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Amazon Founder Jeff Bezos Originally Wanted to be a Theoretical Physicist

The world’s richest man is currently Jeff Bezos, founder of Amazon.

Few people know that he was an undergraduate at Princeton with the goal of becoming a theoretical physicist! What made him change his mind? Watch the video below.

Summary: Jeff Bezos was stuck on a Partial Differential Equation (PDE) question for 3 hours. Even while collaborating with his room mate, he could not find the answer. Upon consulting his Sri Lankan genius classmate, “Yosantha”, Yosantha solved the problem almost instantaneously in his mind!

Also check out our previous posts on Partial Differential Equations:

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NTUC Income Insurance Review

NTUC is a widely recognized name in Singapore, with most people having bought something from their flagship grocery store NTUC Fairprice.

NTUC is also very reliable and has various insurance policies that are beneficial to those who buy it. Most Singaporeans like to go overseas during the school vacations, a good travel insurance is essential to safeguard your health and wellbeing. NTUC Income is one of the few travel insurances that provides coverage for pre-existing medical conditions.

Check out NTUC Insurance today! (Please click on the link to enter the official NTUC Insurance website.)

Key Product Highlights:

Travel Insurance: 
• Income’s Enhanced PreX plans provide the widest coverage for pre-existing medical conditions
• Coverage for families with unlimited number of children insured under the Family cover
• Coverage for travel delay, trip cancellation, medical expenses and loss of money and personal baggage while overseas
• Check out our great deals here.

Car & Motorcycle Insurance: 
• Income is Singapore’s No. 1 Motor Insurer in terms of market share.
• Up to 69% off car insurance premiums with your existing NCD
• Unparalleled value added services at no extra cost:
– 24/7 Accident Response team
– One-stop post-accident solution for your vehicle claims & repairs
– Mobile app that lets you complete & submit an accident report anywhere within minutes

Enhanced Home Insurance: 
• 15% premium discount with purchase of a 3-year plan
• Comprehensive coverage for home contents, renovations and personal belongings

Foreign Maid Insurance:
• Personal accident, hospital & surgical expenses coverage for helpers
• Wages compensation if your helper is hospitalized
• Buy maid insurance online within minutes

PA Assurance: 
• 40% discount on premiums for children if at least 1 parent is insured under same policy
• Coverage for 21 infectious diseases (e.g Zika, Dengue Fever, HFMD) with optional infectious disease cover
• Coverage for permanent disability and medical expenses for injury due to an accident

URL: Official NTUC Insurance Website

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20% of Singapore’s workforce will be “displaced” by 2028 due to AI

According to the article by Today newspaper, around 20.6% of Singapore’s workforce will be “displaced” by 2028 due to technology and AI. This is quite scary news by the reliable newspaper Today. Although “displaced” is a tricky word and need not mean jobless or retrenched, nevertheless students should be mindful of this when they choose their major in polytechnics and university. Many esteemed jobs like accountancy, may or may not still be viable in 2028, as robots AI may likely have progressed to such a stage that they can easily take over human jobs. Non-degree jobs such as insurance agent and property agent may also be at risk. The bottom line is that if AI has progressed to the stage of being cheap and good, the big bosses will adopt it readily to lower their cost and maximize their profit.

Concerned parents and students should certainly read the below book, especially those who are about to choose their major in polytechnic or university. It is a “New York Times-bestselling guide to how automation is changing the economy, undermining work, and reshaping our lives”. As the saying goes, 男(女)怕入错行, the greatest fear of men (and women) is to enter the wrong profession. Checking out the future prediction of experts like Martin Ford is certainly a good idea. Imagine studying 4 years for a job that suddenly becomes extinct in 2028.

It is not an accident that Computer Science (and related subjects) is now one of the top and most popular majors in Singapore and many countries.

Rise of the Robots: Technology and the Threat of a Jobless Future

Source: Today

Workers in Singapore will be hit hard by technological disruptions with the Republic’s labour market set to face the largest degree of job displacement regionally in the next decade, based on a study on the impact of artificial intelligence (AI) on workers in six South-east Asian economies.

The new study by technology company Cisco and economic forecasting agency Oxford Economics also found that Singapore will have to confront the biggest mismatch between skills and jobs created among the countries in the region.

