最近闲来无事，thesis刚搞好draft，于是决定又重读一下明朝那些事。上次读还是高三接近高考的时候了，那时候十一点晚自习结束上床后，还会用IPad看一两小时的明朝那些事，因为时间也很紧，所以颇有点囫囵吞枣的意思，权当看故事书+积累素材了。不过还是有几个印象深刻的点，比如徐达蓝玉的不世之功，比如方孝孺的诛十族又何妨，比如最后徐霞客的完美结尾：成功，便是按照自己的方式度过人生。

最后这本书里的素材还真在我高考作文上用上了，当年的满分作文没准得记他一功。所以说，人生的很多重要时刻，譬如高考，结婚，并不是那一刻才决定了你的走向，命运早已给你所有的付出、馈赠、获得标上了价码。

好书总是不闲多看的，每次看肯定会有一些新的体会。以此为记。

性格是怎样形成的

历史是什么组成的？有人觉得是王侯将相、英雄豪杰、和所有时代浪潮中的风云人物。有人觉得是奋笔疾书的书生、是走街串巷的匠人、是锄禾日当午的老农、是一个一个平凡的普通人组成的。我是同意后者的，不过似乎很多风云人物并不这么觉得：他们觉得自己是历史的主角，便自然可以是历史的导演。

朱元璋就是想当导演的人。他不想要丞相来制衡君权，于是放纵胡惟庸七年；他想要子孙千秋伟业，于是制定了整个国家的运作方式，事无巨细，皆定规则；他痛恨宦官，责令太监不得干政。

不过似乎他所有试图违背历史进程的操作全都适得其反了：丞相没有了，只是换了个内阁大臣的名号，甚至相权更甚；规则详尽，但不完美，自己的子孙甚至因为规则而被饿死；更别说明朝出了历史上最有名的几位太监了。

说了这么一通，想论证那些风云人物也不可能控制历史进程。其实是想引出下一个观点：

恰恰相反，人的许多行为或思想，并不是那一瞬间自己大脑才做出的选择。而是长年累月经历（后代的角度看就是历史）所塑造的性格，决定了你的行为。

从这个角度看，似乎所有人也只是被历史操纵的一个“角色”，扮演着自己的身份进行人生而已。

陈友谅捕鱼出身，身上总是一股鱼腥味，因此从小被人嘲笑欺凌，他自然对这个社会没有好感、心理阴暗；朱元璋父母被贪官污吏压榨，自然痛恨腐败；最有意思的是从古至今白手起家打天下的刘邦、朱元璋，以及太祖，似乎都对“狡兔死走狗烹”有着执念，反倒是秦始皇、李世民等“二代”可以做到善待功臣。

当年明月似乎很喜欢用人生经历来推断人物性格，再根据这个性格来判断某件模糊事件的真伪。

推到我们个人，大概也是成立的。倘若父母从小争吵、离婚，便也不可能知道如何做一个温柔的、善于爱他人的人。貌似挺多父母吵架的孩子长大后面对矛盾就会把自己埋起来，沉默不语。

当然我们也不必直接摆烂：反正我命由天不由我，我是怎样的便是怎样的，就随便过过吧。虽然我们的性格是由我们经历塑造的，但是经历是我们可以选择的，尤其是有了自我意识、自我独立之后。倘若想要做个开朗洒脱之人，去找个李太白做朋友吧！

朱允文

高中读这本书那会，读到靖难之役便有种不忍心看的感觉。虽然朱允文和朱棣和我没半毛线关系，但我总是不希望看到朱允文战败，读到朱棣各种狗运的时候也是咬牙切齿。

朱棣作为一个很有建树的皇帝，肯定是没惹到我的。究其原因，我觉得可能是我代入到朱允文的角色了。朱允文是根正苗红的皇帝继承人、是百姓爱戴的任君（至少他推行的各种免税政策来看，我脑补一下应该百姓是prefer Yunwen rather than the brutal Zhu Di.），可以说是一个正面典型。而朱棣做的就是把这个正面典型撕裂开、摔到地上、并批判的一无是处。

我个人觉着我就像是朱允文这样的正面典型，所以我很害怕来个朱棣这样的人把我虚伪的正面典型撕裂（吐槽：这么说怎么有点像窥探里的男主？不过我看窥探好像没这感觉）。记得初中时候，我妈向我老师告状说我打游戏，我气的不行，日记里痛骂了我妈一顿。

在往深追究，我似乎是个比较在乎他人看法的人。因此我才会在乎自己的“正面形象”；才会在虚拟的网络里会小心翼翼的看自己发言有没有被人喷；才会在得知高中同学对自己的负面评价后很伤心很不解；才会对于上台演讲、当领袖没有什么畏惧排斥。（因为希望得到他人的崇拜？）

而再往深里说，之所以在乎他人看法，也许是因为自己的自卑？虽然以前说自己很自卑会觉得很可笑，我是个相当自信，很少怀疑自己，高中甚至算自负的人。不过现在窥探自己的灵魂，越发觉得只有自卑才能解释我以上的种种行为。而自卑，也许是童年经历导致的？

兜兜转转，又回到了第一个论题。

从人生经历、面对事物做出的选择，来推断自己的性格，再以自己的性格帮助自己做选择，似乎是个不错的方法。

譬如什么样的姑娘才是适合我的？

结合我的经历，思想，能得出的结论 应该是：

1. 对我是崇拜的；（因为自卑）
2. 对我是能温柔体贴的、有爱意的，换句话说，有点母性光环的；（还是因为童年经历）

于谦

高三那会，读到于谦这一段是我的感觉是这样的：卧槽，做人就要做于谦啊！（有点生子当如孙仲谋那味了）不论是守卫北京力挽狂澜，还是之后两袖清风励精图治，这个“明朝第二牛人”总是散发着我心向往之的魅力。

这次读到这段时，除了心向往之，更多了一些敬佩。要做于谦，也不是有着以身报国、舍身取义的心态就够了的啊！于谦的能力，当得上“国士无双”的称号了，这的能力，不仅是作为领导人的决策力、作为政治家的执政能力、作为军事家的指挥能力，还有人际交往的能力：当王振想对他动刀的时候，无数官员、王侯都为他撑腰，何也？人格魅力或是公道自在人心？

牛啊，真是牛啊。

历史

不论是三国演义还是明朝那些事、不论其中的剧情多么跌宕精彩、不论描述的英雄人物多么令人神往，最终的结局总不算那么令人满意。

因为它们不是戏剧、不是小说、它们终究还是基于历史描述的。正因此，读这种书读到后面，总会有种苍凉感，按当年明月的话来说，就是历史的厚重感。

读到关二爷被吕蒙匹夫偷袭会咬牙切齿；

读到孔明星落五丈原也会流泪难受；

读到崇祯没日没夜的工作最后开会还是嚎啕大哭时也会跟着难过；

读到杨涟被长钉穿脑时眼泪也会止不住的流。

但就算内心再如何波动，我们终究还是无能为力的啊。其实即便我们穿越到那个年代，我们又能做什么呢？大家也都是芸芸众生，似乎很难改变历史的轨迹，就像历史洪流中的一点水滴、又像时代车轮前面一个不起眼的蚂蚱。

不过就算无法改变，还是有很多历史谜团想知道啊。比如建文帝最后到底去哪了。

既然无法改变，那么读历史有什么用呢？

有人说以史为鉴，当年明月反对了这个观点：他认为我们读历史是吸取不了教训的。一千年后，另一个崇祯还是会杀了袁崇焕、袁崇焕也还是会杀了毛文龙。因为我们的行为是由我们的性格决定的，而性格不是读一些史书就能改变的。

