Srini devadas and Eric Lehman Lecture notes Number theory ll Image of Alan Turing removed for copyright reasons s The man pictured above is Alan Turing, the most important figure in the history of mputer science. For decades, his

Number Theory I Number theory is the study of the integers. Number theory is right at the core of math ematics; even Ug the Caveman surely had some grasp of the integers- at least the posi tive ones. In fact, the integers are so elementary that one might ask, What's to study?

Srini Devadas and Eric Lehman Lecture Notes Induction III 1 Two Puzzles Here are two challenging puzzles. 1.1 The 9-Number Puzzle

1 Unstacking Here is another wildly fun 6.042 game that's surely about to sweep the nation! You begin with a stack of n boxes. Then you make a sequence of moves. In each move, you divide one stack of boxes into two nonempty stacks. The game ends when you have n stacks, each containing a single box You earn points for each move; in particular, if you divide one stack of height a b into two stacks with heights a and b, then you score

Why do you believe that 3+3=6? Is it because your second-grade teacher, Miss Dalrymple, told you so? She might have been lying, you know Or are you trusting life experience? If you have three coconuts and someone gives you three more coconuts, then you have--ahal--six coconuts. But if that is the true basis for your belief, then why do you also believe that

It's really sort of amazing that people manage to communicate in the English language Here are some typical sentences: 1. You may have cake or you may have ice cream 2. If pigs can fly, then you can understand the Chernoff bound 3. If you can solve any problem we come up with then you get an a for the course. 4. Every American has a dream What precisely do these sentences mean? Can you have both cake and ice cream or must you choose just one desert? If the second sentence is true, then is the Chernoff bound incomprehensible? If you can solve some problems we come up with but not all, then do you get an a for the course? And can you still get an a even if you cant solve any of the problems? Does the last sentence imply that all Americans have the same dream or might

1 Induction A professor brings to class a bottomless bag of assorted miniature candy bars. She offers to share in accordance with two rules. First, she numbers the students 0, 1, 2, 3, and so forth for convenient reference. Now here are the two rules:

年初为了构建一个需要快速开发的大型应用的时候,我找到了 Struts这个框架使我得 以从杂乱的思绪中解放出来,从而结合EJB构建了一个清晰的系统。从此以后,让我与 Struts 结下了不解之缘,从而也对开源项目有了新的认识。而不是仅仅限于现成的商业解决方案。 我接触的第一本书就是《 Struts in Action》。这之前也只是从从 Apache的 Struts主业 和相关链接和一些文章获取信息。当然这些信息显得杂乱。是《 Struts in Action》才使我对 这个强大的框架有了一个系统的理解和看法。从而用这些认识再来改进原来构建的系统

一、笔试模拟试题 二、上机考试模拟试题

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