在上图中,我们可以看到论文中使用的数据都具有某种周期性(Periodicity)。KPI A,B,C 都是具有明显具有工作日和周末特点的,在工作日和周末分别有着不同的形状;KPI D 则是关于网上应用商店周五促销的,因此在周五周六的时候,其实时间序列会出现一个尖峰(peak);KPI E 的话则是每隔 7 天,会有两个尖刺,然后并且迅速恢复;KPI F 的话则是可以看出时间序列在十一的走势跟其余的时间点明显有区别。除此之外,对于一些做旅游,电商等行业的公司,其节假日效应会更加突出一点,而且不同的业务在节假日的表现其实也是不一样的。有的时间序列在节假日当天可能会上涨(电商销售额),有的时间序列在节假日当天反而会下降(订车票,飞机票的订单量)。因此,在对这些时间序列做异常检测的同时,如何避免其节假日效应就是一个关键的问题了。
从上图可以看到 Period 的核心思路(core idea)。在本文使用的数据中,时间序列的长度较长,一般来说都是好几个月到半年不等,甚至更长的时间。对于一条时间序列(a given KPI),可以将它的历史数据(historical data)进行按天切分,获得多个子序列(sub KPIs)。对于这多个子序列,需要进行聚类以得到不同类别。或者按照日历直接把时间序列的工作日(work day),休息日(off day),春节(spring festival)序列进行切分,将工作日放在一起,休息日放在一起,春节放在一起。把这些子序列进行拼接就可以得到三条时间序列数据,分别是原时间序列的工作日序列(work day subsequence),休息日序列(off day subsequence),春节序列(spring festival subsequence)。然后分别对着三条时间序列训练一个异常检测的模型(例如 Holt-Winters 算法,简写为 HW)。对于新来的时间序列,可以根据当日具体的日期(工作日,休息日或者春节)放入相应的模型进行异常检测,从而进一步地得到最终的结果。
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到了第三年才开始逐渐分流,学习不同的课程。如果是在数学与应用数学专业,就是学习实变函数,泛函分析,拓扑学,微分几何等课程。如果是在信息与计算科学,则是学习实变函数,泛函分析,偏微分方程数值解,运筹学,计算机图形学,信号处理等课程。在不同的专业上面,所学习到的课程内容则是完全不一样的。而该专业的编程工具主要还是使用 Matlab,毕竟用 C++ 这种编程语言写矩阵运算一类的确实不太合适。
当年笔者在南京大学就读的时候,就曾听闻 NJU 的化学系,物理系,地科系,天文系都是 NJU 的王牌院系,自然也有不少优秀的高中生选择这些方向进行攻读。笔者在校期间除了拿到学位,也得到了许多南大老师的帮助和教诲,在此表示感谢。在 2006 年,闵乃本院士课题组获得了国家自然科学一等奖,也是国家对 NJU 在自然科学领域的认可。
在国外留学的时候,就感受到一些院校更加强调学以致用。即使是化学,生物,物理等基础学科,在本科期间也会积极安排实习的机会给学生,让学生们有一定的就业实践,获得必要的社会经历。在新加坡国立大学(National University of Singapore),化学系的本科学生是有机会获得一些实习机会的。
2020 NUS E-Open House:最后一年的实习
除此之外,最后的毕业项目(Final Year Project)也是需要有一定的实践的。例如,可以与近些年比较火的机器学习(machine learning)和数据分析(data analytics)相结合,将学生培养成具备一定的化学数据分析经验方向的人才。
如果有机会的话,其实学校,研究所,工业界帮学生牵线搭桥是非常有必要的,毕竟 NJU 的生源质量整体来看还是非常不错的,有的学生真的只是缺少一个机会而已。在这种时候,如果事先在读书之前,就提前给学生和家长做好一定的职业辅导,是不是也是一种方法呢?下面几幅图来自 NUS 的 2020 E-Open House,化学系的老师在网络上给大家介绍了化学系学生的一些发展方向,其实这样的内容对学生和家长而言可能更有价值和意义。
职业发展:Chief Analytical Chemist
职业发展:Medicinal Chemist
职业发展:Energy Chemist
无论是 NJU 还是 NUS 的学生都是相对优秀的,有的时候给一个转行的机会就能够紧紧地把握住。如果实在是找不到本专业的就业机会,那就只能够找个机会努力转行了。其实,大学最重要的是培养正确的价值观,引导学生们做想做的事情,做喜欢做的事,而不是为了某个目的而把学生的其他路封死。如果一个人真心想做科研,那么他就不会被其他事情所干扰;如果一个人不是真心想做科研,那么他迟早也是要离开的,无论学校是否告诉他一条转行的道路。
