Without worrying about the economics of it a second, how would we find that just as a math exercise?

不需要考虑经济学的理论,用数学的方法怎么来求解啊

耶鲁公开课 - 博弈论课程节选

and how using your knowledge of math can help you solve something in biology.

如何用数学方面的知识解决生物方面的问题。

与教授的面谈 - SpeakingMax英语口语达人

That's going to presumably be given--mathematically if we gave it a number, we'd slap a zero on that.

如果用数学解释,给它一个数字，给它一个零。

耶鲁公开课 - 死亡课程节选

So this is a little bit of math, a little formality, but is everyone okay with that?

这里只是稍微用了点数学符号,还有简单的公式,大家都听懂了吗

耶鲁公开课 - 博弈论课程节选

And this is one of the times when you are actually going to be able to use some of that math they teach you.

这就是时候,用他们教你的,数学知识了。

麻省理工公开课 - 固态化学导论课程节选

What that means is that one way to describe that mathematically is shown here.

用数学方式对此的表达,显示如下

耶鲁公开课 - 生物医学工程探索课程节选

So, if you feel there's not enough math used, I guarantee you that I certainly know enough eventually to snow the whole class, but that's not the point.

如果你觉得我用的数学太少,我可以保证,我知道的数学知识,足以难倒在座的所有人,但这不是重点

耶鲁公开课 - 基础物理课程节选

There're also changes of what you can teach, extends what you can teach, because you can get to concept which are really quite sophisticated that you will never teach it at the introductory level, because the math is the least that you can make it quantitatively, because you have a visualization that shows physically what's going on.

同时这也能改变,教学内容，你能教授的程度，因为你可以定义,那些通常很难的,你在入门阶段都不会遇到的,抽象阶段，因为数学是你最不能,用定量手段来解决的，因为你有一个直观过程,知道什么正在进行。

麻省理工公开课 - 媒体、教育、市场课程节选

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

he knows how to mathematically structure the problem,

他知道如何用数学思维分析问题的结构，

有印象的教授 - SpeakingMax英语口语达人

So, what we're dealing here with is a situation where the ancient Greeks were very much into mathematics as a way of explaining the world and explaining music in particular And they thought these ratios were primary.

那么,我们现在要潜心琢磨,古希腊人热衷于,用数学来解释世界,尤其是音乐的这种情形,他们认为这些比例才是基础

耶鲁公开课 - 聆听音乐课程节选

What mathematicians are doing is using their mind to think about these Platonic ideas of mathematics.

数学家所做的就是用他们的心灵,来思考那些数学的柏拉图理念

耶鲁公开课 - 死亡课程节选

So very similar idea, but the only thing is, I'm slightly abusing notation here by saying that my payoff depends on my strategy and a belief, but what I really mean is my expected payoff.

这和以前的概念差不多,唯一的不同,就是我这里稍微用了一些数学符号,来表述策略带来的收益与所持信念有关,这里的收益指的是预期收益

耶鲁公开课 - 博弈论课程节选

The way the physics works is you will find some laws of motion in mathematical form, you put in the initial conditions of whatever, you solve the equations, and the answer that comes, you have no choice.

在物理问题中,你可以用数学方法得到运动定律,你代入初始条件,然后解方程,获得答案,你别无选择

耶鲁公开课 - 基础物理课程节选

Therefore, mathematically at a given time t, we can trade t for v and put it into this formula.

因此,从数学角度来说,在给定的时刻 t,我们可以用 v 来表示 t,并代入这个式子

耶鲁公开课 - 基础物理课程节选

We have some smaller courses which are very mathematic form, which will not be taught in this format.

我们还有一些和数学,非常相关的小型课程，将不会用这种方式。

麻省理工公开课 - 媒体、教育、市场课程节选

I will use it in moderation and use it to the best effect possible rather than use it because it is there.

我会适量的运用数学以达到最佳的效果,而不是为了数学而用数学

耶鲁公开课 - 基础物理课程节选

But in thinking about math, most of us are inclined to be Platonists.

但在用数学的方式进行思考时,我们都倾向于变成柏拉图主义者

耶鲁公开课 - 死亡课程节选

Again, for the math phobics in the room, don't panic, this is just writing down in words what we've already seen a couple of times already today, well today and last time.

在座的有数学恐惧症的同学不必惊慌,这仅仅是用数学表达式来表示,我们今天学到的一些知识点罢了,其实是这一讲和上一讲的知识点

耶鲁公开课 - 博弈论课程节选

There are others who like to show you how much mathematics you could somehow insinuate into the process.

还有些人喜欢跟你炫耀数学用的多,尽管过程显得非常繁琐

耶鲁公开课 - 基础物理课程节选

Mine is to demonstrate over and over how little mathematics you need to get the job done.

我的方法就是,反复演算,用最少的数学来解决问题

耶鲁公开课 - 基础物理课程节选

So I'm going to find for you this result using calculus in a different way.

我将为你们展示,用不同数学方法得到的结果

耶鲁公开课 - 基础物理课程节选

As I suggested in talking about the example of math last time, it's not a silly view, even if it's not a view that we all take automatically.

就像我上次用数学举例一样,即便这不是一个我们都能接受的观点,这也不一定是个愚蠢的观点

耶鲁公开课 - 死亡课程节选

We prove things in mathematics that have never been proven before or we find new ways to prove these theorems or what have you and we can be creative.

我们用数学去证明从未被证明过的事物,我们探寻新的方法去证明那些定理,或其他诸如此类,总之,我们具有创造力

耶鲁公开课 - 死亡课程节选