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STUDENT: What does it mean, the operator used, when you were calculating the remainder between nine and five?
学生：这是什么意思，当你用这个运算符去算,9除以5的余数的时候？
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As I keep moving down, that part gets smaller, it's not always the initial length of the list, and you're right. But if you do the sums, or if you want to think of it this way, if you think about this more generally, it's always on average at least the length of the list.
等等，随着移动，剩下的部分越来越小，并不是初始那么长了，如果你算一算，或者你这么想，你考虑更一般的情况，平均下来至少是列表的长度。
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If you fail to take the test, you get zero, and I average the zero in.
如果你没能参加，那即是零分，我算平均分的时候会加入那个零分。
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So here I've written for the hydrogen atom that deceptively simple form of the Schrodinger equation, where we don't actually write out the Hamiltonian operator, but you remember that's a series of second derivatives, so we have a differential equation that were actually dealing with.
这里我写出了,氢原子薛定谔方程的,最简单形式，这里我们实际上,没有写出哈密顿算符,但是请记住那你有，一系列的二次导数,所有我们实际上会处理一个微分方程。
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Not to harp on the mathematical features of this, but cubing, AX*X*X you know, if you're starting to do AX star, X star, X, every time you want to cube some value in a program, it just feels like this is going to get a little messy looking, if nothing else.
不要总是说这个的数学特性，但是体积，你们懂的，如果你开始做，在一个程序中，每次你想算几个数值的体积，感觉它就变得,有一点凌乱的，如果没有其他的。
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Now, you may say this doesn't amount to a very limited government, and the libertarian may complain Locke is not such a terrific ally after all.
现在或许你会说，这并不算真正有限的政府，而自由主义者会抱怨洛克并不算他们的好盟友。
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Then to get the monthly payment, you take the square bracketed thing and you divide by the mortgage balance and that's the monthly payment; that's how it's calculated.
如果要算每月偿还额,你用贷款余额,除以这个方括号的值,这样就得出每月偿还额,这就是每月偿还额的计算方法
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Admittedly, it's not great, but you've done good work."
说实话，其实并不是很让人满意，但是你做的也算不错了“
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In addition, this is just the cost of the vaccine, not the cost of the doctor or nurse who injects it into, you so you have to figure that cost in as well.
另外,这个仅是疫苗本身的成本,还没算上医生或者护士的成本,所以你还得同时考虑这些成本
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Well we could begin with George Washington Alright, for your sake, we toss in John Kennedy ... who cut taxes. -Because... the Kennedy tax cuts and the Reagan tax cuts ... were both major tax cuts. -Did you hear me ask him ? for a one-word answer? Did you hear me?
那干脆从乔治·华盛顿谈起得了，真是的,好吧，看在你的面子上，姑且把他算上吧,他好歹也减税了，-因为。,肯尼迪的减税和里根的,都不可等闲视之，-我不是让他,只回答一个字吗？他怎么说这么多？
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Now, we are done because now we can ask how high does it go, and you go back to your y of 1 is 15+10-5, which is what?
现在问题解决了,因为我们可以算出,最高点的高度,你回到这个式子,求出y=15+10-5,是多少
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It turns out that if you look at the 2.5--sorry, the quarter million people on the movie database and compute their Bacon number, 2.8 the average Bacon number is 2.8.
结果发现，这2。5…对不起，如果你算一下电影数据库里这25万人，他们的平均Bacon数为。
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How would we go about, I mean I don't want to do it because I'll probably get it wrong, but if I wanted to solve out for this X and the Y, since this is a QR class, let's just talk about it a second.
我们怎么解呢,我的意思是我现在不会去计算,因为我可能会算错,但是如果你真的很想解出X和Y的值,介于这是一节需要快速反应的课,那我们花些时间来探讨一下吧
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STUDENT: So, how do you come to a conclusion as to which you should use then, if you can determine the size based on solution, or based on input, so how do you decide?
学生：所以，你怎样决定你该用,哪个来算呢？现在如果你可以选择是，基于解决方案的大小，还是基于输入的大小，你应该怎样决定呢？
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But if, over the course of the semester, you get better, then we will give, at the end of the semester, when we're figuring out your semester grade, we'll give the later, stronger papers more than their official weight.
但如果，在这学期中，这门课，你进步了，那么我们会，在学期末，我们算出你的分数后，我们会给那一两篇较晚时候写的，较好的论文比之前规定的更大的比重。
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But regardless of how you measure it, for a full half-dozen years, in the midst of this bull market, colleges and universities were over-allocated to fixed income relative to where they had been in June of 1987.
但不管你怎么算,整整六年时间,处于牛市之中,大学的基金,由于1987年6月那次崩盘的影响,过度投资于固定收益债券
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And not only can you punish with death people who come after you seeking to take your life, you can also punish a thief who tries to steal your goods because that also counts as aggression against the law of nature.
不仅可以处死那些,跟踪你想谋害你的人，还可以惩罚想偷你东西的小偷,因为那也算侵犯了自然法。
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And also I wanted to mention in terms of checking your Lewis structures, regardless of what they are, you should always go back and I had 10, and then count 2, 4, 6, 8, 10, because you always need to make sure you have the same number of valence electrons that you calculated in your actual structure.
我还想提一点关于检查,你的路易斯结构的建议，不管它们是什么，你总是应该回去检查一下,我有十个，然后数一数，二，四，六，八，十个，因为你总是需要确保实际价电子的数量,与你在结构中算出的数量相等。
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Compound that 13.4% over ten years and there's just an enormous gap between those mutual fund numbers that are in the prospectus and in the advertisement--the time-weighted returns and the dollar-weighted returns that talk about the actual experience of the investment community.
按13.4%复利算一下10年期的结果,你会发现在招股说明书和广告里给出的,用来反映投资机构实际业绩水平的,时间加权回报率,和货币加权回报率数字之间,有着巨大的差异
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You take all the risky assets ... and you analyze them first to get their-- you have to do a statistical analysis to get their expected returns, their variances, and their covariances.
你需要对所有的风险资产进行分析,首先要得到它们的-,你必须要做一个统计分析,算出它们的预期收益率，方差，和它们的协方差。
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So if $200,000, Julie, is too low a figure because it doesn't include the loss of a loved one and the loss of those years of life, what would be what do you think would be a more accurate number?
朱莉，要是20万美金不够,因为没有算丧失亲人,和生命的损失，那你认为什么数目更合适？
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And I won't ask you to check whether it got the right answer.
我不用你算这到底,是不是正确的答案。
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And conceptually, the idea of cubing a value feels like you could package that up into a little box, a little tool that takes input, a value, and returns output the answer A* so you don't have to constantly do A star, A*A So this program ,at the end of today, is pretty much the same thing.
概念上，算一个值的立方就像是,你可以把一个值打包放在一个小盒子里,一个用来接收输入的工具,一个值，然后返回一个答案,所以你并不需要一直使用，等等。，A，star，，A，，and，so，forth。,这个程序，最后，是一个差不多的东西。
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