The findings were released on Wednesday (Sept 12) on the sidelines of the World Economic Forum on Asean (Association of South-east Asian Nations), a high-level gathering on innovation and entrepreneurship in Hanoi.

Data showed that about one-fifth of Singapore’s full-time equivalent workforce (20.6 per cent) will have their jobs displaced by 2028. This is higher than the figures for Vietnam (13.8 per cent), Thailand (11.9 per cent), the Philippines (10.1 per cent), Indonesia (8.1 per cent) and Malaysia (7.4 per cent).

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Life Beyond Grades (

Do check out this new website (, which as its name implies is about emphasizing that school life is not all about grades, even in Singapore. It is kind of an official website, being funded by National Youth Council (see their FAQ.)

It is good that nowadays parents, teachers and the education sector has started to realize that grades is not everything in life. The FAQ section is very interesting and actually kind of reveals the future direction that Singapore education is heading towards. A few key points:

  • “Why can’t we do away with the PSLE” –> Implication: PSLE is never going to be scrapped, at least not in the near future.
  • “Why can’t we do away with CL2” —> Mother Tongue is here to stay for the time being.

Their article section is quite new, but also contains good articles. Do check out the “What is LQ” talk featuring Jack Ma.

Related: Check out Jamie Yeo’s PSLE score here. Hint: It is enough to enter most if not all secondary schools.


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The most addictive theorem in Applied mathematics

Math Online Tom Circle

What is your favorite theorem ?

I have 2 theorems which trigger my love of Math :

  1. Chinese Remainder Theorem:韩信点兵, named after a 200 BCE Han dynasty genius general Han Xin (韩信) who applied this modern “Modular Arithmetic” in battle fields.
  2. Fermat’s Last Theorem:The Math “prank” initiated by the 17CE amateur Mathematician Pierre de Fermat kept the world busy for 380 years until 1974 proved by Andrew Wiles.

Note 1: Lycée Pierre de Fermat (Classe Préparatoire) happens to be my alma mater named after this great Mathematician born in the same southern France “Airbus City” Toulouse.

Note 2: His another Fermat’s Little Theorem is used in modern computer cryptography.

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Win Mercedes-Benz CLA 180 Coupé by donating to charity

This charity is featured in Straits Times and the New Paper. Basically, you buy a $20 ticket (comes with T-shirt) which will go to a charity of your choice. The main point is that there is a chance to win a Mercedes-Benz. Most youngsters in Singapore can’t afford a car, not to mention a Mercedes, so this is a great prize. (If you don’t drive, you can sell the car.) Also, foreigners (excluding US citizens) can take part (see their FAQ for more details)

Currently, there are only 577 tickets purchased, so your chance of winning is 1/577 which is quite high compared to other lotteries like 4D or Toto. The draw date is 02 Nov 2018, which is quite close. They will apparently go ahead with the draw even if their target number of tickets (50000) is not met.

To take part, go to their official website at:

Please use this referral code RGNTSAWS when signing up. Thanks!

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WiFi Password = Integral Answer

Math Online Tom Circle

China Nanjing Aviation University set the WiFi password as the answer of this integral (first 6 digits).

Can you solve it?

Answer : Break the integral (I) into 2 parts:

I = A(x) + B(x)

$latex A(x) = int_{-2 }^ {2} x^{3}. cos (x/2).sqrt{4-x^2}dx$

$latex B(x) = int_{-2 }^ {2} 1/2.sqrt{4-x^2}dx$

A(x) = – A(-x) => Odd function
=> A =… since its area canceled out over [-2, 2]

B(x) = B(-x) => Even function
$latex implies B(x) = 2.int_{0 }^ {2} 1/2.sqrt{4 – x^2}dx$
$latex implies B(x) = int_{0 }^ {2} sqrt{4 – x^2}dx$

Let x = 2 sin t => dx = 2 cos t. dt

x = 2 = 2 sin t => sin t = 1 => t = π/2

x = 0 = 2 sin t => sin t = 0 => t =…

$latex B(x) = int_{0 }^ {pi/2} sqrt{4 – 4.sin^{2} {t}…

View original post 96 more words

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Alibaba launches scholarship programme in S’pore with generous funding

Source: Today Online

Alibaba has partnered with NTU to launch a scholarship program on computer science topics like artificial intelligence, data analytics and cloud computing.

