Name: Lec 3｜MIT 6.042J コンピュータサイエンスのための数学, 2010年秋学期 (Lec 3 | MIT 6.042J Mathematics for Computer Science, Fall 2010)
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a proof is going to have seven characteristics

Good proofs are correct-- that's obviously important--

complete-- you've got to have all the details there.

They should be clear so we can understand what's going on.

You don't want to crush somebody with all the details.

You want to get to the key points, and be crisp.

It's the mathematician's notion of beauty.

Like you go to the art museum, and the artists will say,

In mathematics, you say, wow, that's an elegant proof.

you can get from a mathematician, anyway.

And there's a lot of judgment that goes into that.

Sometimes you'll see proofs where things are

All the pieces are there, but they're in the wrong order.

Sometimes-- and they teach this in some high schools--

And the classic thing there is, say you're

Well, the proof sometimes will start with what

and you'll write a check, because you went

It can be correct if the implications go this way.

Because really, you're starting with a fact-- 1 equals 1--

So if, in fact, the implications work this way,

But most people, especially as you get farther along,

So don't use this technique, because it'll confuse people.

Just start with 1 equals 1 and work your way from there--

Now, good proofs are very much like good code.

In fact, one of the reasons we care so much about teaching you

how to write a good proof in computer science

is so that later on, you'll be able to prove

that your programs are doing what you expect-- what they're

Now, there are many famous examples where programs did not

The Airbus A300 was one of the first commercial jets totally

It could take off, fly, and land totally by software.

It was a major advance in the airline industry.

the software accidentally opened the rear door just

It was the first plane crash in commercial history because

There's a famous radiation device for cancer patients

It's famous because it got into a race condition

to just slam the patient with radiation-- so much so,

And they had multiple examples of this, and of course,

How many of you all remember the 2000 election?

OK, this will probably be the last class that remembers that.

But that's where Al Gore was going up against George Bush--

very close election-- all came down to recounting

But in fact, Al Gore got negative 16,000 votes

I think they got rid of a lot of them in the election

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Lec 3｜MIT 6.042J コンピュータサイエンスのための数学, 2010年秋学期 (Lec 3 | MIT 6.042J Mathematics for Computer Science, Fall 2010)

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