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And we do so by a quantity called the average valence electron energy.
我们可以通过,一个叫做平均价电子能的量来解决这一问题。
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because then you can solve new problems on midterms and what not if you understand the conceptual part.
因为这样你可以解决中期的新的问题，如果你不理解的话，就不好说了。
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Now, this is a pretty familiar widget of little gadget that you might see on most websites today, but my God, what an uninteresting problem to solve ourselves.
这是一个大家都很熟悉的小工具,现在在大多数的网站上都可以看到，天哪，如果我们自己解决这样的问题那将是多么无趣！
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Also we will have students doing workshops and problem-solving where the students will solve problems as a group, a group of three and turn in a common work sheet.
我们还有学生做研讨会,以及问题解决,从而学生可以以三人小组为单位,解决问题,最后上交平常的作业。
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There are other problems that are much more naturally thought of in a recursive fashion.
有一些问题不递归,也可以很简单的解决。
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The strategy then often is to figure out how, what sort of program can solve these problems and then we go on to ask, "How could this program be instantiated in the physical brain?"
心理学家们通常要先弄清,什么样的程序可以解决这些问题,然后我们会接着问到,"这个程序在我们的生理大脑中,是如何进行编译的"
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You can have your own mnemonic device to figure that out, but anyway.
反正你可以用你自己的记忆方法,来解决这个问题。
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You will be able to solve all the problems we have in mechanics.
你就可以解决我们即将碰到的所有力学问题
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so that you can solve it in the best and most efficient manner.
这样便可以用最好，最有效的方式解决问题。
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Perhaps you could start your resolution by finding the source of the problem.
也许你可以通过寻找问题的起源来找到解决方案。
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And so with this example here, I thought I'd propose that we consider exactly how you'd go about tackling something like this.
有了这个例子，我想我们可以,考虑一下应该如何下手,解决这样的问题。
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In Week 2 we'll look at things like cryptography and functions and the tools that by which you begin to assemble solutions to problems; in Week 3 we'll introduce what are generally ; known as algorithms and data structures; mechanisms by which you can solve problems more efficiently, effectively.
第2周,我们学习加密技术及其功能,还会学到一些操作工具,通过这些工具的使用来收集解决问题的办法,第3周,我们将介绍;,算法和数据结构,以及可以更有效地解决问题的机制。
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That's a big issue. You can fix one thing, you break something else.
你可以解决一个问题，但你破坏了其它的程序。
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I just reduced it to a smaller version of the same problem.
我刚刚把它简化为一个更小的同类问题,这就是我可以写出能解决更短字符串的例子。
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So you can actually say, how do I know which methods are associated with the class? For that, we can call dir. And what it does, is it gives me back a listing of all the things, dir all the methods, that are associated with it.
我们开始建立类了，我们得到了这些方法,因此实际上你可以说，我怎么知道，哪些方法是关联与这些类的？,为了解决这个问题，我们可以调用，这个方法的作用。
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All right, this is what's called a recurrence relation, there are actually cool ways to solve them. We can kind of eyeball it.
好，这就是所谓的递归关系,也就是解决问题的相当好的办法,我们可以来看看。
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The next phase, concrete operations, from seven to twelve, you can solve the conservation problem, but still you're limited to the extent you're capable of abstract reasoning.
下一阶段,具体运算阶段,七到十二岁,儿童可以解决守恒问题,但儿童的抽象推理能力仍然有限
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You can take a problem that might be relatively intuitive to solve but when you scale this thing up as is increasingly the case in the web, in large data systems, and so forth, you actually have to now think smart, you actually have to think efficiently and you have to solve this problem effectively.
你可以把一个问题用比较直观的方法解决,但如果你把此类问题的数量增大,正如越来越多的互联网，和大规模数据系统中出现的问题等等,你应该考虑怎样才能更简便，怎样才能更高效,你应该用行之有效的方法处理问题。
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The second question I want to ask is what's the base case? When do I get down to a problem that's small enough that it's basically trivial to solve? Here it was lists of size one. I could have stopped at lists of size two right. That's an easy comparison.
第二个问题是什么是基础条件？,我要将问题分解到何时才使得问题,小到可以解决的基本问题？,这里是当列表的长度为1有时候,我也可以在长度为2的时候停止分解,那是一个非常简单的对比。
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I think that book will give you all the basic principles you need in calculus of one variable, more variables, elementary complex numbers, maybe solving some problems with vectors and so on, which you're going to get into.
我想那本书会给你所需的所有基本知识,包括一元和多元微积分,简单的复数运算,可以解决一些与矢量有关的问题,而这正是你们将要学的
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Pardon? I could square x but maybe I should just do something pretty simple here. Suppose-- whoops.
对不起我没听清，我可以求x的平方,但是好像这里我做点简单的,改动就可以解决问题了。
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And you can very quickly take this feature to an extreme 10 and start putting X and Y and A and B and 10 and all your variables up top because it would seem to solve all of your problems and stop all of your thinking, but it's generally not a good thing.
你可能迅速地使这个特征成为一个极端,开始把X和Y和A和B和0,和所有的变量都放在最前，因为好像它可以,解决你的所有问题，并中止你的想法，但通常这不是一件好事情。
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The point is the arrow A, somebody has chosen to write in terms of i prime and j prime as Ax prime and Ay prime.
解决问题的关键在于矢量 A,可以用这样的形式来描述,i' ? Ax' + j' ? Ay'
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But can I borrow that idea of taking a problem and dividing it into something smaller.
但是我可以借鉴解决这个问题的思想并将其划分为,更小的问题。
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And I would suggest palindrome as a great example of that. That's easy to think about recursively. It's much harder to think about iteratively. And you want to get into the habit of deciding which is the right one for you to use. And with that, we'll see you next time.
其它的问题可能用递归的方式,可以更好的解决,而直接思考可能很困难,这时你就得养成做出,正确选择的好习惯了,下周再见。
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in the context of a web page. And increasingly that is where the human computer interaction is, and so will you be empowered by terms and not to just to make a website per se but to make an application, something that's of interest to you, something that solves problems, something that lets you tell someone through the most electronic means possible that you saw them somewhere on campus.
以网页内容的形式表现出来,人机交互的运用将越来越多，而且你将学会编程,不仅能制作网站，还能做出应用程序，一些你感兴趣的东西，一些解决问题的手段，还有一些可以让你通过使用,现有的电子手段来分辨出,校园里面看到的一个人的东西。
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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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