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.

Steps to Success: Crossing the Bridge Between Literacy Research and Practice introduces instructional strategies linked to the most current research-supported practices in the field of literacy. The book includes chapters related to scientifically-based literacy research, early literacy development, literacy assessment, digital age influences on children’s literature, literacy development in underserved student groups, secondary literacy instructional strategies, literacy and modern language, and critical discourse analysis. Chapters are written by authors with expertise in both college teaching and the delivery of research-supported literacy practices in schools. The book features detailed explanations of a wide variety of literacy strategies that can be implemented by both beginning and expert practitioners. Readers will gain knowledge about topics frequently covered in college literacy courses, along with guided practice for applying this knowledge in their future or current classrooms. The book’s success-oriented framework helps guide educators toward improving their own practices and is designed to foster the literacy development of students of all ages.

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.

The lectures are at a beginning graduate level and assume only basic familiarity with Functional Analysis and Probability Theory. Topics covered include: Random variables in Banach spaces: Gaussian random variables, contraction principles, Kahane-Khintchine inequality, Anderson’s inequality. Stochastic integration in Banach spaces I: γ-Radonifying operators, γ-boundedness, Brownian motion, Wiener stochastic integral. Stochastic evolution equations I: Linear stochastic evolution equations: existence and uniqueness, Hölder regularity. Stochastic integral in Banach spaces II: UMD spaces, decoupling inequalities, Itô stochastic integral. Stochastic evolution equations II: Nonlinear stochastic evolution equations: existence and uniqueness, Hölder regularity.

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 engineer a working pair of shin guards for soccer or similar contact sport from everyday materials. Since many factors go into the design of a shin guard, students follow the Engineering Design Process to create a prototype. Along the way, students keep a notebook documenting each stage of the process and reflect on what their learned during the design.

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.

This book is a companion volume to Volume I, "The Story of Contract Law: Formation." Volume I introduces students to law study and teaches basic doctrines of contract formation along with formation defenses. This book, Volume II, The Story of Contract Law: Implementing the Bargain, covers the rest of basic contract doctrine, namely, laws that
1) determine the content of the bargain (plain meaning, usage and custom, good faith, mistake in transmission, parol evidence, and express and constructive conditions);
2) govern the effect of events that occur after formation (impracticability, frustration, failure of consideration, and risk of loss);
3) set remedies—rescission, damages, specific performance—available to courts when liability exists; and
4) establish the rights of third parties in contracts by assignment or delegation or as third-party beneficiaries.

This book includes many classic teaching cases and introduces new ones. The book also includes many problems, most based on actual cases. The book takes especial care with the doctrine of concurrent conditions, a common-law rule adopted in the late 1700s that required doctrinal readjustment across all the law governing contract performance and remedies.

This volume also continues several themes from Volume I. Volume II continues to tie rules to contract law’s central structural idea, that of fair exchange. Also, to the extent helpful to student understanding, Volume II explains doctrines in part through their chronological development. The book introduces the doctrines in the order best conducive to students’ understanding contract law as a regulatory whole; for this volume, it is the order in which the doctrines arise in litigation. Finally, where possible, this volume repeats ideas at helpful points and suggests ties between doctrines so that the structural coherence of contract doctrine becomes easier to understand.

History of the development of antitoxin for the first cure for a bacterial disease, diphtheria.

Some of the most the most essential works of literature in the world are examples of epic poetry, such as The Odyssey and Paradise Lost. This lesson introduces students to the epic poem form and to its roots in oral tradition.