不过我倒觉得，即便我们不能以史为鉴，历史在怎么样也可以做我们关于人生的教科书。它的作用就像一些很出色的电视剧、小说，在很短的时间内让你体验一次（或多次）不一样的人生、拓展你的人生宽度，这样你对如何过好自己这一辈子也许会有更深的体会：他们的人生都告诉你了，喜欢哪个自己去选吧。

譬如关于原则与妥协。你是会像海瑞一样做一个恪守原则的好人，还是像张居正、戚继光那样为了自己的理想做出一些妥协？

关于这个问题，我此刻的preference应该是后者吧？虽然听起来有点像是为自己懦弱不齿的行为找个借口，但我确实觉得为了心中的信念，我们总会做出一些牺牲的。譬如甲午海战之后的赴日留学、譬如隐形守护者走芳华线的肖遥，即便这样的做法无法被理解、甚至难以被原谅，我想真正的英雄也能做到“吾亦往矣”的气魄。

成功

七年前的大概这个时候，我在高考作文中写下了“我以我心绘风景，风景迷人因我心”的桥段，这故作高雅的句式，其实是仿照去年满分作文“唯愿此心无怨尤”写来的。

大概一个月后，我回忆起自己的高考作文，以及我所敬仰的满分作文大神们，羞愧难当，寝食难安，于是写了一篇文章痛骂自己：https://wadmes.github.io/2014/08/01/%E6%83%9F%E6%84%BF%E6%AD%A4%E5%BF%83%E6%97%A0%E6%80%A8%E5%B0%A4/

当然，我现在再怎么文思泉涌也写不出那样引经据典的文章了。

不过那时候的自己肯定是无论如何都想不到自己高考作文也拿了个满分。更为荒谬的是，至少在我看来，我那篇痛骂自己的文章不管是文采、思想深度都远远高于我的“满分作文”。

所以出现了一个滑稽的事实，我最成功的一篇文章，似乎在我的“满意排行榜”上名落孙山了，而我这篇无人关注的骂了满分作文的作文，反倒榜上有名。这么看起来，这种外界定义的成功与自我的满意有时候并不是一路人、反而经常反着来。因此真要给成功下一个定义的话，按照当年明月的话来说：成功只有一个，按照自己的方式，度过人生。

听着很简单的“随心所欲”，好像并没有多少人能做到。事实上，我们自以为的按照自己的方式，掺杂了太多外界的因素：我们努力学习的原因不是对于学习的热爱，而是惧怕老师的强压、不愿面对父母的失望、或是他人赶超自己的恐惧。类似的，我们做出各种人生决定，譬如就业结婚，不是仅仅考虑自己的喜好，还要考虑父母的意愿、旁人的看法、或是世俗标杆的评判。我们想要考虑的更多更周全，但我们活的反而越来越沉重。

因此，怎样才算自己的方式呢？我的前任满分作文先生说的很通透了：唯愿此心无怨尤。当我们排除掉所有外界的干扰，只问自己一个问题：我做出这样的选择，我的本心会后悔遗恨吗？我想，郑和率领舰队出航的时候他就知道，即便中道崩殂到底不了圣地麦加，他此生也不会有遗憾；我想，杨涟选择弹劾魏忠贤开始，一直到他被折磨致死他都不曾后悔；我想，徐霞客放弃功名跋山涉水记录祖国河山的每一天都是快乐的。他们是有着信念的战士、是尽吾志也而不能至者，可以无悔矣的英雄，而我们，也可以是这样的战士、英雄。

Encoder maps from nodes to embeddings

Decoder maps from embeddings to the similarity score

In our own task, we need to think of how our embeddings will be used. (In previous work, at leaset in the lecture, the embeddings are used for similarity check.)

Random walk

$z_u^T z_v$ = probability that u and v co-occur on a random walk over the graph

therefore, we maximize the probability of node pairs that is traversed by random walk

node2vec

biasd walk: BFS walk (local microscopic view) + DFS walk (global macroscopic view)

Graph Embedding

• avergae/sum node embeddings
• virtual node as the total graph
• hierarchically cluster nodes in graphs

Node features

Importance-based node features & structure-based features

Node degree

Node centrality

Takes the node importance in a graph into account

Eigenvector centrality

We update the following equation in a recursive manner:

$c_v = 1/\lambda \sum_{u\in N(v)} c_u$

that can be rewritten as:

$\lambda \textbf{c} = \textbf{Ac} $

Then, the centrality $c$ is the eigenvector

PageRank is for undirected graph. And the definition is:

$c_v = 1/\lambda \times \sum_{u \rightarrow v} c_u/\textbf{d_u}$

That is, pagerank vector is a stationary distribution for the random walk = principal eigenvector of storychastic adj matrix (connection equals probabilities)

Google proposes solution to solve Spider-traps(all goes to one) and Dead-end (no out)

• remove dead-end by adding outs to all nodes
• add a random probabiloty

Betweenness centrality

A node is important if it lies on many shortest paths between other nodes （在其他点的最短路径上面）

Closeness centrality

A node is important if it has small shortest path lengths to all other nodes. (离所有点都很近)

Clustering Coefficient

点v的邻点相连的比率, that counts # of triangles (node v, one neighbor of node v, another neighbor of v)

Graphlets

count # of graphlets (rooted and connected sub-graph) and use the # as the vector feature.

Edge Prediction

Katz index: count # of paths of all lengths (computed by powers of adj matrix) between a given pair of nodes:

$S_{v_1v_2} = \sum_{l=1}^{\inf}\beta ^l A^l_{v_1v_2} $, $\beta$ is a discount factor.

（越近，即距离越短的，关系越高）

Then:

$S = \sum \beta^i A^i = (I-\beta A)^{-1} -I $

(According to Geometric series of matrices)

Graph level features

Graph Kernel

Goal: Design graph feature vector, and the feature vector can be calculated for similarity.

Method: bag of *( simply uses * as features for graphs, and we compare the features), where * can be:

• node labels
• node degree
• graphlets
• color refinement by recursively updating (WL-test)

四要素

• observation
• feeling
• need
• request

除了用四要素表达自己，四要素也可以用于倾听：倾听、了解他们的观察、感受、需要和请求。（我们不用要求对方也知道四要素）

异化的沟通方式

• 道德评判：过分/自私/等等，每个人三观不一样，所有行为没有好坏，不能将冲突归咎于对方。（恰恰相反，要重视彼此的感受和需要）。

Hi，neway，这里是2021年的四月。我现在还在香港，四月的香港是最温柔的，没有夏季的闷热，没有梅雨季的绵雨，没有冬天开空调也不是不开也不是的纠结。不过这也许是我在香港过的最后一个四月了吧：倘若之后没机会在香港工作的话。

Starting from this post, I will try to use English as my major writing language. I really appreciate it if you can leave some comments on my toy English.

The post is a record of the CS/ECE PhD applications from a CUHK CSE MPhil student. Previously, my major research direction is EDA. Here is my basic background:

• GPA: BS in CUHK 3.53/4.0 (ranking 10%) MPhil in CUHK (3.97/4.0)
• Toefl: 106 + speaking 23.
• Publication: 3 first-author conference papers + 3 best paper awards (one first author)
• No strong (I guess) recomendation letter from prestigious professor

My Application Results

• Reject: MIT,UCB,Harvard, UW CS, UIUC ECE, Columbia CS
• Offer: CMU ECE (accept), Austin ECE, UIUC CS (Only oral offer)

Some tips

CS/ECE

In some universities (like UW and Columbia), CS and ECE are two distinct department. Therefore, please have a look on both departments to find professors with similar research interest. Also, their application systems are usually seperated. (Do not ask me why I know this.)

