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This is an abstract and powerful mathematical statement of the first law of thermodynamics.
这是热力学第一定律的一个抽象,而且具有很强数学性的表述。
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A lot of mathematics majors go into that, and it's like, just like, in New York finance.
很多数学专业的学生都会从商，比若说去纽约金融业。
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I realize I've given you some difficult mathematics, but--it's not that difficult actually-- but I kind of went through it quickly.
我发现我给了你们一些比较难的数学公式，不过，并不是想象的那么难-,我很快就把它们讲完了。
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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
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It's 33, 32, it's only 32 times and you can check that math at home but here lies the power of algorithmic thinking, of computational thinking as they say.
你需要33，32，对，32次,你也可以在家里自己计算，但数学算法的力量是无穷的，这就是科学家们所谓的计算机思维。
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I think math is the most obvious one that would be suitable for adapting to this format.
我觉得数学是最明显的,数学能很好地,适应这种方式。
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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。
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Numbers are hard. That's why we teach whole semesters worth of courses in number theory.
因此我们整个学期关于数学理论,的学习也是物有所值。
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So you can see that we're starting to have a very complicated equation, and it turns out that it's mathematically impossible to even solve the exact Schrodinger equation as we move up to higher numbers of electrons.
所有你们可以看到我们得到了,一个非常复杂的方程，结果是它在数学上是,不可能解出确定的,薛定谔方程,当我们考虑更高的电子数目的时候。
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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
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Imagine you have a math test and this is the front of the math test.
假设要做一个数学测试,这是数学测试卷的正面。
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But the mathematicians told Dirac, "You cannot ignore the negative energy solution because it tells you there's a second solution and you cannot throw them out."
但数学家们告诉狄拉克,你不能忽略负的能量,因为数学告诉我有两个根,你不能随便丢掉
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The Triumph of Death, the dialogue of the mathematician Pascal is quoted by Rabb.
拉布曾引用过一段数学家帕斯卡的对话
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So he looked at their maths, their objective scores.
于是他查看他们的数学，客观的成绩。
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so I'll need to do math and science classes for the rest of my college career.
所以我必须在我余下的学生阶段完成数学和自然科学的课程。
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Why 5,040, you may ask;do we have any mathematicians among us who will give me a quick answer to that?
你会问为什么是五千零四十个呢,在座的有没有数学家能快速给出答案
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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
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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。
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I was like... I'm slower at math than I'm in reading.
我呢……我的数学比不上阅读。
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and I left my math notes in someone's car
而我却把自己的数学笔记落在谁的车里了。
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I'm going to start this lecture with a discussion of how one constructs a portfolio and what are the mathematics of it.
首先我想讲讲,怎样建立一个投资组合,以及与其有关的数学问题。
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Again, don't worry too much about the equation, we're not really going to do any math here, I'm just putting it in for completeness.
对这个方程也不需要太深究,在这里我们不强调数学运算的,我把它写出来是为了表述完整
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So sometimes the extra solution is very interesting and you should always listen to the mathematics when you get extra solutions.
所以有时候这些增根的意义很耐人寻味,当你解出增根的时候,别忘了想一想它的数学含义
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What comes out of the math is that the value of k, there are multiple values, there are multiple solutions.
得到的数学结果是k的值，这有多种值，多种解法。
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And the prospect of having a lot of time to pursue math problems of a richer and deeper sort seems fairly attractive.
要是能有时间,解决更困难更深奥的数学问题,对我相当有引吸力。
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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。
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I don't want anybody to quit this class because they're worried about math or math notation.
我不希望你们因为对数学,或是数学符号的恐惧而放弃这门课
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Anyway we have our second mid-term exam on Monday and it will be like the first mid-term but it will be less mathematical.
无论如何，我们在周一会有我们第二个期中考试,并且它将会像第一次期中考试一样,但是数学方面会涉及的更少。
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The astute or the mathematicians will realize that what will happen here?
机敏的人或数学家将认识到,这里将发生什么？
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So, Rain Man, the character played by Dustin Hoffman, had extraordinary mathematical abilities.
达斯丁·霍夫曼所扮演的雨人这个角色,有着超凡的数学能力
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