The scope of this video lesson consists in studying the sets of Rational and Irrational numbers. It is best suited for an advanced math course: Algebra 2 or higher.

Aims to develop a teaching knowledge of the field through extensive reading and discussion of major works. The reading covers a broad range of topics -- political, economic, social, and cultural -- and represents a variety of historical methods. Students make frequent oral presentations and prepare a 20-page review essay.

This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. MIT students may choose to take one of three versions of Real Analysis; this version offers three additional units of credit for instruction and practice in written and oral presentation.The three options for 18.100:Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible.Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology.Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication. This fulfills the MIT CI requirement.  

This video aims to provide an illustrative lesson about the respiratory system in birds and how the adaptations of that system over time have made it different than that of other living creatures, especially mammals. Birds are omnipresent in our lives, and students will come to understand and appreciate the fascinating inner workings of these beautiful creatures. This lesson discusses avian features and differences for 20 to 25 minutes, with approximately 20 minutes of in-class student activities.

This course uses readings and discussions to focus on a series of short-term events that shed light on American politics, culture, and social organization. It emphasizes finding ways to make sense of these complicated, highly traumatic events, and on using them to understand larger processes of change in American history. The class also gives students experience with primary documentation research through a term paper assignment.

This subject introduces the history of science from antiquity to the present. Students consider the impact of philosophy, art, magic, social structure, and folk knowledge on the development of what has come to be called "science" in the Western tradition, including those fields today designated as physics, biology, chemistry, medicine, astronomy and the mind sciences. Topics include concepts of matter, nature, motion, body, heavens, and mind as these have been shaped over the course of history. Students read original works by Aristotle, Vesalius, Newton, Lavoisier, Darwin, Freud, and Einstein, among others.

The topic of photosynthesis is a fundamental concept in biology, chemistry, and earth science. Educational studies have found that despite classroom presentations, most students retain their naive idea that a plant's mass is mostly derived from the soil, and not from the air. To call students' attention to this misconception, at the beginning of this lesson we will provide a surprising experimental result so that students will confront their mental mistake. Next, we will help students better envision photosynthesis by modeling where the atoms come from in this important process that produces food for the planet. This lesson can be completed in 50-60 minutes, with the students working on in-class activities during 20-25 minutes of the lesson. As a prerequisite, students need an introductory lesson on photosynthesis, something that includes the overall chemical equation. If students have already studied the intracellular photosynthetic process in detail, this video can still be very helpful because students often miss the big picture about photosynthesis. Materials needed include red, white and black LEGO bricks (described in downloadable hand-out) or strips of red, white and black paper plus paper clips (directions provided in downloadable hand-out). In addition to class discussions, the major in-class activity of this video involves the students' modeling with LEGO bricks or colored paper where the atoms come from in photosynthesis.

This calculus course covers differentiation and integration of functions of one variable, and concludes with a brief discussion of infinite series. Calculus is fundamental to many scientific disciplines including physics, engineering, and economics.

There are many misconceptions about the chemistry concept, “Conservation of Mass”. Thus, the aim of this video lesson is to teach students about the chemical concept of Conservation of Mass through several chemistry experiments. The students will carry out experiments while assisting a fortune teller named Pak Belalang to gain victory for his kingdom. In an effort to help Pak Belalang, students should be able to answer all the questions related to the Conservation of Mass that are posed by an evil witch. In this video, materials such as a box of matches, a closed and open container, a box of panadol soluble tablets (Alka-Seltzer), and weighing scales are needed. At the end of the lesson, students will be able to see that mass is “conserved”. The lesson will take up to 60 minutes to complete.

Part One of this video lesson will explore the science that explains soap bubbles, as well as the application of this knowledge to other areas, such as architecture and biology. We first introduce the concept of surface tension. In Part Two of this video lesson, students will learn where the colors of soap bubbles come from and also learn what soap bubbles and telescopes have in common. The students will first make a connection between light and waves waves and will then go on to explore various characteristics of waves through a series of classroom activities.

This subject exposes students to a variety of visualization techniques so that they learn to understand the work involved in producing them and to critically assess the power and limits of each. Students concentrate on areas where visualizations are crucial for meaning making and data production. Drawing on scholarship in science and technology studies on visualization, critical art theory, and core discussions in science and engineering, students work through a series of case studies in order to become better readers and producers of visualizations.

In this undergraduate level seminar series topics vary from year to year. Students present and discuss the subject matter, and are provided with instruction and practice in written and oral communication. Some experience with proofs required. The topic for fall 2008: Computational algebra and algebraic geometry.

Seminar for mathematics majors. Students present and discuss the subject matter and write up exercises. Topic for Fall 2002: Classical geometry, beginning with Euclid's Elements and continuing to applications of Galois theory that solve the geometry problems of antiquity. No prior knowledge of Galois theory required. Instruction and practice in oral communication provided.

Seminar for mathematics majors. Students present and discuss the subject matter, taken from current journals or books. Topics vary from year to year. Topic for Fall 2002: Quantum calculus. Instruction and practice in oral communication provided.

This course is a seminar in topology. The main mathematical goal is to learn about the fundamental group, homology and cohomology. The main non-mathematical goal is to obtain experience giving math talks.

This is an advanced topics course in model theory whose main theme is simple theories. We treat simple theories in the framework of compact abstract theories, which is more general than that of first order theories. We cover the basic properties of independence (i.e., non-dividing) in simple theories, the characterisation of simple theories by the existence of a notion of independence, and hyperimaginary canonical bases.

Flying kites is a popular hobby in Malaysia and very much part of the culture. This lesson looks at kite flying science to introduce basic ideas related to the dynamics of kite flying and can be used as an extension of a physics lesson, especially after the students have learned about forces. It will focus on some of the concepts such as weight, thrust, lift and drag. It is a fun way to introduce the forces acting upon a kite and the scientific principles that allow a kite to fly. The lesson is suitable for students in secondary school. It will help students relate to the effect of forces and gives an introduction to the science of flight. As an added value, the video will also share some information about Malaysian kites which are “tailless”. The Malaysian kite is called “Wau” (pronounced “wow”), and there are many distinctive designs since each Malaysian state has its own official Wau. Malaysia has 14 states. The break activities included are to be conducted in the classroom, and students are to work in small groups on the questions given in the lesson. Students are to carry out two simple experiments to study how air flows on a kite.

Spanish I is very different from other classes at MIT. The central component of the text and workbook is a series of 26 half-hour video episodes. The videos allow students to learn authentic Spanish and experience its cultural diversity while following a good story full of surprises and human emotions. Students also listen to an audio-only program integrated with the text and workbook.

Spanish II continues to develop students' listening, speaking, reading and writing skills using the second part of the video-based program, Destinos, begun in Spanish I. Destinos is a soap opera that allows students to learn Spanish and experience its cultural diversity while following a good story full of surprises and human emotions. Spanish II also includes additional materials, such as Spanish films and other media, various types of reading selections and online resources.

The participants in this seminar will dive into learning basic conversational Italian, Italian culture, and the Mediterranean diet. Each class is based on the preparation of a delicious dish and on the bite-sized acquisition of parts of the Italian language and culture. A good diet is not based on recipes only, it is also rooted in healthy habits and in culture. At the end of the seminar the participants will be able to cook some healthy and tasty recipes and to understand and speak basic Italian.