Toefl Requirements

Some universities set a constraint on Toefl speaking or overall score like UCLA and Princeton, but it is usaully not a hard constraint, at least according to the experience from other students. Please have a try even though your Toefl is less than the requirement. But generally, a 100 overall + 22 speaking is a necessary bottomline.

Timeline

Please do every thing asap! including toefl, personal statement, and GRE(possible). For example, please attend your first toefl asap! Trust me, your toefl preparation before the test and after test is totally different. After your first test, you will have a clear view on your pros and cons.

How to find related professors?

1. Check the professors who are active in your conferences.
2. Check the professors who are active in your research interest (start from the references in your publications).
3. Ask related professors

Exchange

If you are an undergraduate, PLEASE apply for exchange programme! The experience is a very “bonus” for your application. Moreover, during your exchange, you can(and must) contact professors for research, who can help your recommendation letter, or even be your future PhD supervisor.

Some materials from Internet

Interview

面試時間大多是半小時左右，常見的過程如下：

• 自我介紹，約3–4分鐘，但有時教授已經大概看過你的資料了，就會直接切入第2點。
• 叫你介紹自己之前的研究，可能還會問(1)你的研究興趣以及未來想做的題目，包含具體打算怎麼實現、(2)你最有貢獻的研究是什麼，為什么(3)如果到他的實驗室之後想做什麼等等。就像我說的，過程比較像是閒聊，所以他可能會不時問你一些延伸問題，或提供他的想法等等。這是面試的重點，大約10–15分鐘。
• 有些教授也會說說他實驗室現在在做的題目有什麼，解釋給你聽，你當然也可以問一些問題。約5–10分鐘。
• 大部分時候教授都會問你一些比較general的問題，像是(1)為什麼要投這個學校、(2)為什麼要念PhD、(3)你還投了哪些學校、(4)你畢業後想做什麼和(5)你有什麼優點和缺點等等。有少數教授會問technical的問題。約5–10分鐘。
• 最後，每個教授都一定會問你有沒有什麼想要問教授的，這時候你一定要勇敢發問。約10分鐘。我自己常問的問題有：
• ​ What are the current research projects? （如果教授沒有自己講）
• ​ 一些關於他研究的想法 （要事先了解教授的研究）
• ​ Where do the alumni go?
• ​ How do students choose their supervisors? （針對有rotation的program）
• ​ What will the funding arrangement be? （針對津貼沒有統一的學校）
• ​ Why do you choose to work in the academia after you have worked in the industry? (針對去過業界工作一段時間的教授）
• ​ Why do you choose to work in the academia instead of the industry （針對年輕教授）

谈谈你的xxxx项目/论文/科研经历。

所有的面试中几乎都会出现这一问题，准备好这一问题也极其重要。首先对于自己的每个work，要准备几个不同的version并选择适当的version进行present。

用一句话概括这个project及其贡献；

用一个paragraph概括project的high-level idea；

用15分钟讲清楚project当中的核心方法等等。

不要假设面试当中可以给教授看PPT或者slides，要准备好精炼准确的语言进行介绍。虽然教授是领域内专家，但是也要假设他对你的work一点都不了解的前提下进行present，从intuition和high-level idea开始讲，避免一上来就进入极其detail的部分。注意挖掘教授对于你的project可能感兴趣的点并适当准备：比如他的research interest和你的work当中有交集的部分等等，也可以把话题往这一块上引。

我个人认为教授问你之前所做项目的目的有几种：

看你对自己发表的work是否足够knowledgable，了解你在一篇顶会论文里的贡献；

看看你先前锻炼的技能是否有助于在自己的实验室里thrive；

看看research interest是否match。

针对性地提前进行准备可能有所帮助。

简单聊聊教授最近的论文和research interest。面试一般是让教授更好了解申请人的，（我觉得）一般教授不会深入问他自己最近做的project的各种detail。但最好通读一下教授最近出的paper的abstract，以免无话可说。当然如果跟自己的work非常relevant的要仔细读也可以展开说。但我觉得面试中展现自己的能力和水平比拍教授马屁要重要，所以也不用反复强调教授做的东西的各种优点什么的。

谈谈你对xxx领域research的看法，比如什么样的research比较好，怎样的research比较有前途。这是一个比较senior的教授问我的，当时被问到这个比较懵其实，答得也不是太好。我觉得这种问题不是很好速成准备，平时可以多和自己的research advisor聊，看看比较有经验的人对这个领域整体是怎么看的。参加会议的时候注意看自己的area里面热点有哪些，跟作者多进行networking等等；关注一下领域内大佬的linked in，看他们都转发哪些文章。

谈谈来了之后你想做啥。事先想几个跟教授最近感兴趣的方向贴的比较近的看上去promising的idea，可以和自己的research advisor以及熟悉的高年级PhD师兄师姐提前聊一聊。即使不是特别精妙，也不要临时搞一些一看就不太可能work out的idea。我觉得教授问这个问题目的不在于看看你的idea到底好不好，感觉是看你思考的方法；

面试和套磁的过程不要只关注professors

也要关心同一个项目内其他成员的在做什么

有时候中国学生来面试对于一个lab内的学生的关注不如美国学生那么多

可能是因为语言的一些barrier也可能是真的没有很多人强调这点吧

自己的观察确实是美国的学生更加好奇其他的labmember在做什么research

也许是我们更内向喜欢各做各的

但是在面试和刚认识的时候表现出来的自己对别人的兴趣还是一个很积极的信号的

如果你所面试的program提供了机会给你和其他在读学生的接触

问问别人research上的感觉

大方向是做什么甚至可以表达一下自己对于research的迷惑

问问前人的经验都很好

再就是如果有些项目愿意增加一个让学生来面试你的环节，一般来说能说明这些program的人关心自己的学生的感受，关心系里的morale，也可能意味着你博士期间会得到更多来自教授和cohort的精神支持感觉还是很好的

要关心一些这个program如何评价学生的performance

虽说PhD时间很长但其实也很短一下子就过来了

许多program大同小异都会有一套自己评价学生的办法和规定

比如说规定你的GPA不能低于多少，你总是拿C还是不好的

虽然你的亲老板不一定要求你门门是A，但是对于外国学生而言课程成绩保持在一个比较好的水平可以让人觉得你不仅学习能力强，生活和其他方面的适应力强语言沟通能力也不错之类的

还有就是应该问问program里有没有这种每年require学生做到的milestones

比如你本科毕业来申请PhD那你应该第几年之前拿个硕士，你第几年前应该完成candidacy exam

探探口风到底上课上多少比较好?上课重不重要?对于research有帮助的课有哪些?特别是当你的stipend是你的老师发给你的，他们会对你的research产出有更高的期待，有时候对于你选课就会有一些限制，比如希望你少选课或者希望你选跟自己research直接相关的。

如果老师对你上自己的课占用了科研的时间有强烈的反对情绪，你要是考虑到底是自己的问题还是别人的问题，很多老师的个性或者个人经历的原因在培养自己的PhD的时候都希望自己的学生不要走弯路偏，路如果你相信你的老师的决策在选课或者audit课的这件事上就要尽量和老师达成共识。对自己发展好对老师而言也是。

