I say, well, let's grade about five or six of them, maybe ten of them, get a sense of it.
我说,我们给它们中的5或6道题打分了,也可能是10道,大概了解一下。
and I enjoy, like, solving proofs or, like, solving problems, but it's only one part of like, what I do, like as a person.
做证明题或者解决问题对我来说是一种享受,但这只是我生活的一部分而已。
And, that's a good thing to know because if you come out with an answer that's somewhere near the diameter of the universe and it's supposed to be the diameter of an atom, then you will know that you probably made a mistake.
这是我们需要知道的,因为当你做一道题得到的答案,是宇宙的直径,而正确答案是原子直径时,你能很快发现你的错误。
We're actually going to do one more clicker question to get started with today, and as we do, I'll explain something we're going to be trying today, which is a little bit of a friendly competition in terms of answering the clicker questions correctly.
我们将在开始讲授今天的课程之前,再多做一个选择题,我先来说明一下做这件事的原因,这实际上是一个,回答选择题的小比赛。
If you look at x 2 this one right here in your handout. OK.
课堂材料的第二题2,这是关于做乘方的另外一种方法。
I'll give this as an aside; they reduced the size of the newspaper in 2005.
这是题外话,他们在2005年缩减了版面
I want to derive the last result in another way, then I will stop, and that's pretty interesting because it tells you the use and abuse of calculus.
让我用其他方法解答最后一个问题,然后今天就到这 这是一个挺有意思的题,因为它展示了微积分的正确用法和错误用法
You're going to get these personality tests all the time and the personality tests-- You're applying for a business and " one of the tests says "I like to steal from my bosses " Well, I don't think so No That's a little IQ test right there ? So, the question is how do you avoid that problem?
你们以后会做很多这样的性格测试,例如:你求职时做性格测试,其中一题是“我想偷老板的东西“,不,我不会,这相当于一个智商测试,问题在于,你怎么避免那个问题?
And secondly, I think that, even if they don't know how to do a problem,
二是,我觉得,即使他们不知道怎么做一道题,
3 So here what I'm doing is 17 divided by 13, but because of this parenthetical, , -- because of that parenthetical -- that has nothing to do with math; -- this is a programming language thing -- that is a casting operation.
所以这里我要做的是用17除以,但因为这样的题外话,因为那样的题外话-,还是没有做完这个数学题;,这是一个编程语言的东西-,那是一个计算操作。
Which--I think this is a quiz question here, probably number five.
我认为这是一个要测验问题,也许是第五道题
Whether that would ever happen, if Pynchon had decided to let us in on the secret, I don't know. Pynchon, instead, chooses to end the novel before that moment, and so we're left with a kind of emptiness.
如果说Pynchon是想要,让这成为一个谜题的话,那我也不知道,究竟出现了,没有取而代之的是Pynchon选择了,在那一幕之前让小说戛然而止,让我们陷入了,一片空白之中。
And as a reminder, hopefully I don't need to remind any of you, but exam 1 is on Wednesday, so rather than our clicker question being on something from last class, which is exam 2 material, let's just make sure everyone remembers some small topic from exam 1 material, which is the idea of angular nodes.
而作为一个提醒--我希望大家都不需要提醒,但是这周三就要进行第一次考试了,因此我们的这个选择题,不是关于上节课内容的,那是第二次考试的内容,这里只是想确认大家都记得,第一次考试所要求的一些小问题,也就是关于角向节点的概念。
All you need is ten places to write yes or no.
只要写是或否就行,共10题。
So the problem I want to do-- there are many things you could do but I just picked one, and this is the one with round numbers, so I can do it without a calculator.
我想讲的这道题,类似的题目很多,但我就选了其中一个,这道题涉及的数字都是整数,所以我不需要计算器
This may sound like an aside, but this is all finance.
这听起来像是题外话,但的确是金融
So, here's magnesium. It's very light.
我们回到原题,这是镁,它很轻。
It's a huge puzzle.
这是一个大谜题。
This is another aside.
这是题外话
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