时至今日,国内的疫情已经基本稳定,每个省都在走向全面复工的道路,普通的医用口罩其实也不再短缺,无论是网上商店还是线下药店都能够买到口罩。但让人万万没想到的是国外疫情出现了井喷式的增长,从 Google 的疫情统计来看,不少国家的累计确诊人数已经远远超过中国,美国至今已经高达 50 万的确诊病例,甚至还有持续上涨的趋势。疫情刚开始的时候,国外的不少人还说戴口罩没有用,呼吁大家不用戴口罩。虽然笔者也没有直接证据证明戴口罩能够有效地防护,但是为了保险起见,如果买得到口罩,并且能够承受这个经济压力的话,戴口罩其实对个人也没有什么大碍。虽然刚开始的时候不适应,但是戴多了其实也就那么回事。不过戴着口罩思考问题,写代码确实挺累的,但是为了保障身体健康也只能够戴着,别无选择。
新加坡政府控制疫情虽然暂时还没有那么严格,但是也算是下了决心。有一句来自其他地方的笑话,Singapore is a fine city。fine 除了大家都知道的意思之外,另外一层含义就是罚金或者罚款。那为了控制疫情,新加坡政府会给违反规定的民众开出相应的罚单也属于合理的范围。刚开始的时候愿意给警告信,但从 4 月 12 日起就直接开罚单了,每次 300 新币(约人民币 1500 元)。
每次提到数学这个词,大家能够想到的就是初等代数,平面几何,组合运算,微积分,线性代数,概率论等方向。但在整个数学领域(Earth of Math)上,还有很多更有意思的领域和研究方向,包括数论,几何,拓扑,分形几何,分析,概率统计,博弈论,代数等诸多方向,每一个方向都有很多优秀的数学家在从事相关研究。
Earth of Mathematics
当年在数学系的时候,所研究的方向是分形几何(Fractal Geometry)和复动力系统(Complex Dynamics),位于 Earth of Math 的左侧,称之为分形湖泊(Fractal Lakes)。所谓分形,其实是一个粗糙或者零碎的集合形状,可以分成多个部分,且每个部分放大之后与整体有某种相似性,即具有自相似性的性质。而动力系统则是基于某种固定的规则,描述一个空间内的所有点随时间的变化情况,例如钟摆的晃动,水的流动,湖泊里面鱼类的数量。备注:动力系统并不是指汽车的动力系统和发动机引擎,这两者毫无关系。
针对不同的定义域,函数的迭代有着完全不同的研究方法。当时的研究方向是复动力系统(Complex Dynamical Systems)。复动力系统理论的研究始于 1920 年,当时是由数学家 Fatou 和 Julia 研究的,因此复动力系统中的两个重要的集合就是以 Fatou 和 Julia 来命名的,分别称之为 Fatou set 和 Julia Set。随着计算机技术的演进,在上世纪八十年代这些集合可以通过计算机进行可视化,分形几何和复动力系统理论开始蓬勃发展起来。在与双曲几何、分形几何、现代分析学和混沌学等学科发展相互促进的同时,围绕双曲猜想以及 Mandelbrot 集合的研究工作,成为当今复动力系统的研究热点。
举个例子,函数 ()的 Julia 集合的动图如下:
Julia 集合
当然,科研的时候可不是做一点可视化就算完成任务了,还是需要按部就班的学习各种数学知识和技能。
之前在学校研究动力系统的时候,收集过一些书籍,在此列举给大家,希望对初学者有一定的帮助。One Dimensional Real and Complex Dynamics(实与复动力系统)需要学习的资料如下:
如果是在 NUS 的 IMS(Institute for Mathematical Sciences)举办的学术会议,一般来说只要是在校的研究生都是可以参加的。记得当时参加的第一个学术会议是关于 PDE 的,标题叫做 Hyperbolic Conservation Laws and Kinetic Equations:Theory, Computation, and Applications(1 November – 19 December 2010)。笔者去听这个系列讲座是因为在 2010 年选择了一门 PDE 的研究生课程,而这个讲座则是作为课程的一部分。
IMS 的偏微分方程学术会议
笔者参与的另外一个学术会议则是关于动力系统的,标题叫做 Workshop on Non-uniformly Hyperbolic and Neural One-dimensional Dynamics(23 – 27 April 2012),主要是关于非一致双曲动力系统方向的研讨会。笔者记得当时所修的课程应该只有概率论(Probability II)一门课,因此上课的任务不算很重。参会的时间恰好是学期快结束的时候,科研的任务也不算特别繁重。因此,积极参与各种学术会议也算是科研的其中一部分,一来通过参会可以了解当前的学术研究情况,二来可以认识学术界的各种人士,也算是扩大学术交流圈子的好机会。
从数学家族谱(Mathematics Genealogy Project)上面可以看到:Gian-Carlo Rota 的导师是 Jacob T. Schwartz,Rota 于 1956 年在耶鲁大学获得数学博士学位,其博士论文的题目是 Extension Theory of Differential Operators。
Rota 的数学族谱
在 1997 年,Rota 发表了两篇关于人生经验和忠告的文章,分别是 “Ten Lessons I wish I Had Been Taught” 和 “Ten Lessons for the Survival of a Mathematics Department“。下面就来逐一分享这两篇文章中的一些观点。