面试我问的问题

这个引人而异，可以问教授lab里做的project啊、lab氛围啊、整个组怎么work的啊（第一年自己lead项目还是work with other senior PhDs）

你现在正在面试多少个人？

注意对你的每个项目有个30s和5min版本的介绍（30s侧重一句话motivation和一句话你们做了啥，5min可以有一点例子，不需要太多tech detail，老师感兴趣会问），自己如果有哪个方面有短板记得想好解释（比如你gpa不好）

但是为了表示尊重与感谢自己人生中还能有此经历，决定把自己的优势一条一条的整理成点，邮件发给学姐（我看到她在记，并且向我核对）同时CC了T老师，非常感谢他愿意给我机会。

最后的时刻当然又是答疑时刻了，我又按照地里前辈的标准答案问，我如何能够contribute to your group，学长听了这个问题很高兴，和我说了一大堆（没太听懂……似乎是关于我优势的点？）

2)你未来想做啥．POI问我到底是只想做system还是system和networking都愿意做．

3)谈了下自己的一个research项目，问我有没有idea．这倒是第一次碰到这种面试问题，心里一惊．．．幸好之前碰到过类似的system问题．

4)你从PhD学习中想获得什么．之前已经碰到两次这个问题了，这次干脆准备了个答案，背了一下．

5)你喜欢东海岸还是西海岸？POI然后开始安利波士顿的好．

6)你还申请了哪些学校？拿到了哪些面试和offer？你给这些学校排个序，MIT应该排在哪里？

Recommendation letter

推荐信写什么？

\1. 被推荐人的全名。

\2. 推荐人和被推荐人的关系，i.e., 推荐人是如何认识被推荐人的，认识了多久，有多了解。

比如大一的时候此人就上过我的课，之后又跟我做过project；此人上我课的时候每周都会在office hour和我交流，还做过我的grader assistant；此人在我手下实习了三个月，表现不错。

\3. 推荐人认为被推荐人具有的优点，并且有details支持。

例如此人很勤奋，在跟我做的一个project上花了很多时间，我前一天布置的xyz任务他通宵了一晚上以后第二天就交给我了，而类似的任务给其他人可能要一个星期以后才能给我。此人很有创造力，在某个project中提出了一个feasible的想法，大大加快了project的进度。

需要特别提到的是，推荐信是为申请服务的，而gradute program还是比较看重的在技术方面的能力（研究能力）的，因此即使是来自industry的推荐信，也尽量体现出你的这方面能力和潜力。

推荐信可以涉及的内容是比较广泛的。我最初也在这方面犯了错误——想当然地认为推荐信写的内容要和推荐人密切相关，直到我看到了这篇文章GSAS GUIDE FOR TEACHING FELLOWS ON WRITING LETTERS OF RECOMMENDATION ，其中作者提到了“4. A letter of recommendation can also be used to explain some weakness or ambiguity in a student’s record. If appropriate - and probably after consulting the student - you might wish to mention a family illness, financial hardship, or other factor.”

实际就是只要是教授可能知道的情况你都可以放进去写。比如第一年gpa低，是因为家里父亲病重，照顾他花了很多时间。这个解释可能已经在你自己的statement of purpose里提到过了，如果再次由推荐人在信里确认，无疑有力很多。当然前提是这是真实放生的事情，不能编造。其他方面，像很好的实习、出色的学生工作等都可以体现在推荐信里。

还有一方面不能忽视的是personal character。俗话说性格决定命运，一个人的性格和未来的成功息息相关，因此personal character也是关注的一个点。在推荐信里适度提一下被推荐人的好性格绝对也是加分项。比如此人has a good sense of humor，常常逗得大家直乐，或者此人很easygoing，和大家都处得很好等等。

SOP

除了正式性之外，SoP 也是唯一可以陈述你在某些情况下表现不佳的理由的文件。例如，你可以解释读研究生过程中遇到的任何艰难困苦，或者解释为什么你在大学的某个学期/季度做得不太好。SoP 的结构应如下：

1. 用引人注目的一段话介绍研究兴趣，使读者想要继续阅读。这是最重要的一点：如果你无法在这一段勾起读者兴趣，他们不太可能继续读下去。
2. 你在研究生学习期间的研究经历（大约一页）。
3. 确定将来要做什么研究。
4. 确定你想合作的人以及原因。
5. （可选）在适当的情况下解释情有可原的情况。

然而，披露苦难和弱点（如学习障碍和精神疾病）也可能是一把双刃剑：读你申请的人可能不会选你，也可能因为这些克服困难的经历而对你抱以同情和钦佩。如果你披露此类事实，则你的 SoP 需要非常精细化。如果你没有专业作者的反馈，请不要尝试这样做。对于一些社会上可以接受的故事，就不需要专业的反馈：从极度贫困到上大学，现在你想通过博士学位来发挥自己的潜力，这样就很容易写出一个令人信服的故事；讲述在患精神分裂症或躁郁症时遇到的困难就很难令人信服。

Toefl tips (also from Internet)

Speaking

逻辑

影子跟读

of for 有时候连读是 e的音 it is really import for us to study hard ， a lot of

no matter 发d， break up 发g， happy habby

Q1 sample

跟风

因为 同龄压力。你知道的，我们班上每个人都会xx，我不想被他们隔离。所以我会做同样的事为了融入他们

It is because of the peer pressure. You know, nowadays everyone in my class chooses to X. I don’t wanna be isolated or even bullied. I remembered when I was in primary school, I was ridiculed by my classmates since I do’nt watch ultraman. Therefore personally, I would like to do the same thing to involve with them.

放松

打篮球让我放松，所以在一些重要考试前我都喜欢打篮球。

Moreover, Playing basketball always makes me feel relaxed. I remembered when I was in college, one time, I prepared for an important final exam, I asked my roommate to play basketball with me, which relaxed me a lot. And finally I got an A level grade on that subject.

帮助养宠物

Last week, my neighbor Mr.Yu had to go to Japan for a business meeting. But nobody could take care of his cat Niannian, which made him very worried. When I knew this, I offered to help him. He was happy which made me very happy as well.

很忙

when i was in high school, i was really busy, i needed to get up at 6.00 and kept study until sleeping, therefore i really had no time to X.

困难 父母 手机

两年前我去大学的时候，那是我第一次离开我父母。一开始我晚上根本睡不着因为我很想念我的爸妈。感谢手机，让我每天都可以和我父母聊天，让我走出孤单。

Two years ago when I went to the university, it was the first time I was apart from my parents.

At first I could not fall asleep at night and often thought of my parents.

Thanks to the cell phone, I could talk to my parents everyday and this really brought me out of the loneliness.

单车 出行 环保

公共交通总是比私家车更方便，尤其当尝试找车位的时候。比如两年前我开车去学校，经常要花20分钟找停车位。然后我决定骑单车/公共交通，然后我就再也没有迟到过了。

• First, it is more convenient than private cars especially when you are finding parking. For example, I used to drive my cars to school two years ago and it often took me 20 minutes to find parking. Then I decided to ride a bicycle to school and I was never late for the class since then.

空气污染

它是环境友好的，而且可以减少许多碳排放。五年前，北京有许多沙尘暴。天空是黄的，人们甚至面对面都看不清对方的脸。在政府 限制碳排放之后，这种现象缓解了很多

Besides, it is environmental-friendly and it can reduce a lot of carbon emission. 5 years ago, there were many sandstorms in Beijing. The sky was yellow and people couldn’t see each other even face to face. ‘After the government limited carbon emission, this phenomenon was alleviated.

