Thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems. 18.310 helpful but not required.

Content varies from year to year. An introduction to some of the major topics of present day combinatorics, in particular enumeration, partially ordered sets, and generating functions. This is a graduate-level course in combinatorial theory. The content varies year to year, according to the interests of the instructor and the students. The topic of this course is hyperplane arrangements, including background material from the theory of posets and matroids.

Content varies from year to year. An introduction to some of the major topics of present day combinatorics, in particular enumeration, partially ordered sets, and generating functions. This course serves as an introduction to major topics of modern enumerative and algebraic combinatorics with emphasis on partition identities, young tableaux bijections, spanning trees in graphs, and random generation of combinatorial objects. There is some discussion of various applications and connections to other fields.

In this lesson, students will first be introduced to adding two constant functions graphically to develop an understanding of how to add two functions together.  Next students will add a constant function to a linear function and discover how that translates the graph of the linear function.  Students will also begin building the connection between the graphical sums and algebraic sums.  Students will be exposed to adding two linear functions together graphically before function notation is introduced.  Students will also be exposed to adding a constant and exponential function together as exponential functions are a key function type in Secondary Math 1.   Lastly, students will be challenged with adding a linear function and quadratic function together.  Students will make the connection that adding a linear function and quadratic function together will result in a quadratic function.

The primary purpose of this problem is to rewrite simple rational expressions in different forms to exhibit different aspects of the expression, in the context of a relevant real-world context (the fuel efficiency of of a car).

The primary purpose of this problem is to rewrite simple rational expressions in different forms to exhibit different aspects of the expression, in the context of a relevant real-world context (the fuel efficiency of of a car). Indeed, the given form of the combined fuel economy computation is useful for direct calculation, but if asked for an approximation, is not particularly helpful.

Students investigate the products of a combustion reaction. Students will learn tests to identify gases.

The Folger Shakespeare Library provides the full searchable text of "The Comedy of Errors" to read online or download as a PDF. All of the lines are numbered sequentially to make it easier and more convenient to find any line.

This inquiry kit features Library of Congress sources relating to the major political parties in colonial America.

Visualize how comets carrying chemicals necessary for life could have made their way to Earth billions of years ago in this video segment adapted from NOVA.

Amino acids, essential ingredients for life, may have been delivered to Earth by comets billions of years ago, as visualized in this video segment adapted from NOVA.

The Comic Creator invites students to compose their own comic strips for a variety of contexts (prewriting, pre- and postreading activities, response to literature, and so on).

Multidimensional, challenging, and popular with students, comics provide an excellent way to introduce the concept of genres.

This lesson uses comic strip frames to define plot and reinforce the structure that underlies a narrative. Students finish by writing their own original narratives.

The Apollo 11 Command Module, "Columbia," was the living quarters for the three-person crew during most of the first manned lunar landing mission in July 1969. This 3D image from Google Arts & Culture site allows students to view the Apollo 11 Command Module in augmented reality. Augmented Reality allows you to project 3D models into the real world through the camera on your mobile device. This image is best viewed in the Google Arts & Culture mobile app.

In this keyboarding lesson, students practice typing commas, periods, and capitals using Typesy. At the start of each lesson, students set a goal and consider the importance of keyboarding. At the end of the lesson, students record their WPM.

September 17th is Constitution Day, commemorating the day in 1787 when, at the end of a long hot summer of discussion, debate and deliberation, the delegates to the Constitutional Convention signed America's most important document.

Committees improve the organization of the Senate and House of Representatives. Members of Congress cannot be experts on all issues. For this reason, the Senate and House of Representatives developed committees that focus on particular subjects.

Julie Motta walks through a read-aloud activity for first grade and highlights how she engaged the students with the story, brought in content-area connections, and included informal assessment to check comprehension.

This article describes common misconceptions held by elementary students about the history of the polar regions, fossils, and geologic time. The article provides ideas for formative assessment, teaching strategies, and the National Science Education Standards.