And all this is, is saying that when you take a mixed second derivative, it doesn't matter in which order you take the two derivatives.

麦克斯韦关系的本质是,当你考虑混合的二阶导数时，求导的顺序不影响最后的结果,现在，我们利用这些关系。

麻省理工公开课 - 热力学与动力学课程节选

And check the answers, and say yeah that's what we expected. But it also involves reasoning. About why that's an appropriate set of inputs to test it on it.

然后说对，这就是我想要的结果,但是它跟推理也有关系,表现在关于为什么这是一个,测试我们程序的适合的输入集。

麻省理工公开课 - 计算机科学及编程导论课程节选

You know that you're not going to decide the election, so what does it matter?

你知道你并不能决定选举结果,那投票还是不投票又有什么关系

耶鲁公开课 - 金融市场课程节选

Independent experiments are experiments that occur without relation to each other.

独立试验的概念就意味着每一个试验,和其他试验的结果没有关系

耶鲁公开课 - 金融市场课程节选

That's the question we're going to try and address. If we can do this, this is good, because first of all, it removes any questions about what machine I'm running on, it's talking about fundamentally, how hard is this problem, and the second thing is, it is going to do it specifically in terms of the input. Which is one of the things that I was worried about.

这是一个我们接下来要去,尝试和解决的问题，如果我们能做到的话会很不错，因为首先，它解决了结果可能和我,运行的计算机有关系的问题，因为这从根本了告诉了，我们这个问题的复杂度，第二件事情,就是这种方法可以依据输入的大小来计算,而这正是我最担心的地方。

麻省理工公开课 - 计算机科学及编程导论课程节选