当地文化

X有时可以是当地文化的一种象征，这是熟悉当地文化的很好的机会不论是对外国人，游客或是小孩。我仍然记得当我学习X的时候，我被X深深吸引了然后从那时起我就对X产生了兴趣。

X sometimes can be an icon ˈīˌkän of culture ˈkəlCHər, it is really a fantastic chance to learn about local culture especially for foreigners, travelers and even children. I still remembered that when I learnt X at the first time, I was deeply attracted by X, and since then, I become interested in X.

省钱

它很省钱,尤其是钱对我很重要。因为我爸妈在我很小的时候就离婚了，我必须支付学费靠我自己，因此，我想存钱只要我可以。

Firstly, it saves a lot of money. money is very important to me since my parents were divorced when I was a child, I need money to pay for the tuition by myself. Therefore, I would like to save money as long as I can.

时间

任何题都可以扯到时间

Firstly, it saves a lot of time, time is very important to me Since my parents were divorced when I was a child, I need time to do part-time job to pay for the tuition, by myself. Therefore, I would like to save time as long as I can.

可以发现自己的兴趣

First, it can help us find what we love to do. Two years ago, I took part in the training camp of RNG club, which was one of the most famous e-clubs in China.During the training camp, I developed an AI model to help data analysis and that was also when I found what I loved to do.

朋友 新鲜感 社交

X 我可以遇到各种各种的朋友 来自不同国家和地区。这样我可以拥抱不同的文化和生活方式。两年前，当我上X，我交到了许多朋友，kevin来自us，Johnny from Japan, 我也变得更 openminded和sociable

I can make various friends from different regions so that I can embrace diversified culture lifestyles. Two years ago, when I X, I made lots of friends from different countries, and I became more openminded and sociable.

促进就业

It will contribute to the proliferation of employment. I mean it can provide people with a large amount of jobs. As a result, it will in turn enhance the social stability and economic development.

老朋友/父母 更理解你

朋友/父母知道我们更好，因此可以给我很多切实的建议基于我的个性当我陷入困难或者想要做决定的时候。以我自己做个例子，两年前，当我犹豫选哪个科目做我的major的时候，我的朋友/父母建议我学计算机因为我很适合解决问题，现在我真的很开心听从了他们的建议。

Friends/ Parents know us better and they can give us practical suggestions based on our personality when we are in trouble or we want to make decisions. Take myself as an example, two years ago, when I went to the university, I needed to select my major, my friends/parents advised me to study computer science since I was good at solving problems. Now I am really happy to follow their suggestions.

kindle读书

随着科技发展，看书变得越来越方便。当我还是个小孩的时候，我只能在我的房间读书，那真的很不方便。当我想要读，两年前，我买了kindle，它很方便携带 从那时起我可以随时随地看书，在地铁上，stree car上，甚至在厕所里。

With the development of technology, reading becomes more and more convenient. When I was a young kid, I had to stay in my room to read books, which was really inconvenient. Two years ago, I bought a Kindle, which was easy to carry, as a result, I could read book anytime and anywhere. In the subway, in the street car and even in the toilet.=

现代 VS 传统，人工智能，时间增多 效率增加

随着人工智能的发展，人们工作时间下降很多因为AI可以帮助解决重复性的工作。因此，人们会有更多的业余时间并且花费更多的注意力在娱乐/健康上。

With the development of artificial intelligence, people’s working time will decline significantly since AI will help to tackle with repetitive works. Therefore, people will have more spare time and pay more attention on the entertainment/health care.

健康

两年前我去大学的时候，我很胖，朋友都叫我“肥宝”，但在我开始每天打篮球，我变得更健康、帅气 以及自信。

First, it helps me keep healthy and confident. Two years ago when I went to the university, I was very fat and my friends even called me “the fat baby”, but after I joined a basketball club and played basketball, I became more healthy, more handsome and therefore more confident.

拓宽眼界 增长知识

爱好书

The book that really shaped my attitude to the life is a novel called Stories about Ming Dynasty.

As you may see from the title, The book narrates a fantastic 300 years history of ming dynasty in ancient China, but the fragment that impressed me the most was the last chapter of the book. After hearing so many romantic and attractive stories and seeing the success and failure of countless emperors, politicians and Military commanders, the book is ended by the story of XuXiake, who is the most famous travel writer in China. He traveled through China for more than 30 years and documented his travels extensively.

As you may know, there is an old saying in China “万般皆下品 惟有读书高” that every position is inferior to being government officials by learning.

In the ancient China, a position like travel writer is usually regarded as worse and even shameful, especially when compared with being a government official. The motivation that the book ends with the story of a traveler writer is to express the attitude to life, that is, there is only one way to success, which is to follow your heart instead of be influenced by external things like money, power, or judgment from others.

I slid into a depression on several days, luckily, I cheered up again by reading a book, which influenced my attitude to the failure. The book is the biography of Sushi, who was one of the most famous poets in China while his target of his life is being a successful politician. Unluckily, his career as a politician was really not going on smoothly. He was frequently demoted from Beijing to Hubei, from Hubei to Hangzhou, and finally, to the Hainan island, which was pretty far away from Beijing and very poor at that time. His story really impressed me a lot. On the one hand, I knew that life contained many ups and downs no matter how talented you were even though you were the most famous poet in China. One the other hand, Sushi was not a successful politician but could you say that he was a loser？Nope. He was demoted as a politician, but therefore he had enough time and experience to write so many excellent poems. There is an old saying in China “塞翁失马焉知非福”, which tells a story that an old man lost his horse but finally the horse came back even with another mare. And I cannot agree with the story anymore.

Remembering that I’ll be dead soon is the most important tool I’ve ever encountered to help me make the big choices in life. Because almost everything — all external expectations like money or power, all pride, all fear of embarrassment or failure — these things just fall away in the face of death, leaving only what is truly important. Remembering that you are going to die is the best way I know to avoid the trap of thinking you have something to lose. You are already naked. There is no reason not to follow your heart.

张居正 “你还很年轻，将来你会遇到很多人，经历很多事，得到很多，也会失去很多，但无论如何，有两样东西你绝不能丢弃，一个叫良心，另一个叫理想。”

于谦“ 在这个污浊的世界上，能干干净净度过自己一生的人是值得钦佩的”

旅游景点 放松增收

I volunteered to teacher the kids in a remote mountain village in the west of China. Those kids couldn’t afford to buy shoes, much less tuition and fee. If this money could help them to finish their school, my friend will feel prou

网课 通勤

Take online class for example.

First, it is more convenient for students because if they don’t understand the content, they can choose to pause or replay. As for me, I always pause the video when I want to take a note or think about the topic in the class.