The scholarship funding is very generous: monthly salary of 5,000 SGD for 4 years, with other benefits like CPF, insurance, etc. This is at least 40-50% more than most PhD scholarships in Singapore. Each PhD candidate will also have the opportunity to be mentored by at least one supervisor from his/her enrolled university and one co-supervisor from Alibaba.

It sounds like a very good opportunity for those interested in IT. Hopefully Alibaba will set up more of such facilities and programs in the future.

The official application page and other details can be found on the NTU webpage:

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How to type Chinese characters in LaTex (on Mac, using TeXShop)

This is one of the easiest ways to type Chinese characters in LaTeX on Mac, using the default TeXShop editor. (If you know of an easier way, please let me know in the comments below!)

I have tried for hours, experimenting with different packages, before “discovering” the following steps. Hope it helps!

Step 1) Add “\usepackage{ctex}” to the beginning of the document. This will load the main package ctex.

Step 2) It is very important to save the LaTeX file in UTF-8 format, otherwise all Chinese characters will appear as question marks. The preferred way to do this is via:

TeXShop > Preferences > Encoding = Unicode (UTF-8). (see image below)

This will “permanently” set the format as UTF-8 by default. If you don’t do this, an annoying thing that can happen is that your TeX file reverts to “non-UTF8” upon saving. That means, the Chinese characters may appear correctly at first, but once you re-save the file, all Chinese characters become question marks again.

Alternatively, if you don’t want to set UTF-8 as default, you may add the following line to the very first line of the TeX document:

% !TEX encoding = UTF-8 Unicode

This will make TeXShop remember to save it in UTF-8 format every time.

Step 3) Just type Chinese characters directly into the LaTeX file. No “wrapper” is needed around the Chinese characters.

Step 4) When you compile the document, be sure to compile it by XeLaTeX. You can select this option next to the “Typeset” button. If you compile it using normal LaTeX, you will get the following error:

“Critical ctex error:”fontset-unavailable

CTeX fontset `fandol’ is unavailable in current mode.”

For Windows users, I suppose the above steps still work. I have not tried it personally though. Other packages may work only for Windows/Mac specifically since each system have different preloaded Chinese fontsets.

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Chinese Lessons in Singapore (Video)

Source: How has Singapore’s Chinese Language syllabus evolved?


Quite interesting to see how Chinese lessons are like nowadays. To be honest it doesn’t seem much different from 10 years ago? One aspect that has changed is email writing. Nowadays it is rare to write letters, hence the modern syllabus focuses on writing emails instead. Also more multimedia like videos are being used.

One notable statistic is this: “At Tanjong Katong Secondary, Mrs Lee said about 70 per cent of students come from an English-speaking background.” This is a very high percentage compared to the times of the past. To master Chinese is increasingly hard for such students, great effort needs to be put in for improving their command of the Chinese language.

Notable Quotes:

She agreed that it can be difficult at times to speak Mandarin fluently. But she makes it a point to practice by having conversations in Mandarin with friends and family members, and exposing herself to Chinese shows.

“I enjoy it when the teacher shows videos in class,” she said. “I understand how the characters feel, and how they speak. I can learn a lot from the way they phrase their sentences.”


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[Quora] Common Core Math

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Spot The Mistake?

Math is rigor. Where went wrong?

Math Online Tom Circle


$latex displaystyle {Bigl(frac{2}{3}Bigr)} ^{x} = {Bigl(frac{3}{2}Bigr)}^{3}$

$latex implies displaystyle frac {2^{x}} {3^{x}} = frac {3^{3}} {2^{3}}$

$latex implies displaystyle{2^{3}}. {2^{x}} ={3^{3}}. {3^{x}}$

$latex implies displaystyle2^{3+x} =3^{3+x}$

Since the exponents (3+x) on both sides are equal,

=> 2 = 3

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GEP PSLE Discussion

It is well known that GEP students spend Primary 4 and 5 doing miscellaneous stuff that appear to be not directly related to PSLE, yet majority of GEP students score 250 and above for PSLE. Hence, the main question is:

Does GEP help PSLE?