Ten Lessons I wish I Had Been Taught
Ten Lessons I wish I Had Been Taught
讲座(Lecturing)
每次讲座或者分享的时候都有几个需要注意的事情。
(a)每次讲座都应该只有一个重点。(Every lecture should make only one main point.)
Every lecture should state one main point and repeat it over and over, like a theme with variations. An audience is like a herd of cows, moving slowly in the direction they are being driven towards. If we make one point, we have a good chance that the audience will take the right direction; if we make several points, then the cows will scatter all over the field. The audience will lose interest and everyone will go back to the thoughts they interrupted in order to come to our lecture.
(b)不要超时。(Never run overtime.)
Running overtime is the one unforgivable error a lecturer can make. After fifty minutes (one micro-century as von Neumann used to say) everybody’s attention will turn elsewhere even if we are trying to prove the Riemann hypothesis. One minute overtime can destroy the best of lectures.
(c)提及听众的成果。(Relate to your audience.)
As you enter the lecture hall, try to spot someone in the audience with whose work you have some familiarity. Quickly rearrange your presentation so as to manage to mention some of that person’s work. In this way, you will guarantee that at least one person will follow with rapt attention, and you will make a friend to boot.
Everyone in the audience has come to listen to your lecture with the secret hope of hearing their work mentioned.
(d)给听众一些值得回忆的东西。(Give them something to take home.)
Most of the time they admit that they have forgotten the subject of the course and all the mathematics I thought I had taught them. However, they will gladly recall some joke, some anecdote, some quirk, some side remark, or some mistake I made.
板书技巧(Blackboard Technique)
(a)开讲前保持黑板干净(Make sure the blackboard is spotless.)
By starting with a spotless blackboard you will subtly convey the impression that the lecture they are about to hear is equally spotless.
(b)从黑板的左上角开始书写(Start writing on the top left-hand corner.)
What we write on the blackboard should correspond to what we want an attentive listener to take down in his notebook. It is preferable to write slowly and in a large handwriting, with no abbreviations.