Second, kids are vulnerable to temptation like computer games. If teachers encourage them to use computers, they might indulge in video games. Then kids would have less time to exercise and engage in social activities, and this will again lead to kids’ physical problem.

idiom

1. No brainer: something that requires little to no thought. Eg, to me, it’s no brainer, (毫无疑问), all high school students should wear school uniform.
2. Drives me crazy: a way to describe something you hate. eg. It drives me crazy when
3. Not my style, 不是我的菜
4. to make a long story short 总之

and 后面不要停 一定要前面停

https://www.youtube.com/c/KathyTOEFLTeacherLessons/videos

可以首先扫一遍tpo和机经，不详细说每道题，先用中文想一下你会用什么例子来回答，比如某道题我会用兴趣爱好的例子来回答，那就在这道题旁边标一个“兴趣爱好”，然后扫完了所有题目，将所有的标签汇总，你会发现其实你只用准备10多个段子就可以应付大概所有150道左右的独立题目了。然后，你再详细扩写这10个段子，注意添加细节和口语化，避免用太难的句子。最后，一定要用这10个左右的段子再重新扫一遍所有的题目，体会套用段子的感觉。

最后，关于发音。大家如果用iPhone或者iPad，可以用Siri来练习。我每道题3&5题都会过一遍siri，然后看哪一个单词

Need: 人/动物 require: 无生命

Q3 Annoucement + Discussion

记录：Change + Reason

According to the announcement, 。。。

The man/woman agrees/disagrees with this for two reasons.

First …, also …

In addition,… also,…

（For these reasons, the woman doesn’t agree with this announcement)

Q4

解释 xxx的定义，以及教授是怎么illustrate这个xxx的。

记下：

1. definition
2. 最后一句话（往往和lecture内容有关系） or 属性+开端+结果

The article defines X which is XXX(definition).

The professor illustrates this concept with the example of Y, Y is an X because (give connection reasons and examples).

That’s why Y is a good example of a X.(建议一定要有总结）

Listening

态度 Significant, particularly，at least，in fact, usually （并且大写的时候）

一来motivation 比如a new theory 听清楚并做好笔记；有时候来的目的不是一开始就说了的

只选自己听到有类似关键词的

看清题目

分层之后，有些选项会把两层的东西放在一起来干扰视线

首先锁定B，排除D 剩余AC，web site不可能听不到，那么一定是bulletin board听漏了 死马当活马医

大词谨慎选：His research is highly respected throughout the world. 这种肯定能听到，没听到就肯定不是

D.probably 几乎肯定；很可能；大概；带有肯定倾向，但教授态度是偏中立的。

在提到actor之前，有一个明显的语气变化，所以语气变化的地方有时很重要

Writing

独立写作：首先搞一个好模板，这里的好模板的要求是不要那么多废话，人家ets一看就能看出来，好模板就是能够给你提供思路，让你不管遇到什么题都有话可说。对于内容，我觉得托福对于思想深度要求不高，只要自圆其说就好。托福作为一个语言考试，考察的就是语言能力，我们要向ets展示我们的语言功底，比如用不同的句式：倒装、虚拟语气、反问、形式主语等等，因此我们可以在模板中把这些内容标记上，比如第二段要用上一个倒装，第三段用上一个虚拟，这样文章就会活泼很多，字数也会多很多。

https://www.youtube.com/watch?v=1125jntOqH4

independent essay

X and Y both constitute an indispensable part of Z. When it comes to the trade-off between X and Y, people varying in personalities as well as backgrounds have diversified tendencies. One notion is that XX. Personally, I would frown on this claim and reckon that it fails to be representative. I feel this way for two reasons, which I will explore in the following essay.

End

In brief, I would assert that XX is of paramount importance and it is better to XX due to X and Y. Only in this way can we

integrated

The reading and the lecture are both about xxx. The reading passage proposes three main aspects that X. The lecturer, however, disreputes the claims made in the article and states that Y.

To begin with, the reading holds that … . The article mentions that …. . Nevertheless, the lecturer challenged the argument by claimng that …. Additionally, he points out that ….

Secondly, the author suggests that …. In the article, it is said that. On the contrary, the lecturer asserts that … . He goes on to say that …;

Finally, the writer posits that … the author contends that…. In contract, the lecturer’s stance is … he notes that…

In the final analysis, the professor convincinglyx shows that none of the evidence/explanation in the reading passage provides sufficient support for …

Reading

Sentence insertion

1. 注意target sentence中的代词
2. transition words
3. repeat a synonym(同义词)
4. goes into more details about a previous topic

同义词

1. 找but / however 后面的反义词

同义句

可以直接排除的选项：

1. changes the main topic
2. Adds information
3. Miss important information

Some mathematical English

$A$ : capital A

$A^T$: capital A superscript(下标：subscript) capital T

$A^{-1}$: capital A to the minus one

$1/2$: one over two

Some forgotten terms

Banded matrix: like a diagonal matrix, but it has also elements above the main diagonal and below the main diagonal.

Triangular matrix: only has elements above (upper) or below (lower) the main diagonal.

Skew-symmetric matrix: $A^T=-A$ (so that the diagnoal element is zero)

Orthonormal vectors: the two vectors $u,v$ (usually, when we say a vector, its dimension is n by 1, a column vector), are both orthogonal $u^Tv = 0$ and normalized (||u|| = ||v|| = 1)

orthogonal matrix:

• $Q^{-1}= Q^T$
• $QQ^T = I$
• In the multiplication above, if selected rows are the same, results are 1 (diagonal element), otherwise, 0
• That is, the row/column vectors are othernormal vectors
• $(Q X)^T(QX) = ||QX||^2 = X^TQ^TQX = X^TX = ||X||^2$: an orthogonal matrix preserves the norms and lengths.

LU decomposition

Elementary matrix: the identity matrix with one of the zeros replaced by a number

Consider matrix multiplication R = M$\times$A:

$R_1$ (the first row of R) is calculated by the combination sum: $m_{11}\times A_1 + m_{12}\times A_2 +…$

Inverse of elementary matrix: swap the sign of non-zero element (Think $MM^{-1}A = A$)

Eg:

$$M = \begin{bmatrix}
1 & 0 & 0 \
0 & 1 & 0 \ -1& 0 & 1 \end{bmatrix}$$

$$M^{-1} = \begin{bmatrix}
1 & 0 & 0 \
0 & 1 & 0 \ 1& 0 & 1 \end{bmatrix}$$

$$M = \begin{bmatrix}
1 & 0 & 0 \
0 & 1 & 0 \ -1& 0 & 1 \end{bmatrix}$$

LU decomposition: A = LU, L is a lower triangular matrix and U is a upper triangular matrix.

Then, when we try to solve Ax = b, we can actually solve (LU)x = b cause y = Ux, Ly = b are easier to compute compared with Ax= b. (Note L,U are triangular matrices).

Note: it is NOT computational-friendly by LU decomposition if we only calculate Ax=b once. However, if there are multiple b, we can decompose A one time, and benefit from the effecient computation by triangular matrix.

Vector Space

vector space = set of vectors (in this course, column matrices) + set of scalars (real numbers)

should be closed under vector addition and scalar multiplication

Linear Independence

The set of vectors ${u_1,…,u_n}$ are linearly independent if $c_1u_1 + … +c_nu_n = 0$ has only solution $c_1=c_2=…=c_n$.

meaning: no vector in the set can be written as a linear combination of other vectors.

span: we say a set of vector ${u_1,…,u_n}$ span a vector space only consisting of all linear combinations of ${u_1,…,u_n}$.

basis of a vector space is a set of minumum # of vectors that span the space.

The munumum # above is dimension.

Null Space

Null(A) is a vector space of all column vectors x s.t. Ax = 0.

That is, the dot product between row vector and the null vector (vector in the null space) is zero.

Thereofore, row space is orthogonal with null space.

Therefore, dim(Row(A)) + dim(Null(A)) = n (why?)

