Very difficult problems, but in my judgement, all solvable if we generate the country in the kind of bipartizan political cooperation and political courage that will be necessary to fix them.
这些问题很不容易解决,但我认为,不是不能解决,只要我们,以这种两党制的合作形式治理国家,还要有治理它们的政治勇气。
Typically up till now, we've looked at things that can be done in sublinear time. Or, at worst, polynomial time. We'll now look at a problem that does not fall into that. And we'll start with what's called the continuous knapsack problem.
至今为止我们已经处理过,亚线性问题,最多也就是多项式问题,我们现在要看的问题则是不能用这些解决的,我们将要开始讲连续背包问题。
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。
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