When slides are used instead of the blackboard, the speaker should spend some time explaining each slide, preferably by adding sentences that are inessential, repetitive, or superfluous, so as to allow any member of the audience time to copy our slide. We all fall prey to the illusion that a listener will find the time to read the copy of the slides we hand them after the lecture. This is wishful thinking.
多次公布同样的结果(Publish the Same Result Several Times)
The mathematical community is split into small groups, each one with its own customs, notation, and terminology. It may soon be indispensable to present the same result in several versions, each one accessible to a specific group; the price one might have to pay otherwise is to have our work rediscovered by someone who uses a different language and notation and who will rightly claim it as his own.
说明性的工作反而更有可能被记得(You Are More Likely to Be Remembered by Your Expository Work)
When we think of Hilbert, we think of a few of his great theorems, like his basis theorem. But Hilbert’s name is more often remembered for his work in number theory, his Zahlbericht, his book Foundations of Geometry, and for his text on integral equations.
每个数学家只有少数的招数(Every Mathematician Has Only a Few Tricks)
You admire Erdös’s contributions to mathematics as much as I do, and I felt annoyed when the older mathematician flatly and definitively stated that all of Erdös’s work could be “reduced” to a few tricks which Erdös repeatedly relied on in his proofs. What the number theorist did not realize is that other mathematicians, even the very best, also rely on a few tricks which they use over and over. But on reading the proofs of Hilbert’s striking and deep theorems in invariant theory, it was surprising to verify that Hilbert’s proofs relied on the same few tricks. Even Hilbert had only a few tricks!
别害怕犯错(Do Not Worry about Your Mistakes)
There are two kinds of mistakes. There are fatal mistakes that destroy a theory, but there are also contingent ones, which are useful in testing the stability of a theory.
使用费曼的方法(Use the Feynman Method)
You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, “How did he do it? He must be a genius!”
不要吝啬你的赞美(Give Lavish Acknowledgments)
I have always felt miffed after reading a paper in which I felt I was not being given proper credit, and it is safe to conjecture that the same happens to everyone else.
写好摘要(Write Informative Introductions)
If we wish our paper to be read, we had better provide our prospective readers with strong motivation to do so. A lengthy introduction, summarizing the history of the subject, giving everybody his due, and perhaps enticingly outlining the content of the paper in a discursive manner, will go some of the way towards getting us a couple of readers.
为老年做好心理准备(Be Prepared for Old Age)
You must realize that after reaching a certain age you are no longer viewed as a person. You become an institution, and you are treated the way institutions are treated. You are expected to behave like a piece of period furniture, an architectural landmark, or an incunabulum.
Ten Lessons for the Survival of a Mathematics Department
Ten Lessons for the Survival of a Mathematics Department
不要在其他系讲自己系同事的坏话(Never wash your dirty linen in public)
Departments of a university are like sovereign states: there is no such thing as charity towards one another.
别越级打报告(Never go above the head of your department)
Your letter will be viewed as evidence of disunity in the rank and file of mathematicians. Human nature being what it is, such a dean or provost is likely to remember an unsolicited letter at budget time, and not very kindly at that.
不要进行领域评价(Never Compare Fields)
You are not alone in believing that your own field is better and more promising than those of your colleagues. We all believe the same about our own fields. But our beliefs cancel each other out. Better keep your mouth shut rather than make yourself obnoxious. And remember, when talking to outsiders, have nothing but praise for your colleagues in all fields, even for those in combinatorics. All public shows of disunity are ultimately harmful to the well-being of mathematics.
别看不起别人使用的数学(Remember that the grocery bill is a piece of mathematics too)
The grocery bill, a computer program, and class field theory are three instances of mathematics. Your opinion that some instances may be better than others is most effectively verbalized when you are asked to vote on a tenure decision. At other times, a careless statement of relative values is more likely to turn potential friends of mathematics into enemies of our field. Believe me, we are going to need all the friends we can get.