Kiasuparents has a very robust discussion going on, and here are some of the insightful snippets. For the full discussion, check out the Kiasuparents forum.

Summary: GEP only starts preparation for PSLE at P6 April (!!) For PSLE, students need to be exam smart and be careful to answer “according to the marking scheme”. GEP teaches many higher level concepts which are not in the syllabus, for example “good bacteria”. Content wise, GEP English/Math/Science at P4-P5 is already at or surpassing the mainstream PSLE level. For Chinese/Mother Tongue, there is not much difference between GEP and usual syllabus.

Viewpoint 1: GEP helps PSLE but not directly

bhcbl wrote:After DS 3 years journey in the program, my thoughts are as follow:

– Does GEP help PSLE … NoNot directly. I do think my son did better in PSLE than he would have done in his previous school coz his classmates were stronger, and because the teaching suited him. Revision was short and sharp, and he didn’t have to do too many revision papers
– Does GEP help DSA … No (definitely not directly under the new policy, maybe the exposure in broader Math and Science help HDP in a way) No, because GEPpers don’t have a special pass to DSA any more. But the GEP education does provide more opportunities to develop knowledge in various areas that could help in the interviews and portfolios
– If we get to choose again, will we still opt to be in the program … yesAgree with everything below
Stretches … eg. Book review on books for older reader, more difficult Math concept …
Broaden … eg. Ancient civilizations, magic square, ancient number system, history
Self-learning … various research and projects (at least 4-5 a year)
Time management … homework, projects, research, self-studies
Filing … they have no textbook
Also, I think it was just alot more fun for DS (after some confusion in P4 while getting used to the system). He enjoyed classes, enjoyed his classmates (mostly), and I loved the smaller classes and the opportunities for various additional classes / camps etc.
So as you can see, in the three years, most of their times are spend on thing that have nothing to do with PSLE or PSLE prep until around P6 Apr.

Think about the following: in English, they learn to infer and read between the lines, but in PSLE compre, if you do that likely you will get marks deducted; Have parents experience the problem of teaching your child Math … using algebra to solve, and then convert to the model method to explain … this is some of the things that Gep students need to go through for Math PSLE (imagine for a 12 years old child). Or PSLE syllabus issue … if you ask any Gep student whether bacteria is good or bad … they will tell you both and give you a good list of examples … but too bad that is not in PSLE syllabus: Bacteria is bad (marks likely deducted if you start talking about bacteria is good).
Our take: the GEP system is a great system, but the problem is in the past they don’t need to rely on PSLE because there is DSA, but now they have to with the change in MOE policy. It is quite cruel to do that to a child… teach them more boarder and advance stuff but in exam ask them to forget about all these.

To us, we think that education is a journey, while PSLE is just a small part of the journey. Therefore, we will still go for GEP if we could choose again. Lastly, you will see most GEP students don’t need to adjust to secondary school: 8 subjects … they are already used to very pack schedule; additional topic like history, literature, geography … these are covered in one way or another in their 3 years program (but not tested in PSLE).

So hope that this could help you in your decision in your child education journey. If you are hoping that GEP mean PSLE or DSA or good secondary … under the new policy, you may be disappointed. If you are hoping to have a challenging and stretch program for your child … likely you won’t be disappointed.

Viewpoint 2: GEP definitely helps PSLE (and DSA too)

(by entei17) Does GEP help PSLE

Yes, definitely. In fact two years in advance. If you look through the learning scope and common tests papers for English, Higher Chinese, Maths and Science, the P4 Geppers are already doing P5-6 stuff in the mainstream.

English already has situational writing which is not introduced till P5 mainstream. Vocabulary and Grammar are pitched at P5-6 or maybe secondary levels. Comprehension format is very similar to PSLE, except that the passage is lengthier and more difficult to understand (need inference) than PSLE. As revision and practice for common test, I let my child do past year PSLE papers instead, because the P4-5 revisions books are not compatible. All the Extensive Reading List assignments, Single Shard literature, Synthesis and Transformation etc also help to build up their English foundation, so they can read more and advanced their appreciation of the language. Some of the assignments are an overkill, requiring a Herculean effort, or mission impossible. They have a comprehensive English curriculum, but I’m not sure whether all the Geppers could keep up.

