What's it like to do mathematical research? The "Project Laboratory in Mathematics" course from MIT's OpenCourseWare provides some fine insights into this endeavor. The course was originally developed by Professor Haynes Miller and features information about how to help students "explore puzzling and complex mathematical situations." The site includes selected video lectures from the course, instructor insights, and a selection of projects and examples, such as "The Dynamics of Successive Differences Over Z and R." Also, the site includes information on how to customize this course for a variety of settings, along with examples of classroom activities and helpful resources.

"1.040 Project Management focuses on the management and implementation of construction projects, primarily infrastructure projects. A project refers to a temporary piece of work undertaken to create a unique product or service. Whereas operations are continuous and repeating, projects are finite and have an end date. Projects bring form or function to ideas or need. Some notable projects include the Manhattan Project (developing the first nuclear weapon); the Human Genome Project (mapping the human genome); and the Central Artery Project (Boston's "Big Dig"). The field of project management deals with the planning, execution, and controlling of projects. The course is divided into three parts: Part 1: project finance Part 2: project evaluation Part 3: project organization This course will cover the basic tools, skills, and knowledge necessary to successfully manage a project through its inception, design, planning, construction, and transition phases. There will be several guest lectures discussing current projects, and a construction site visit to MIT's Media Lab extension."

Examines alternative economic, political, and social perspectives of property rights and their policy and planning implications. Focuses on institutional and governance structures, power and control mechanisms, distributional consequences of different property rights arrangements, and problems of incomplete contracts as presented in theory and practice. Deals with property-rights issues related to two or more of the following: land, natural resources, infrastructure, or industrial organization.

Seminar covering topics of current interest in biology. Includes reading and analysis of research papers and student presentations. Contact Biology Education Office for topics. 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. The instructor for this course, Dr. Kosinski-Collins, is a member of the HHMI Education Group. Maintenance of the complex three-dimensional structure adopted by a protein in the cell is vital for function. Oftentimes, as a consequence of environmental stress, genetic mutation, and/or infection, the folded structure of a protein gets altered and multiple proteins stick and fall out of solution in a process known as aggregation. In many protein aggregation diseases, incorrectly folded proteins self-associate, forming fiber-like aggregates that cause brain cell death and dementia. In this course, the molecular and biochemical basis of the prion diseases, which include bovine spongiform encephalopathy (mad cow disease), Creutzfedt-Jakob disease and kuru will be examined. Also discussed are other classes of misfolding diseases such as Alzheimer's disease and Huntington's disease. The proteins involved in all of these disorders and how the proteins' three dimensional structures change during the course of these afflictions is covered as well as why prions from certain species cannot infect animals from other species based on protein sequence and structure. The course will then address possible detection methods and therapies that are under development to treat some of the protein aggregation diseases.

For students and teams who have started a sustainable-development project in D-Lab (SP.721, SP.722), the IDEAS Competition, Design for Demining (SP.786), Product Engineering Processes (2.009), or elsewhere, this class provides a setting to continue developing projects for field implementation. Topics covered include prototyping techniques, materials selection, design-for-manufacturing, field-testing, and project management. All classwork will directly relate to the students' projects, and the instructor will consult on the projects during weekly lab time. There are no exams. Teams are encouraged to enroll together.

In the past building prototypes of electronic components for new projects/products was limited to using protoboards and wirewrap. Manufacturing a printed-circuit-board was limited to final production, where mistakes in the implementation meant physically cutting traces on the board and adding wire jumpers - the final products would have these fixes on them! Today that is no longer the case, while you will still cut traces and use jumpers when debugging a board, manufacturing a new final version without the errors is a simple and relatively inexpensive task. For that matter, manufacturing a prototype printed circuit board which you know is likely to have errors but which will get the design substantially closer to the final product than a protoboard setup is not only possible, but desirable. In this class, you'll learn to design, build, and debug printed-circuit-boards.

Examines evidence (and lack thereof) regarding when and how an individual's thoughts, feelings, and actions are affected by gender. Topics include: gender development; gender differences in cognition and emotion; gender stereotypes; how gender is related to physical and mental health, sexuality, close relationships, and work.

This course covers theory and evidence on government taxation policy. Topics include tax incidence, optimal tax theory, the effect of taxation on labor supply and savings, taxation and corporate behavior, and tax expenditure policy.

Theory and evidence on government expenditure policy. Topics include the theory of public goods; education; state and local public goods; political economy; redistribution and welfare policy; social insurance programs such as social security and unemployment insurance; and health care policy.

Explores the role of government in the economy, applying tools of basic microeconomics to answer important policy questions such as government response to global warming, school choice by K-12 students, Social Security versus private retirement savings accounts, government versus private health insurance, setting income tax rates for individuals and corporations.

This course will examine public opinion and assess its place in the American political system. The course will emphasize both how citizens' thinking about politics is shaped and the role of public opinion in political campaigns, elections, and government.

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 ability to quantify the uncertainty in our models of nature is fundamental to many inference problems in Science and Engineering. In this course, we study advanced methods to represent, sample, update and propagate uncertainty. This is a "hands on" course: Methodology will be coupled with applications. The course will include lectures, invited talks, discussions, reviews and projects and will meet once a week to discuss a method and its applications.

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.

Subject assesses the relationships between sequence, structure, and function in complex biological networks as well as progress in realistic modeling of quantitative, comprehensive functional-genomics analyses. Topics include: algorithmic, statistical, database, and simulation approaches; and practical applications to biotechnology, drug discovery, and genetic engineering. Future opportunities and current limitations critically assessed. Problem sets and project emphasize creative, hands-on analyses using these concepts.

Principles of mass transport and electrical signal generation for biological membranes, cells, and tissues. Mass transport through membranes: diffusion, osmosis, chemically mediated, and active transport. Electric properties of cells: ion transport; equilibrium, resting, and action potentials. Kinetic and molecular properties of single voltage-gated ion channels. Laboratory and computer exercises illustrate the concepts. For juniors and seniors. Students engage in extensive written and oral communication exercises.