This task is part of a series presenting important foundational geometric results and constructions which are fundamental for more elaborate arguments. They are presented without a real world context so as to see the important hypotheses and logical steps involved as clearly as possible.

This task is designed to get at a common student confusion between the independent and dependent variables. This confusion often arises in situations like (b), where students are asked to solve an equation involving a function, and confuse that operation with evaluating the function.

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

This course is about solving complex problems. Our favorite problems are not just technically complex but also characterized by the presence of many different social actors that hold conflicting interests, objectives, and perceptions and act strategically to get the best out of a problem situation. This course offers guidance for policy analysts who want to assess if and how their analysis could be of help, based on the premise that problem formulation is the cornerstone in addressing complex problems. After this course, students would have obtained a theoretical insight into different models of decision-making processes, their implications in terms of supporting decision making and the potential roles that analysts; they can make a structured problem analysis in a complex situation, and can lay down their findings in an ‰"issue paper‰;" they know how to use a range of different methods and techniques to support attainment of these objectives; can formulate plans for a further analysis and closer examination, including the specification and the choice of possible mathematical models to be used.The completion of the practical part of this course will be an issue paper (written in pairs).

The course is a survey of models for analyzing and supporting design and decision-making in multi-actor settings. Participants: will learn to recognize the difference between games and decisions, and will identify their occurrence in public policy. will be able to apply a principled technique for resolving dilemmas through the appropriate selection of policies. will learn to formulate, design and communicate games and decisions. will learn to implement by computer (and otherwise logically analyze) games and decisions.

Analyzes the impact of trade and financial flows and regional integration on the domestic politics of advanced industrial states. Pressures for harmonization and convergence of domestic institutions and practices and the sources of national resistance to these are examined. Cases include European Union and West European states, US, and Japan. This is a graduate seminar for students who already have some familiarity with issues in political economy and/or European politics. The objective is to examine the ways in which changes in the international economy and the regimes that regulate it interact with domestic politics, policy-making, and the institutional structures of the political economy in industrialized democracies.

IThis course introduces students to the conduct of political research using quantitative methodologies. The methods are examined in the context of specific political research activities like public opinion surveys, voting behavior, Congressional behavior, comparisons of political processes in different countries, and the evaluation of public policies. Students participate in joint class projects and conduct individual projects.

This subject is designed for upper level undergraduates and graduate students as an introduction to politics and the policy process in modern Japan. The semester is divided into two parts. After a two-week general introduction to Japan and to the dominant approaches to the study of Japanese history, politics and society, we will begin exploring five aspects of Japanese politics: party politics, electoral politics, interest group politics, bureaucratic politics, and policy, which will be broken up into seven additional sections. We will try to understand the ways in which the actors and institutions identified in the first part of the semester affect the policy process across a variety of issues areas.

This graduate reading seminar explores the role of religious groups, institutions, and ideas in politics using social science theories. It is open to advanced undergraduate students with permission of the instructor.

This course is being offered in conjunction with the colloquium The Politics of Reconstructing Iraq, which is sponsored by MIT's Center for International Studies and Department of Urban Studies and Planning. Fundamentally, the course focuses on contemporary post-conflict countries (or in-conflict countries) and the role of planning and reconstruction in building nations, mitigating conflicts, reshaping the social, spatial, geopolitical, and political life, and determining the country's future.

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.

This video lecture looks at the painting techniques of Jackson Pollock: "One: Number 31, 1950". Abstract Expressionist New York. The Museum of Modern Art, October 3, 2--April 11, 2011. Filmed by Plowshares Media Images courtesy of Pollock-Krasner Foundation/Artists Rights Society (ARS), New York; and The Museum of Modern Art, New York. Music by Chris Parrello Chris Parrello, Ian Young, Kevin Thomas, Ziv Ravitz.

To gain a better understanding of the roles and functions of components of the human respiratory system and our need for clean air, students construct model lungs that include a diaphragm and chest cavity. They see how air moving in and out of the lungs coincides with diaphragm movement. Then student teams design and build a prototype face mask pollution filter. They use their model lungs to evaluate their prototypes to design requirements.

Students learn how a bill becomes law in the U.S. Congress and research legislation related to global warming.

To develop an understanding of modern industrial technologies that clean up and prevent air pollution, students build and observe a variety of simple models of engineering pollutant recovery methods: scrubber, electrostatic precipitator, cyclone and baghouse. In an associated literacy activity, students become more aware of global environmental problems and play a part in their solution by writing environmental action campaign letters.

Students take a close look at truss structures, the geometric shapes that compose them, and the many variations seen in bridge designs in use every day. Through a guided worksheet, students draw assorted 2D and 3D polygon shapes and think through their forms and interior angles (mental “testing”) before and after load conditions are applied. They see how engineers add structural members to polygon shapes to support them under compression and tension, and how triangles provide the strongest elemental shape. A PowerPoint® presentation is provided. This lesson prepares students for two associated activities that continue the series on polygons and trusses.

Students learn about the role engineers play in designing and building truss structures. Simulating a real-world civil engineering challenge, student teams are tasked to create strong and unique truss structures for a local bridge. They design to address project constraints, including the requirement to incorporate three different polygon shapes, and follow the steps of the engineering design process. They use hot glue and Popsicle sticks to create their small-size bridge prototypes. After compressive load tests, they evaluate their results and redesign for improvement. They collect, graph and analyze before/after measurements of interior angles to investigate shape deformation. A PowerPoint® presentation, design worksheet and data collection sheet are provided. This activity is the final step in a series on polygons and trusses.

This art history video discussion examines Polykleitos' "Doryphoros (Spear-Bearer)," Roman marble copy after a Greek bronze original from c. 450-440 B.C.E. (Museo Archaeologico Nazionale, Naples).

Overview of engineering analysis and design techniques for synthetic polymers. Treatment of materials properties selection, mechanical characterization, and processing in design of load-bearing and environment-compatible structures.