Higher Chinese uses the same textbooks as the mainstream i.e. 生字 are similar, but the test/exam paper formats are similar to P5-P6/PSLE. Geppers would have no problems adjusting to the PSLE requirements. As GEP selection test only tested English, Math and General Ability, Geppers’ average Chinese ability are generally on par with the mainstream. Those that are good in English are generally not good at Chinese, although there are a handful who are good at both, or in all the subjects. I don’t have any evidence to back this up, but one reasons why some Geppers who didn’t score well in the PSLE are probably pulled down by their Chinese.

Maths are pitched at P5-P6 mainstream topics, but enriched and more interesting. I’ve seen many mentioned about Ancient civilizations, magic square, ancient number system, history. These are all covered over a week or only a few assignments. Most of the worksheets are still the usual topics but pitched at a higher level that stimulates their thinking. The only problem is Geppers think faster and have a tendency to skip/leave out some of the workings, which may prove a problem to the marking scheme in the PSLE.

Science topics follow the PSLE syllabus and the usual topics, enriched and deeper thought. We use P5/PSLE questions for revisions. The key here is (no pun intended) is still keywords and key concepts when answering open-ended questions, which is not dissimilar to the mainstream and PSLE requirements.

If whether GEP prepares PSLE every single day from P4-6 by drilling them to do past year papers after past year papers, then clearly they don’t. They spend a lot of time doing other stuff which indirectly raise their ability – maybe it helps in PSEL, maybe it doesn’t.

– Does GEP help DSA

DSA based on Sports/CCA are irrelevant here unless GEP’s heavy workload deprive them time to train or participate more actively, which could be a consideration. If not GEP and mainstream compete evenly based on their sports achievement.

Based on history, the majority of Geppers score 250 and above. Some don’t because of their mother tongue (as mentioned above), which even if they are in the mainstream, won’t be any different. Some are simply misclassified into the GEP – no matter what the GEB says about their tests. Parents know their child best whether they have the ability.

So even without DSA, for those scoring 260 and above they would still get into the top IP schools. The only one you have no choice but to try for DSA is NUS High, because there are very few places left in the posting exercise after the PSLE. However, this may also backfire on the Geppers because the schools know the Geppers would score high, and therefore still come to their school, and therefore may not need to give you a CO. With government’s push for social mobility and anti-elitism, they may just want to mix it up a bit more in the elite schools and therefore less Geppers as the first cut – just pure guess, since PSLE would still bring back the higher scoring Geppers anyway through meritocracy.

But compare to the mainstream, does GEP equip you better to do DSA? I think very so, as GEP affords you opportunities to participate in the MO, SO as well as many other competitions, and as early as P4, which may not be the case in the mainstream. So you have a better chance to build up your academic portfolio.

Finally, do check out our most popular GEP post: Recommended Books for GEP Selection Test and How to Get Into GEP.

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Do Not Press This if you are Overseas (Singtel Customers)

If you are an Apple iPhone user, and from Singtel, remember not to press “OK” when you see this message: “iMessage: Your carrier may charge for SMS messages used to activate iMessage.”.





This message appears when you swop SIM card, turn off the phone, or in various other situations.

Singtel treats this as “International SMS”, and can charge a fee for it. I got hit with a $5 fee as I was frequently swopping SIM cards (to check for any SMS received on my local card). The charges appear as “AutoRoam (PAYR) SMS”.


The solution is to press “Cancel” whenever the message pops up. If you are already get the charges by Singtel, you can try calling in/online chat with them to waive the fee. I managed to get a “one-time waiver” which will supposedly occur within two billing cycles.

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Where to buy dumplings (饺子) in Singapore


Dumplings (饺子) is a staple food in Northern China. However it is rare to find it in Singapore. Often in NTUC Fairprice, or other supermarkets, Gyoza (Japanese Dumplings) or Korean dumplings can be found, but not Chinese dumplings. Making your own dumplings is possible, but very time consuming.