Left Null Space: $x^TA = 0$

Column Space

$$Mx = \begin{bmatrix}
a & b \
c &d \end{bmatrix} \begin{bmatrix}
x_1 \
x_2 \end{bmatrix} = x_1\begin{bmatrix}
a \
c \end{bmatrix}+x_2\begin{bmatrix}
b \
d \end{bmatrix}$$

Consider row space: $$x^TM = \begin{bmatrix}
x_1 &
x_2 \end{bmatrix}\begin{bmatrix}
a & b \
c &d \end{bmatrix} = x_1\begin{bmatrix}
a &
b \end{bmatrix}+x_2\begin{bmatrix}
c &
d \end{bmatrix}$$

$x^TM$ gives you a vector that is in the row space of M

Above: linear combination of columns of the matrix (in the column space); Mx gives you a vector that is in the column space of M.

Dimension of column space eqauls to the dimension of row space, i.e., dim(Col(A)) = dim(Col(A$^T$)), where the dimension is called rank of A.= number of linearly independent columns

Relationships of Null Space, Column Space, and Row space.

1. The column space of M can be represented by the space spaned by $Mx$. for any x.
2. Similarly, the row space of M can be represented by the space spaned by $x^TM$ for any x.
3. Dim(Col(A)) = dim(Row(A)) = rank
4. Dim(Null(A)) = n - r
5. Dim(Null($A^T$) = m - r

Orthogonal Projections

Project vector down into a subspace. The projected vector is the vector in the subspace that is closest to the original vector.

One example: Solution of the Least-Squares Problem

Ax = b (x is the target ), $A\in \R^{m\times n}, m>n$

b is the y-axis data point value, A is a matrix related to x-axis data point value. The equation Ax=b assumes that the line (represented in x) can go through all points, which is impossible.

Therefore, this is considered as over-determined.

Remeber that Ax gives you a vector that is in the column space of A. If Ax=b is over-determined, that means b is not in the column space of A since there is no solution.

But to find the best solution, what we can do is to project b into the column space of A.

So, we cannot solve Ax=b, instead, we solve Ax= $b_{projCol(A)}$.

write $b = b_{projCol(A)}$ + $b - b_{projCol(A)}$

Consdier the term $b - b_{projCol(A)}$ is orthogonal to the column space of A, (because $b_{projCol(A)}$ is a projection of b to Col(A)), the term is in the subspace Null(A$^T$).

Therefore, we multiply Ax=b by $A^T$ to get rid of the term.

$A^TAx = A^Tb$, normal equation, which has a solution (previous equation is un-solvable) as long as $A^TA$ is invertable,

$x = (A^TA)^{-1}A^Tb$

$Ax = A(A^TA)^{-1}A^Tb = b_{projCol(A)}$

here, $A(A^TA)^{-1}A^T$ is called the projection matrix that projects b into the column matrix of A.

Determinants

Leibniz Formula for calculating determinants

$\det(A)=\sum_{\sigma \in S_n}\text{sgn}(\sigma)\prod_{i=1}^{n} a_{\sigma(i),i}$

where $sgn(\sigma)$ is +/- when the permutation $\sigma$ needs even/odd times of permutations from a normal order. $S_n$ is the permutation group.

Properties

1. Det I = 1
2. det changes sign when row interchanges
3. det is a linear function of all rows. (multiply the first row by a constant, then det is also multiplied by the constant, add works in a similar way)
4. by 2 3: det = 0 if there are equal rows
5. det D/L/U = product of diagonal elements
6. Det(AB) = detA * detB
7. Gaussian Elemination does not change the det

Eigenvalue

Given a matrix $A\in \R^{n\times n}$:

$Ax = \lambda x $, $x$ is the eigen vector and $\lambda$ is the eigen value

That is, $(A-\lambda I )x = 0$.

If $A-\lambda x$ can be inversed (the determinant is not zero), then x=0 is a trivial solution.

Therefore, $A-\lambda x$ cannot be an invertiable matrix (det is zero)

General Summary

What to do everyday

• Pomodoro
• Before sleep, recap + prepared Daily TO-DO with a specfic ddl (8.00pm for example)
• When you wake up, work on the most important and most disliked task first, at least one Pomodoro

What to do (general)

• Ask questions (engaged in) during some disliked activities, e.g. boring lecture.

• have a big picture. (For example, pre-view the chapter headings and figures before class)

What not to do

• do not cram one time, learn by spaced repetition
• do not worry about your product, which may discourage you and make you procrastinated

Week 1

Diffuse: Let the thinking flies by taking a showering, exercise …. When you are trying to propose new ideas, a diffuse mode is better.

Sleep: New synapses are built.

Reason. for Procrastination

1. feel unhappy
2. switch to a more plesant task
3. feel happy temperarily

Solution: Pomodoro(番茄工作法): 25 minutes without internetrruption + a few minutes awards (diffuse mode)

Practice for permanent

Math symbol is abstract, making it difficult to remeber and understand. However, we can remeber some abstarct symbols (like emotion). The reason is practice.

Memory

Working memory(short term memory)：stored in an ineffecient blackboard

Long term memory: stored in an immense warehouse (need to repeat at lease a few times)

spaced repetition: better than practcing one thing for multiple times ONE DAY. （leave time for mortar 砂浆 to dry)

Sleep

• remove toxins when sleeping.
• strength something important to learn
• When you are sleeping, It’s as if the complete deactivation of the conscious you in the prefrontal cortex at the forefront of your brain helps other areas of your brain start talking more easily to one another, allowing them to put together the neural solution to your learning task while you’re sleeping. (diffuse mode) -> focused mode learn before sleeping

Others

How to concertarte in something you dislike, e.g. a boring lecture?

A: Ask questions. Because you learn more when you are engaged in something.

Enriched enviorment is going to help you learning better. In the un-enriched enviorment, exercise will also help you.(new neurons are born ) : use your muscles rather than brain.

Second week chuncks

Chuncks: compact packages of information that your mind can easily access

In you foucs mode, you generate chuncks.

How to form a chunk?

• First build some small mini chuncks (small music passages)
• And then merge them together to form a chunk (john passages together to play a song)

In math&science, we learn some sample problems with worked out solutions.

Other important things:

• Docused attention
• understand the basic idea
• understand solutions to basic questions are not enough (you should be able to do it by YOURSELF)
• You should have a big picture. (For example, pre-view the chapter headings and figures before class), so that you know when and which chuncks and constructed/used, and how chuncks are connected to each other.

Illusions of Competence

Try to remeber a piece of material?

BAD: re-read (re-study); Many underlining and highlighting

GOOD: recall->re-read(re-study)->recall; (in some sense linke test); recall when outside your usual study place.

More advaced study(after you know basic ideas): concept mapping

Week 3: Procrastination

Willpower is not easy. Do not waste willpower on fending off procrastination except when necessary.

Habits

Four parts:

1. Cue（信号，也有皱眉的意思）not neither helpful nor harmful. It is our routine that matters.
2. Routine (Zombie mode)
3. Reward
4. Belief

Procastination is a simple habit that follows the four steps above

Process vs. Product

• To avoid procrastination, concentrate on process instead of product.
• Process relates to simple habits that coincidentally allow you to do unpleasant task

For example, a hard homework

• avoid focusing on the product: the answers to the questions
• Focus on doing a Pomodoro (番茄工作法), a 25-minutes work session

How to overcome pricastination

• Plan:
  • develop a new ritual（仪式）, e.g. leave your phone in the car when attending class. May not work perfectly a first.
  • Weekly list + daily TODO list with a quitting time (write this before you go to sleep)
  • Work on the most important and most disliked task first, at least one Pomodoro
• Reward
• believe your system will work

Week 4: How to Become a Better Learner

• exercise
• metaphor or analogy
• Change your thoughts and admit the mistake
• work with other person to avoid blind spot (but should not be a socialization group)
• For test:
  • start hard, jump to easy
  • this test makes me afraid -> this test makes me determined to do my best!

