- But there's one potential gotcha here -- and this is where you have to be kind -- of piecing together the little clues along the way -- what have I done that's interesting here that had I not, I would have had a mathematical error?

但是这里有一个可能性-,这就是你需要把,一些线索拼凑在一起-,我这里所做的是很有趣的，如果我不这样做，我可能已经犯了个数学错误？

哈佛公开课 - 计算机科学课程节选

I'll show those again, but what I want to do mostly today is try to put a mathematical statement of the second law in place that corresponds to the verbal statements that we saw last time.

今天我还将跟你们讲这些，但今天的重点是,对上次口头表述内容中的热力学,第二定律,的数学推导,我们上次看到的。

麻省理工公开课 - 热力学与动力学课程节选

So, what we are going to study now is a non-living object and we're going to pick it to be a mathematical point.

我们现在所要研究的的,是一个没有生命的物体,我们要把它看作一个数学上的点

耶鲁公开课 - 基础物理课程节选

John is a mathematical economist and we both love mathematics, but maybe John is going to do more of it than I am.

约翰是个数理经济学家,我们都热爱数学,但是约翰会讲授更多关于数学的内容

耶鲁公开课 - 金融市场课程节选

The answer was, find a mathematical expression depending on the number of inputs.

很不错，答案是，找到一个通过输入数字,计算出来的数字表达式。

麻省理工公开课 - 计算机科学及编程导论课程节选

It's a mathematical thing too.

那也和数学有关

耶鲁公开课 - 聆听音乐课程节选

So the mathematical notions of infinity or logical notions like logical entailment are beyond a child of this age.

因此,对于无限这个数学概念,或者是,像逻辑蕴涵这样的逻辑概念,超出了该年龄阶段儿童的理解范围

耶鲁公开课 - 心理学导论课程节选

He now has super-human mathematical talent, can read and remember the contents of an encyclopedia volume in a few minutes, and speak a language fluently after reading one textbook.

他现在有超过人类的数学能力，能阅读,能在几分钟内记住百科全书的内容,通过阅读一本教科书就可以,流利地讲一门语言了。

哈佛公开课 - 计算机科学课程节选

Second thing I would say that was valuable "Thank goodness, I did one year at Stanford Business School and learned how to read a balance sheet and understand the basics of cost accounting which is not mathematical rocket science.

我要说的第二件事是很重要的,感谢上苍，我在斯坦福商学院学了一年,学会了怎么看资产平衡表，知道恶劣,成本会计的基本知识。

斯坦福公开课 - 微软CEO-Steve.Ballmer谈科技的未来课程节选

In the second lecture, I talked about the pooling of risks and the basic theme of that lecture was that we now have a mathematical theory, probability theory.

第二课，我讲了风险汇聚及分摊,那节课的主题是,一门数学理论，即概率论。

耶鲁公开课 - 金融市场课程节选

I cannot make the object simpler than being just a mathematical point.

找不到比质点更简单的模型了

耶鲁公开课 - 基础物理课程节选

So the object is a mathematical point.

这个物体就是一个数学意义上的点

耶鲁公开课 - 基础物理课程节选

The second law is going to define entropy, and is going to tell us about the direction of time, something that conceptually we, clearly, understand but is going to put a mathematical foundation on which way does time go.

第二定律定义了熵，它告诉我们,时间的流向，虽然我们清楚地,知道这个概念,但还是要为时间流动的方向,建立一个数学基础。

麻省理工公开课 - 热力学与动力学课程节选

So I don't know your mathematical background, but the textbook has an appendix, which is a reasonable measure of how much math you should know.

我不太清楚你们的数学功底,但教材上有附录,它能清楚地告诉你,你应该掌握多少数学

耶鲁公开课 - 基础物理课程节选

I want to talk about Kahneman and Tversky's Prospect Theory, which is a very important and a little technical-- psychologists can become mathematical and technical as well.

我会谈到,卡尼曼和特维斯基的前景理论,这是很重要的理论,同时需要一定的数学计算,心理学家也可以精于计算,和擅用技巧

耶鲁公开课 - 金融市场课程节选

That's, there are whole courses on that, there's some great courses here on that, it takes some mathematical sophistication, we're going to push that off a little bit.

有一些课程是专门讲这个的，那些课一般都涉及，一些复杂的数学问题，我们只是简单的讲一些基础知识。

麻省理工公开课 - 计算机科学及编程导论课程节选

If you look at John Geanakoplos's course on Financial Theory, his mathematical concepts are central to his outline of the course; but this being a Financial Markets course, I'm dividing it up more in terms of markets and institutions.

如果你们听约翰·吉纳科普洛斯的,金融理论课,他的大纲中心部分,是金融学中的数学概念,而我们这是金融市场课,于是我从金融市场和,金融机构的角度来划分这一课

耶鲁公开课 - 金融市场课程节选

In that autistic people show no impairments dealing with the physical world, they show no impairments on-- they don't necessarily show any impairments on mathematical skills or spatial skills, but they have a lot of problems with people.

因为孤独症患者并未表现出生理上的缺陷,所以他们并不会在数学技能或空间技能上,表现出什么缺陷,但他们却在人际交往方面存在很多问题

耶鲁公开课 - 心理学导论课程节选