Recently I found out about “Yongle Kitchen”, which sells authentic Shandong style dumplings. Check out their video below, it looks very professional.

The recommended way to buy their dumplings is through Qoo10Click here to enter their Qoo10 Official Shop!

Do check out their 10 different flavors!

You may also click on the banner below to enter their Official Shop:

[$12.00](▼34%)[YongLe Dumplings]42 Pcs Dumplings in 10 Different Flavours!


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Morse Inequalities

Let X be a CW complex (with a fixed CW decomposition) with c_d cells of dimension d. Let \mathbb{F} be a field and let b_d=\dim(H_d(X;\mathbb{F})).
(i) (The Weak Morse Inequalities) For each d,

\displaystyle c_d\geq b_d.

where \chi(X) denotes the Euler characteristic of X.


The proof is by linear algebra (see Hatcher pg. 147).

By rank-nullity theorem (秩-零化度定理), \dim C_d=\dim Z_d+\dim B_{d-1}.

By definition of homology, \dim Z_d=\dim B_d+\dim H_d.

\therefore c_d=\dim B_d+\dim B_{d-1}+b_d.

In particular, c_d\geq b_d.

Taking alternating sum gives \displaystyle \sum_d(-1)^d c_d=\sum_d(-1)^d b_d.

Reference: A user’s guide to discrete Morse theory by R. Forman.

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VPN that works in China (2018): Lantern Pro Review

The Great Firewall of China is exceptionally intelligent, it is rumored to use machine learning, deep learning and various other strategies to block users from accessing websites such as Google, Facebook, etc.

You probably have realized that most VPNs are not working well in China anymore, as of 2018.

Lantern Pro Review (China)

The one “VPN” that remains good to use is Lantern Pro. It isn’t actually a VPN, but rather a “network sharing” tool. As such, it remains relatively unaffected by the ban on VPNs by China. I have personally tested Lantern in August 2018 and find it working in good condition.

There is a free version, and also a paid version that is more stable and faster. You can first try the free version (data limit of around 800 MB) to see if you like it or not. The installation is extremely simple, basically you just click one button to connect.


Lantern Referral Code: Use my code YJVD2WT and get 3 months free when you sign up!

Note that you need to install it before you enter China. Once you enter China there is no way you can download the installer as the entire website is blocked.

Use this referral code YJVD2WT and both you and I will get free months (1 or 3 months depending on which plan you buy).

PureVPN (Mac, iOS) not working in China (2018)

Unfortunately, to my disappointment, PureVPN is not working in China as of 2018. I previously wrote a post on PureVPN, it used to be good, but now it has been defeated by the Great Firewall of China.

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The Inextricable Relationship Between Exams and Weather

Singapore is a country that prides itself on its scholastic achievements – with tuitions centers in almost every neighbourhood advertising its rockstar tutors and top-scoring students. The first day of school starts like clockwork, nobody misses a beat, everyone is punctual, assignments are due, and classes start rushing to finish the curriculum again.

This relentless pace for Singapore’s education system is because the exams are just around the corner. It may seem scary for readers that have graduated years ago but yet to have children. The pressure of school is cranked up to 11 on a scale of 10 almost immediately. Especially so for those in crucial streaming years (primary 4 / secondary 2) or graduating years (primary 6 / secondary 4 and 5 / junior college 2).

The importance of exams to the Singaporean society is paramount. As a meritocratic society, education is seen as the equalising force among the varying socio-economic classes. With a thriving bureaucratic government, the best and the brightest in national examinations tend to get the best scholarships and positions in public service afterwards. The fact is that every exam is one step closer or further away from securing the place in society.

Singapore is just above the equator – a hot and humid city with students all seeking a cool place to study. To combat the elements, the only way is cranking up the air conditioner. Almost every home in Singapore has one so to get some much respite from the hot and humid air. Students furiously studying for exams (colloquially termed “mugging” and those who do so called “muggers”) are more than likely doing so under the cool breeze of artificial temperature control.

It will be a common sight to see public places with free strong air conditioners like libraries, fast food outlets, cafes, even airport being full of students cramming away. Expect also to see plenty of midnight oil being burnt in the bedrooms and living rooms of students during the next few months. Because of the humidity of the climate being at an average of 84.2%, no matter what the temperature is, the weather is still often uncomfortable and sweat-inducing.

