedestal. In this lesson, students learn about the effort to convince a skeptical American public to contribute to the effort to erect a pedestal and to bring the Statue of Liberty to New York.

Help clarify the nature of symbols for your students as they study the Statue of Liberty, complete research on a national symbol, and use their research to communicate a message of their own.

Students learn that math is important in navigation and engineering. They learn about triangles and how they can help determine distances. Ancient land and sea navigators started with the most basic of navigation equations (speed x time = distance). Today, navigational satellites use equations that take into account the relative effects of space and time. However, even these high-tech wonders cannot be built without pure and simple math concepts — basic geometry and trigonometry — that have been used for thousands of years.

Have you ever considered going to a pharmacy to order some new cardiomyocytes (heart muscle cells) for your ailing heart? It might sound crazy, but recent developments in stem cell science have made this concept not so futuristic. In this course, we will explore the underlying biology behind the idea of using stem cells to treat disease, specifically analyzing the mechanisms that enable a single genome to encode multiple cell states ranging from neurons to fibroblasts to T cells. Overall, we hope to provide a comprehensive overview of this exciting new field of research and its clinical relevance. This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literature to discuss and learn about current biological research in a highly interactive setting. Many instructors of the Advanced Undergraduate Seminars are postdoctoral scientists with a strong interest in teaching.

The classic Stern-Gerlach Experiment shows that atoms have a property called spin. Spin is a kind of intrinsic angular momentum, which has no classical counterpart. When the z-component of the spin is measured, one always gets one of two values: spin up or spin down.

Students learn about the strength of bones and methods of helping to mend fractured bones. During a class demonstration, a chicken bone is broken by applying a load until it reaches a point of failure (fracture). Then, working as biomedical engineers, students teams design their own splint or cast to help repair a fractured bone, learning about the strength of materials used.

Estimation and control of dynamic systems. Brief review of probability and random variables. Classical and state-space descriptions of random processes and their propagation through linear systems. Frequency domain design of filters and compensators. The Kalman filter to estimate the states of dynamic systems. Conditions for stability of the filter equations.

Fundamentals of detection and estimation for signal processing, communications, and control. Vector spaces of random variables. Bayesian and Neyman-Pearson hypothesis testing. Bayesian and nonrandom parameter estimation. Minimum-variance unbiased estimators and the Cramer-Rao bounds. Representations for stochastic processes; shaping and whitening filters; Karhunen-Loeve expansions. Detection and estimation from waveform observations. Advanced topics: linear prediction and spectral estimation; Wiener and Kalman filters.

This problem can be solved in more than one way. The choice in solution method may reflect the comfort and mathematical sophistication of the student.

This is a multi-step problem since it requires more than two steps no matter how it is solved. The problem is not scaffolded for the student, but each step is straightforward and should follow from the previous with a careful reading of the problem.

In this activity, students act as engineers to determine which type of insulation would conserve the most energy.

Students learn about composite materials, tension as a force and how they act on structural components through the design and testing of strips of plastic chair webbing.

The transition from high school and home to college and a new living environment can be a fascinating and interesting time, made all the more challenging and interesting by being at MIT. More than recording the first semester through a series of snapshots, this freshman seminar will attempt to teach photography as a method of seeing and a tool for better understanding new surroundings. Over the course of the semester, students will develop a body of work through a series of assignments, and then attempt to describe the conditions and emotions of their new environment in a cohesive final presentation.

Students work through an online tutorial on MIT's App Inventor to learn how to create Android applications. Using those skills, they create their own applications and use them to collect data from an Android device accelerometer and store that data to databases. NOTE: Teachers and students must have a working knowledge of basic programming and App Inventor to complete this lesson. This lesson is not an introduction to MIT's App Inventor and is not recommended for use without prior knowledge of App Inventor to produce an end product. This lesson is an application for App Inventor that allows for the storage of persistent data (data that remains in memory even if an app is closed). This required prior knowledge can come from other experiences with the App Inventor. Also, many additional resources are available, such as tutorials from MIT. This lesson could also be used as an enrichment project for students who are self-motivated to learn the App Inventor software.

Students learn that wind and storms can form at the boundaries of interacting high and low pressure air masses. They learn the distinguishing features of the four main types of weather fronts (warm fronts, cold fronts, stationary fronts and occluded fronts) and how those fronts are depicted on a surface weather analysis, or weather map. Students also learn several different ways that engineers help with storm prediction, analysis and protection.

This book, revised as the Third Edition July 2019, is designed to teach contract doctrine beginning with the most fundamental concepts and building on these until the structure of contract doctrine as coherent and cohesive regulation appears. The order of presentation is, in fact, the order in which contract doctrine developed historically, but it is also, in general, the order in which arguments are introduced in litigation.

The book begins with the most basic, core concept of contract law—exchange. The book teaches exchange using simple cases drawn from the actual development of the exchange concept’s most obvious manifestation—the doctrine of consideration. These cases have basic but engaging facts. They do not take long to read, but they must be read carefully. They make an excellent introduction to law study.

Logically, every doctrine of contract formation is centered on whether and when a fair exchange occurred. In litigation, the plaintiff alleges a promise and consideration—an exchange (a plausible one, and therefore fair enough at that point). Defenses to formation are a response to the allegation that a fair exchange occurred. Allegations of both promise and consideration show that the defendant assented. As between assent and exchange, exchange is the more fundamental concept, but because the law talks so often about assent, assent is covered at length afterward so that the function of the assent doctrines is apparent.

Other doctrines, such as remedies (just an introduction in this first volume), waiver, seals, the Statute of Frauds, definiteness, and general public policy limitations are placed where students can best grasp their import in the context of the other doctrines.

Along the way, most of the doctrines in the book are repeated in the cases, questions, or in class discussion. This repetition cements understanding, builds trust, and also allows students to see how the doctrines mesh together to regulate coherently.

This book is intended for use in the first three-credit half of a six-credit course.