善待擅长教学的老师(Do not look down on good teachers)
Mathematics is the greatest undertaking of mankind. All mathematicians know this. Yet many people do not share this view. Consequently, mathematics is not as self-supporting a profession in our society as the exercise of poetry was in medieval Ireland. Most of our income will have to come from teaching, and the more students we teach, the more of our friends we can appoint to our department. Those few colleagues who are successful at teaching undergraduate courses should earn our thanks as well as our respect. It is counterproductive to turn up our noses at those who bring home the dough.
学会推销自己的数学成果(Write expository papers)
When I was in graduate school, one of my teachers told me, “When you write a research paper, you are afraid that your result might already be known; but when you write an expository paper, you discover that nothing is known.”
It is not enough for you (or anyone) to have a good product to sell; you must package it right and advertise it properly. Otherwise you will go out of business.
When an engineer knocks at your door with a mathematical question, you should not try to get rid of him or her as quickly as possible.
不要把提问者拒之门外(Do not show your questioners to the door)
What the engineer wants is to be treated with respect and consideration, like the human being he is, and most of all to be listened to with rapt attention. If you do this, he will be likely to hit upon a clever new idea as he explains the problem to you, and you will get some of the credit.
Listening to engineers and other scientists is our duty. You may even learn some interesting new mathematics while doing so.
联合阵线(View the mathematical community as a United Front)
Grade school teachers, high school teachers, administrators and lobbyists are as much mathematicians as you or Hilbert. It is not up to us to make invidious distinctions. They contribute to the well-being of mathematics as much as or more than you or other mathematicians. They are right in feeling left out by snobbish research mathematicians who do not know on which side their bread is buttered. It is our best interest, as well as the interest of justice, to treat all who deal with mathematics in whatever way as equals. By being united we will increase the probability of our survival.
把科学从不可靠中拯救出来(Attack Flakiness)
Flakiness is nowadays creeping into the sciences like a virus through a computer, and it may be the present threat to our civilization. Mathematics can save the world from the invasion of the flakes by unmasking them and by contributing some hard thinking. You and I know that mathematics is not and will never be flaky, by definition.
This is the biggest chance we have had in a long while to make a lasting contribution to the well-being of Science. Let us not botch it as we did with the few other chances we have had in the past.
善待所有人(Learn when to withdraw)
Let me confess to you something I have told very few others (after all, this message will not get around much): I have written some of the papers I like the most while hiding in a closet. When the going gets rough, we have recourse to a way of salvation that is not available to ordinary mortals: we have that Mighty Fortress that is our Mathematics. This is what makes us mathematicians into very special people. The danger is envy from the rest of the world.
When you meet someone who does not know how to differentiate and integrate, be kind, gentle, understanding. Remember, there are lots of people like that out there, and if we are not careful, they will do away with us, as has happened many times before in history to other Very Special People.
参考资料:
Rota, Gian-Carlo. “Ten lessons I wish I had been taught.” Indiscrete thoughts. Birkhäuser, Boston, MA, 1997. 195-203.
Rota, Gian-Carlo. “Ten Lessons for the Survival of a Mathematics Department.” Indiscrete Thoughts. Birkhäuser, Boston, MA, 1997. 204-208.
