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OK. And then the exponentials, as you saw is when typically I reduce the problem of one size into two or more sub-problems of a smaller size.
好，然后说到指数级，正如你所见，典型的例子是,我讲一个问题分解成为,两个更小规模的子问题。
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and stuff is much more important than doing tons of problems particularly...
比只是解决问题要重要得多……
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The sense of values we have, the things that we get excited about are different, and the problems may be more difficult.
我们的价值体系,我们的兴趣范围都是和你们不一样的,这些问题可能会更难
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If you'd like to sit down with one of us more intimately and more sort of tranquilly, and work through problems for more than just a couple minutes at a time.
如果你希望和我们其中一个人坐下来，更亲密的,更平静的，每次用几分钟的时间,来解决问题。
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What do they do? One of the problems that it produces is the more people you have, up to a point that's good.
他们都干些什么呢,其中一个问题是,人越多,产出就越大,这在达到临界点之前是好事
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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 other thing I want to let you know is that instead of having a new problem-set that you'll be assigned this Friday, what we'll do instead is we'll give you some practice problems, and these will be just more of the same type of problems that you saw before but that's another chance to try them out more.
另外一件我想要告诉大家的是,这周五将不会像往常一样,给大家布置新的作业,而是给你们一些练习题，这些题目只是另一些跟原来同样类型的习题,你们应该都已经见过类似的,但这是尝试再次解决这类题目的机会。
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What made things go so awry that people and food used to be more in sync in terms of health and well-being, although there were problems in some ways.
是什么让一切偏离正轨,尽管有些方面存在种种问题,过去人与食物的关系,就健康方面而言,要比现在更为和谐
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And the dominant problems concern consist of a lack of social connectedness, problems with language, problems dealing with people, and more generally, a problem of what the psychologist, Simon Baron-Cohen has described as "mind blindness."
主要症状包括缺乏社会联系,语言障碍,社交障碍,总而言之,会产生一种心理学家西蒙·伯龙·科恩,称之为"精神性盲"的症状
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Then next week we'll do more complicated problems that involve motion in higher dimensions, how to go to two dimensions or three dimensions.
下周我们将会处理更复杂的问题,包括更高维数的物体运动,如何处理二维以及三维运动
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For those perhaps familiar with some of the jargon do we introduce what we call link lists and hash tables and tries, increasingly sophisticated data structures, that allow us to solve problems that are much bigger and much more interesting than the very familiar one that we started with here.
那些对编程的术语较熟悉的同学,我们会教授,链接列表，哈希表，以及日益复杂的数据结构,以便帮助我们解决其他的,比现在所学的更大也更有趣的问题。
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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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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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