Open course ware

HODGES: The basic goal of 12.000 is to provide freshman at MIT with an opportunity to put together concepts and ideas that they get in a more formal way, in particular in the science core at MIT in their first year and put those in turn together with social issues, fundamental social issues in the context of big environmental problems. The subject changes from year to year in terms of its theme. We tend to focus on different areas at different times. But, on the other hand, the overarching goal is to have them think about how you approach really complicated problems that require multiple perspectives and don't necessary have any simple solutions. I mean most of the problems that they tend to deal with, in the other subjects that they take in the freshman year, have straightforward known solutions. So it's like taking a problem set, working on it and solving those problems in particular. But most of the problems that really keep you awake at night are not those kin...

PROFESSOR: Another basic proof technique is called Proof By Cases, which we prove something by breaking it up into pieces that are easy to prove but that together cover all possibilities. Let's look at an explicit, simple example from computer science. Here's a Java logical expression. The way to decipher this is that the double vertical bar means "or" in Java. And the double ampersand means "and" in Java. So this is a conditional test, an IF test, that is the guard on a bunch code to be executed if this test comes out to be true. Let's read the test. If x is greater than 0, or x is less than or equal to 0, and y is greater than 100, go ahead and do the code that's in there indicated by the vertical dots. We're going to assume here that x and y are variables that are declared to be of type floating point, [? or a ?] real number, or integers for that matter. OK. Now what I claim is this code can be improved if it's rewritten in t...