这周结束了2A前两个小学期也就是一个大学期的考试，随便写点什么回顾一下学了什么以及后面的展望。
【P1】 = 统计 + 量子力学2 + INF411 + 动力系统（sup)
【统计】第一次给了我一个感觉统计也可以非常非常理论。应该说这个统计课就是告诉我们，在什么样的假设下，我们脑洞打开设计的方法是有道理的（estimateur）, 或者随机变量之间应该有怎样的一种依赖性（regression），以及我们设计了一个方法，然后根据这个方法找变量的关系,这个方法的准确性是多少（test）。稍显美中不足的，过于理论了，甚至都没有拿这些方法做过什么。当下统计学习如此火热，我们当然要懂些原理，可是连一点点直觉都没有好像不太好。
【量子力学2】继续上学期的内容加强深化了些。物理毕竟外行没有学精，就记得好像我们推出了Pauli不相容原理，这个挺让我映像深刻的。
【INF411】继续打程序……链表二叉树深度优先广度优先最短路动态规划都一个个做了遍，原来算法计算机真的不难。
【动力系统】因为最后没有参加考试所以后来劲就送了，只能等到来年再来过了。不过我个人觉得这门课内容对我而言是有提升的。本科对ODE的了解就停留在解解方程了，而事实上呢？法国整个动力系统的框架完全是建立在更一般抽象的体系上的么。当然基石还是Cauchy Lipthiz.还有整个Flot的想法应该是渗透到了力学还有PDE当中去的。
不过最后因为和Section疯玩了一把，期末复习相当不到位，中间也没有抓的特别紧。说实话是要检讨的。成绩考出来也没有那么理想（但也不至于毁灭），想到未来成绩还是有用的，所以P2果断端正态度……
【P2】 = Distribution + 数值入门 + INF421 + 狭义相对论（sup）
【Distribution】在Coursera上已经上过了课拿了证书，再看老师上课的内容说实话还不如当时电子课。整个课程进度甚至比电子课更慢，留下了之后一大本关于PDE的内容，当中还有不少是很重要的，比如关于Laplacian的正则性。不过还好这门课开课的时候终于又捡回了TC的状态做掉了绝大部分习题。要给自己打分至少是个80分吧。
内容：分布理论就是把内积结构的一种推广。分布，紧支撑分布，缓增分布，Hopf方程，基本解和正则性。卷积一块是是比国内说的细的多，紧支撑分布可以各种和其他玩意儿做卷积。
（在此再次感谢当年李老师和雷老师教诲，X工程师教育再好，预科制度再棒，流水线生产比不过讨论班手把手拆招练出来的本事……）
【数值入门】整个学期最花精力的一门课。一方面因为刚刚上手觉得不花功夫难以学好，另一方面是这个里面的方程降低比上一门还要多些。事实也证明最后这门课学的得心应手。反思之处：还要多花时间写写数值解的程序啊。然后这门课虽然入门，但是体系里面该说的也说了特别多了。
内容：差分格式，变分和有限元，优化和算法。差分主要做热传导和波动，变分有限元则什么都能做。优化中说了些定性描述，优化算法还是有意思的。
当然目前的数学工具用的不多，可以感觉是各种数分习题的实践版本，我觉得一定有把小波这些高级工具用上的炫酷进阶版。
【INF421】stabe matching, DP, 各种最短路最小生成树，TPS，做了个Projet TTP，还有胡来的随机算法和启发式算法。
课程还不错无奈德国老师英语听着真累。反正每次我都带头做DM……当中还想出过一个关于随机树联通性的证明，也是佩服自己。
【狭义相对论】又当科普课上了，总算会用lorenz 变换写各种光啊波啊等等。
【小结】：说真的不是每一门课都那么喜欢，但是也强迫着自己拿出至少85分热情去面对了所以学着还挺好（？）吧。后面有概率模型，统计物理，BIG Data，还有NS方程。以及我们不能把PSC就这样落下啊。最后两个学期，是体现120分热情的时候了，小宇宙烧起来~
2016年1月23日星期六
Three interesting questions
Yesterday, we talk about three interesting questions in the cuisine and luckily I have found the answers by myself for this three enigma. Now, I share them with you.
[Probability and a series of number]
A series of integers are coming but we don't know the total number of these integers. We have a fix number of memory. Try to design a way to give one number of them randomly.
Idea: Because we don't know the number, so in fact we keep the random during all the process. We start from the simple case. We we given one number, we just keep it. But once we have two, we must update it with the prob 0.5. That is the key. Once we know the total number until now, we have the method to update the data randomly.So two memory is OK.
[Find the polynomial]
We are given a polynomial of degree integer positive. We have two chance to test the polynomial by value. How we find it?
Idea: Intuitively, this is not so logical because in maths we know we can construct a polynomial of certain zeros. But pay attention to the positive integer coefficient. The addition of one polynomial cannot always be correct.
The correct way to think by maths: if we can separate the coefficient, we get it. But to separate the coefficient we have to know the range, so the first chance we can use it to test the range of coefficient. For example, we put 1 in it. We get the range. We put 100000~0 to it, then we get the coefficient.
RMK: It is said that this method can be used to attack the HashCode.
[The most frequent number]
Once again, we are given a series of integer and we know that there is one number which appears more than half of it. We don't know the number, try to find it.
Idea: this is one in which I use the most of time. I got the answer by intuition and then prove it by maths. We get one number, count the number from it, count the number it occurs. If the frequency is lower than half, erase all the data and re gain the number.
A better arrangement can reduce the memory to two. But the heart of this idea is that if we do partition of the interval, at least from one point, the frequency of this number is always above 0.5.
[Probability and a series of number]
A series of integers are coming but we don't know the total number of these integers. We have a fix number of memory. Try to design a way to give one number of them randomly.
Idea: Because we don't know the number, so in fact we keep the random during all the process. We start from the simple case. We we given one number, we just keep it. But once we have two, we must update it with the prob 0.5. That is the key. Once we know the total number until now, we have the method to update the data randomly.So two memory is OK.
[Find the polynomial]
We are given a polynomial of degree integer positive. We have two chance to test the polynomial by value. How we find it?
Idea: Intuitively, this is not so logical because in maths we know we can construct a polynomial of certain zeros. But pay attention to the positive integer coefficient. The addition of one polynomial cannot always be correct.
The correct way to think by maths: if we can separate the coefficient, we get it. But to separate the coefficient we have to know the range, so the first chance we can use it to test the range of coefficient. For example, we put 1 in it. We get the range. We put 100000~0 to it, then we get the coefficient.
RMK: It is said that this method can be used to attack the HashCode.
[The most frequent number]
Once again, we are given a series of integer and we know that there is one number which appears more than half of it. We don't know the number, try to find it.
Idea: this is one in which I use the most of time. I got the answer by intuition and then prove it by maths. We get one number, count the number from it, count the number it occurs. If the frequency is lower than half, erase all the data and re gain the number.
A better arrangement can reduce the memory to two. But the heart of this idea is that if we do partition of the interval, at least from one point, the frequency of this number is always above 0.5.
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