在运维领域,服务侧的异常会由多方面的原因造成,有的时候是因为网络的抖动,有的时候是因为机器的故障,有的时候甚至是因为人为的变更。本篇博客会介绍一种机器异常定位的方法,论文是来自于清华 Netman 实验室的《FluxRank:A Widely-Deployable Framework to Automatically Localizting Root Cause Machines for Software Service Failure Mitigation》。本篇论文主要介绍了如何从服务的故障定位到局部异常的机器,也就是说在发现服务故障的同时,进一步推断出是由哪些机器出现问题而导致的。
对于一条业务指标(时间序列)而言,大多数情况下是处于正常的状态(normal)。但是如果出现了错误的变更,发布了错误的程序,或者服务器突然出现了故障,都会导致业务指标出现变化,就从正常(normal)变成异常(abnormal)。这个时候就会出现一个故障的开始时间,也就是 failure start time ,这个时间戳是运维领域非常重要的时间戳,它由异常检测(anomaly detection)产生,无论在告警收敛(alarm convergence)还是根因分析(root cause analysis)都非常依赖这个时间戳。而另外一个时间戳虽然没有故障开始时间那么重要,但是也有着其实用价值,那就是缓和开始时间(mitigation start time),它表示故障虽然还没有恢复,但是出于稍微平稳的走势,并没有持续恶化。在出现了故障之后,通常都会发送相应的告警给运维人员,那么在发送告警的时候,如果将异常定位的结果随之带出,则会大大减少运维人员排障的时间。在故障缓和的时间内,运维人员通常需要进行必要的操作来排查故障,例如切换流量(switch Traffic),回滚版本(Rollback Version),重启实例(Restart Instances),下线机器等操作。除此之外,为了定位问题(Root Cause Analysis),运维人员需要分析源码(Code Analysis),查看日志(Log Analysis)等一系列操作。如果能够将这一系列操作融入相应的机器学习模块中,将会节省运维人员大量的排障时间。
贝叶斯网络
通常来说,故障定位也称为根因分析或者根源分析(Root Cause Analysis),都是为了排查产生这次故障的原因。在机器学习领域,为了进行因果分析(Causal Analysis),则需要使用相应的模型来进行建模。其中较为经典的统计分析方法则是贝叶斯分析法,其中的贝叶斯网络(Bayesian Network)则是经典模型之一。下面来看一个简单的例子。
在同一个模块下,如果出现故障机器的占比较大,那么故障将集中于这个模块下,可以通过 ratio 这个指标进行排序工作。
实验数据
在 FluxRank 论文中,作者们收集了 70 个真实的案例,然后根据实验效果获得了结果。
部分真实案例
在标记的时候,除了标记异常机器(Root Cause Machines,简称为 RCM)之外,也需要标记相关的指标(Relevant KPI,简称为 RK)。Root Cause Digest(简称为 RCD)把包括两个部分,不仅包括 RCM 的一个聚类结果,还包括聚类结果中的 top-five KPIs。
通过对 FluxRank 进行实验,可以得到如下实验数据:
FluxRank 的实验结果
其中 Recall@K 指的是: 或者
参考资料
FluxRank: A Widely-Deployable Framework to Automatically Localizing Root Cause Machines for Software Service Failure Mitigation,Ping Liu,Yu Chen,Xiaohui Nie,Jing Zhu,Shenglin Zhang,Kaixin Sui,Ming Zhang,Dan Pei,ISSRE 2019, Berlin, Germany, Oct 28-31, 2019。
Introduction to Statistical Quality Control,6th edition,Douglas C.Montgomery。