然后到了我的管家，高武了。他是高二来到我们班的，一开始他孤僻的性格加上奇葩的声音使他看起来很不合群，还经常被我们201耻笑…后来他坐到了我后面，可能由于我看他老实吧，他成了我管家，帮我打理琐碎事务，说来惭愧，作为我的管家我愣是没给过他工资。（后来玩开后笑萍一直拿这个怂恿高武，搞得后来他越来越不老实了。）高武是个胸有大志的人，但他的志向从来不会告诉别人，我还是在他的本子上看到密密麻麻的笔记才知道的，因为那笔记只包含了四个字——武定中原…霸气！同样的，他也不会说出自己的心事，我知道他有心事——他的家庭，他的前途，他的成绩，但他一概不提，他总是一个人憋在心里，他会午睡时一个人孤独的成四十五度角仰望窗台外明朗的天空和远方如中国画一般墨绿的山峰，他会睡觉时翻来覆去思考与他有关的一切事，他会在他许多很“非主流”的本子上记下他所思所想，这也许是他的思考方式吧。

额，在这里研究他的心理似乎有点不厚道，不说这方面了。

高武不善言辞，很多时候都是默默的承受，还是我最压抑的日子，他从没鼓励我什么的，但高考完，小姨问起我我们班有没有人名字里有个武，那时我才知道，原来高武一直发短信给我小姨，让我小姨来安慰我。听完我内心诧异了许久，原来那个呆呆木木的高武也会关心人诶，原来世界上还有许多人挂念，关心着我，这种感觉真是别样的幸福。

这段是我高中刚毕业时写下的和高武有关的回忆。我觉得我有一些需要补充的必要。我第一次和高武的接触应该是由此在201讨论他的时候：应该是说他奇怪的声音和某些特点，譬如止不住的咳嗽？总之睡在宿舍门口上铺的我看到了高武正在偷听：那个瘦弱矮小性格冷淡的男生正侧着身子将耳朵放到门边听着我们对他的讨论，我已忘记我们是否带着嘲讽意味，但愿没有。

后来他坐我后面，具体怎么成了前后桌的我也忘了，不过很高兴的是我并没有对这个有点“被排挤”的同学有一点不满或是不乐意接触的意思。记得班上有过另外一个新来的同学也是经常咳嗽，结果她前排的那位同学对此很不满，总是觉得她咳口水到自己的头发上了，这方面我倒是无所谓，毕竟我自己就很邋遢。

总之成了前后桌之后我和他的关系直线上升，直至经常一起吃饭。我比较邋遢，爸妈给的钱和一些零钱也总是扔在一起，见高武整理的井井有条，便索性委托高武帮我管理财物。还称之为管家。甚至都达成了少年之约，待我功成名就需要管家的时候，一定请高武来当我家总管。学习上，虽然我偶有教高武一些我的学习方法，不过他也不怎么问我题目，可能和很多同学一样，不想因为问题太简单被我耻笑吧。

高中毕业后，高武也曾联系我，问我“李巍，你现在过的怎么样？”。我过了很久才看到消息，回到“很好啊，高武，你呢？”。然后便没有下文了。这也是我最追悔莫及的一点，倘若我早点回复，或者跟高武继续聊天保持联系，至少我还能在他身前给他更多的一点温暖。

这是我能补充的所有片段了，我再怎么想，也没有一个向后的时光机可以倒转。不过再翻看上面的回忆，这个天然前进的时光机倒是让有些问题在现在得到了答案，譬如他的家庭、他的前途、他的心事，我总算了解了一些，虽然为时已晚。高武本身家庭就很贫困，他家在一个离镇上都还有接近两小时车程的山沟沟里，我问了当地村长，还好那个地方和镇上每天都有班车来回，不过即便如此高武往返学校来回都需要至少十小时的车程。出发前我其实对找到高武的住处也有着一丝担忧，我只知道他是哪个村的，其他一概不知，万幸我在乡卫生所，其实也就是一个很小的医药门面，碰到了他们村的村长，在村长的指引下，我找到了他的住处。他父亲当时正在收割稻田，村长下田里叫他，叔叔便赤着脚走回了家里，脚上还沾满了水田里的泥土。高武是在过年的时候在他姑父家出的意外，当时他帮姑父一家拍照一直往后退，便不慎跌下楼。骨灰也留在了姑父家，没有带回来。他的妈妈因为吃农药过世了，我不清楚是高武去世前还是之后，但总之他父亲现在一个人孤苦伶仃的生活着。我随着叔叔进了门，看着基本家徒四壁的光景，想到我本应该很早就来他家里看看，我眼泪又止不住的流。但是我没有像第一次知道消息时一直痛哭，我内心告诉自己不能再流泪了，高武的爸爸才是最伤心的那个人，我不能再勾起他更多的痛苦的回忆。我将买的水果牛奶给了叔叔，但是他硬是拒绝了我给的钱，无奈，我只能加上叔叔的微信，告别了高武的故乡。

说到高中，自从知道了那件事后，很不想再和过去的时光有什么瓜葛：有点我以我心对明月，奈何明月照沟渠的意思。但是对于高武，确实是让我感动到耿耿于怀的：那个在草稿本上写满武定中原，看起来深不可测的高武，高考前两个月一直和我小姨发短信说我压力很大让小姨安慰安慰我。高中刚毕业时，对于这些，粗线条的我只是感动，然后一带而过。但现在越发觉得，要做到这一步，实在是太无私伟大了。人生在世，大多数人只是为了自己：和你相处是为了自己的前途或是为了自己能开心，倘若你对我的前途无用、或是你惹的我不开心了，我屁股一拍就可以溜了，临走时还可以忿忿道对方如何如何不好。而像高武，便是我钦佩和想成为的，温暖而不张扬，照顾他人情绪而不仅仅是为了自己。可惜的是高中后便和他断了联系，纵使一直qq找他也了无音信。

上面这段，是今年四月份我碎碎念时念叨的关于高武的片段。当时我还不知道高武的噩耗，我只当高武和我无数同学朋友一样，只是有了各自的生活所以少了联系，但当再次遇见时，便又能相视大笑，共忆少年时。

直到我再赶ICCAD的前一两个星期，无意中得知了他的意外。一瞬间我的双脚像没了知觉一样瘫倒在地，我倒在地上嚎啕大哭，脑子里一片空白，只有难过。我哭了不知多久，把自己眼泪哭干了，力气哭没了，肚子哭饿了，便去找水喝，可是水也拿不稳，我便继续倚在打水的台子上哭。

距离高武离开已经快六年了，距离我知道这个消息也半年了，但终究仍然莫名其妙有一些时刻，那种难以置信、悲痛欲绝的感觉会涌上我的心头。我是个缺爱的人，也因此我很珍惜那些温柔的、会表达爱的、无条件对我好的人。可惜当我认识到自我、认识到哪些人是这样的人的时候已经晚了。不过按照活在心中便不是死亡的概念，高武一直不会离去，我也要带着他的温柔，和他一样，做一个体贴、无私、善良的人。