从 NUS 的巴士线路图上可以看出,NUS 不仅无缝对接着地铁站 Kent Ridge MRT,也对接着 Kent Ridge Bus Terminal。因此无论从学校的任何地方,都可以通过 Shuttle Bus 到达地铁站或者公交站。不过话说回来,笔者刚到 NUS 的时候是 2010 年,当时还没有开通 Kent Ridge MRT,要坐地铁只能够去 Clementi 或者 Buona Vista,而且只能坐 95 路或者 96 路公交车出行。到了 2011 年的时候,随着修建了 6 年的 Kent Ridge MRT Station 建成,NUS 的学生们就可以很方便的出行了。
NUS 的 Shuttle Bus 是免费给所有人乘坐的,包括老师,学生,外来的工作人员等。除了免费这一个福利之外,NUS 的 Shuttle Bus 也别具特色,学校会将 LOGO 印在 Bus 上,可以让人一眼认出这个是 NUS 的 Bus。而 Bus 的大小是按照线路来分的,通常来说 A1,A2 的车型相对偏大,而 B1,B2,C 车的车型相对偏小,这也是根据是否经过宿舍区,和路线上人数的多少而定的。
2015 年的 Shuttle Bus
在 NUS 里面,除了学校的穿梭巴士之外,还有很多其余的穿梭巴士,其中比较有名的就是 West Coast Plaza 的 Shuttle Bus 了。在 UTown 和 Kent Ridge MRT Station 还没有建好的时候,West Coast Plaza 就是 NUS 学生经常去购物的地点了。因此,免费的穿梭巴士就成为了首选。但是 West Coast Plaza 的穿梭巴士则小了许多,跟香港的小巴能够装载的人数差不多。除此之外,在 PGP 附近,笔者好像也见过 Science Park Shuttle,只不过从来就没有坐过,也并不知道这辆车的目的地是哪里。
NUS Utown 的游泳池虽然没有金沙酒店的游泳池那么高端,但是也是 NUS 的一大亮点之一。UTown 是 NUS 于 2011 年修建的大学城,承担了教学,住宿,学习,娱乐,健身于一身的诸多功能。在 UTown 建成之前,Prince George Park 其实只提供给本科生住宿,而 master 或者 PHD 想住学校宿舍的话,就只能够选择 BoonLay 的宿舍或者 Common Wealth 两处的宿舍。因为宿舍实在是不够用,必须要优先解决本科生的住宿问题。当 UTown 建成了之后,有不少的博士生都选择搬进去,而搬进去的时候,可以选择自己的室友。如果是熟悉的朋友自然是好,如果是没有熟悉的朋友就只能够跟其他陌生人一起居住了,不过就算是陌生人也是 NUS 的学生,因此整体来看也不会出现太大的问题。
UTown 夜景
UTown 的游泳池就位于 Stephen Ready Centre 的第三层,它对学生免费的。因此只要是 NUS 的教职工,就可以通过证件在开放时间内进入游泳池。一般到了午后或者周末,游泳池里面总是有很多学生在游泳或者晒太阳。相对于 Swimming Pool,这里更像是一个休闲的地方。无论是学生还是老师,觉得科研或者学习疲惫了,就可以来游泳池运动并且放松一下。
其实 NUS 的食堂还是相对较多的,在 Engineering,Science,Business 等院系都有自己的食堂。无论是学校内的人,还是外部的工作人士,都可以选择到这些食堂吃饭。在大学城 UTown 的 Town Plaza 也有食堂,无论是中国美食还是其他国家的食物,基本上在这里都能够找到。对于数学系的博士生而言,每天到了午餐或者晚餐的时候,除了在 Science 吃饭之外,还可以选择到 UTown 或者 Prince George Park 吃饭。而每到周末或者节假日,也就只有这两个食堂开门了,其他食堂(例如 Science Canteen 等食堂)在节假日期间是不会对外开放的。在博士生日常思考人生的同时,思考每一顿饭吃什么也是一件非常重要的事情。
位于新加坡西海岸的新加坡国立大学(National University of Singapore)是一所综合性大学,近十年在泰晤士报(Times)世界大学排名和 QS 世界大学排名上,NUS 都长期名列前茅,属于亚洲的顶级学府。NUS 的前身成立于 1905 年,今年恰好是 NUS 115 校庆的年份。发展至今,NUS 已经是拥有多个学院的综合性大学,其中包括理学院(Faculty of Science),工学院(Faculty of Engineering),商学院(Business School)等诸多学院。
NUS 的地图
NUS Open Day(新加坡国立大学开放日)
学校的排名除了全体教职工的努力之外,优秀的生源也是保障学校能够持续运营的必要条件。因此,在每个学年的第二个学期,大约在 2,3月份的时候,NUS 都会开展 Open Day,目的之一就是对新加坡的本地学生和国际学生宣传 NUS。除了宣传自己的硬件设施,专业特色,教授质量之外,还会宣传校园生活(Campus Life),基础设施和历年优秀学生的就业情况。
当年笔者还在 NUS 就读的时候,就有幸参加过 NUS 的 Open Day,不过当年只是为了凑热闹而去观看了一些活动,并没有在申请学校之前就享受到这些福利。每年到了 Open Day 之际,都会有大批中学生或者理工院校的学生前来 NUS,通过参观 NUS 的情况,来判断 NUS 是否适合自身的发展。
NUS Open Day 2015
NUS E-Open House
由于 2020 年的开局实在是不利,世界上的诸多国家都受到了新型冠状病毒的影响,自然新加坡也不例外。可能是因为这个原因,2020 年的 NUS Open Day 就从线下(Offline)搬到了线上(Online),通过网络这一个重要的媒介来开展 Open Day。今年的 NUS E-Open House 应该是历史上首次在网上举办的校园开放日活动,同时校方在 NUS 的官网上也进行了大力的宣传。
由于本次的 NUS E-Open House 为期九天,从 2020-02-26 到 2020-03-05,个人感觉 Open Day 不如称之为 Open Week。在这段时间,NUS 的所有学院将会通过网络向全世界展示 NUS 的魅力。在这段时间里,学生和家长,包括想要继续深造的职场人士都可以通过社交网络了解到 NUS 的方方面面。
School of Continuing and Lifelong Education(持续与终身教育学院)
学习不仅仅是学生时期的事情,在这个高速发展的时代,学习这件事情将会伴随我们每个人一生的时间。于 2016 年成立的 School of Continuing and Lifelong Education 会给每个成年人提供持续教育的机会。它主要是为了想学习新技能的成年人或者想拿到学位的成年人而设置的。在这个学院有本科项目和硕士项目,还有短期项目或者各种培训。如果想拿到某些证书或者学位,其实这里是个不错的选择。
当年在新加坡国立大学(NUS)读书的时候,身边就有一些攻读 Master 学位的同学,当时他们就已经在公司工作了,在工作之余会选择 part time 的硕士在进行攻读。只要达到了学分或者做完了相应的 Project 就可以拿到 Master 学位。
Department of Mathematics(数学系)
新加坡国立大学数学系的前身可以追溯到 1929 年的 Raffles College。当时理学院开设了数学,化学,物理三门课程,不过总共也就只有十个学生和三位教师,其中有一位是数学教师。第一届数学系的领导(从1931年到1959年)是 Alexander Oppenheim 教授,他是在美国芝加哥大学获得的博士学位。从 1929 年开始,在新加坡的教育系统中,数学教育事业得到了巨大的发展,对现在的新加坡国立大学和南洋理工大学的建立起到了至关重要的作用。
随着 NUS 的建立,数学系就进入了一个新的时代。新的校区在 Kent Ridge,1986 年理学院和数学系就在这里成立。这个时候,数学系就有了巨大的发展,不仅在本科生的招生规模方面有了巨大提高,在研究生项目规模上也有了一定的深度的提升。
在本次的 NUS E-Open House 中,Science 的每个院系都提供了相应的宣传资料,并且所有学科统一模板,由各个学科的教授来向大家介绍这些专业的背景,学习内容和相关优势。在 NUS 的数学系(Department of Mathematics),则是由 Prof Tan 来给大家介绍院系的相关内容。
俗话说,数学是科学的基础。数学不仅仅是数学书上的一道道定理,而是可以解决现实生活问题的重要工具。在天气预测方向,动力系统(Dynamical System)有着独特的应用;在机器学习领域,微积分,线性代数与概率论则为这门学科提供了理论基础。在金融领域,Black-Scholes 方程,Monte Carlo 模拟则是其中的重要模型。从这些学科的发展来看,数学不仅可以为这些学科提供理论基础,也是解决这些学科难题的重要工具之一。
在中学的时候,笔者接触过《帝国时代》(Age of Empires),《暗黑破坏神2》(Diabol 2)等系列游戏;在大学期间,则开始玩《魔兽争霸3》(WarCraft 3),《Dota》;到了博士生的时候,接触到的游戏就更多了,包括但不限于《暗黑破坏神3》(Diabol 3),《炉石传说》(HeartStone),《坦克世界》(World of Tanks),《Fifa 2015》。