These are hardly the best conditions for students to focus and study. Extreme temperatures causes students to be annoyed and hence distracted. According to experts, the best temperature to be productive is at 23.5 degrees Celcius. With the average Singapore temperature in the day in the low thirties and at night in the high twenties, natural conditions are definitely not beneficial.

Does it mean that all students need to do is to set the air conditioner to high fan and low temperature? Unfortunately no. The same study also added that while that might work for the majority, 30% of people will be too cold or too hot. That means 1 in 3 will have to keep tweaking the air conditioner time and time again (yet another distraction to the studying process).

So what is a parent or student to do? Leave it up to fate on what the weather conditions are like outdoors? All the while constantly dealing with a fluctuating levels of comfort from the air-conditioner (a device purchased for the express purpose of delivering comfort)? Thank goodness that technology can step in to help.

With Ambi-Climate , a smart AI-enabled air conditioner controller, what we will have is a device that can recognise the students’ unique needs, and tailor temperatures for optimal comfort without having to ask. While traditional air conditioners only account for temperature and ignore other key factors – humidity, sunlight, changes in outdoor weather, and your daily metabolic cycle – Ambi Climate takes everything into account to help create an optimal, personalised home environment while saving up to 30% on energy

By connecting to your air conditioner and learning from your feedback, Ambi’s unique A.I. engine and smart sensors will work their magic to match the students’ needs and adjust to what they deem comfortable. Also, Ambi has an away mode, that efficiently keep your home within desired temperature or humidity thresholds. After setting a threshold of your choice (heating, cooling or drying), Ambi Climate will fulfill your preference in the most energy-efficient way; it will only turn the AC on when needed to maintain the threshold. Your home stays safe and you save money! This will come as good news for muggers as they can enjoy the breeze to keep them concentrated on the upcoming exams at hand.

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153 St. Peter Fish

Math Online Tom Circle

Bible Math: 153 St. Peter Fish
[John 21:3-11]
3  So they went out and got into the boat, but that night they caught nothing.
6 He said, “Throw your net on the right side of the boat and you will find some.” When they did, they were unable to haul the net in because of the large number of fish... It was full of large fish, 153, but even with so many the net was not torn.

1) 153= 1! + 2! + 3! + 4! + 5! = (1+2+6+24+120)

2) $latex 1^3+5^3 +3^3$ = 1 + 125 + 27 = 153

3) Take any multiple of 3, e.g. 78
-> $latex 7^3+8^3$ = 855

-> $latex 8^3+5^3+5^3$ = 762

762 -> 567 ->684 ->792 ->1080 ->513 ->153 (Always!)

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French Baccalaureate Math

Math Online Tom Circle

Below are two French Baccalaureate Math textbooks (Volume 1 & 2) for Grade 12th (or Junior College Year 2, GCE A Level, Lycée: Terminale C) students in the late 1970s.

There was a strong Bourbaki style of influence in this Math teaching, which was later criticized as being too abstract and less applied for 18-year-old students.

Nevertheless, the syllabus proved to be excellent for those Math-inclined young minds who later entered the special 2-year Classe Préparatoire aux Grandes Ecoles – Preparatory class (equivalent to Bachelor of Science) for graduate schools in crème de la crème top universities (Grandes Écoles ) such as Ecole Normale Supérieure or Ecole Polytechnique , where the solid Preparatory Math trainings (Maths Supérieures, Maths Spéciales) are extremely rigorous and high standard, incubating most of the French great mathematicians, Fields Medalists and Nobel Prize Scientists.

Voici les 2 tomes de Mathematiques Terminales C et E

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Singapore PSLE Math baffled Anxious Parents

Math Online Tom Circle

One afternoon 5 friends rented 3 bikes from 5 p.m. to 6:30 p.m. and took turns to ride on them. At any time, 3 of them cycled while the other 2 friends rested.

If each of them had the same amount of cycling time, how many minutes did each person ride on a bike?

Note: PSLE (Primary Schools Leaving Exams) is the Singapore National Exams for all 12 year-old pupils at Primary 6 year end. The result of which will determine which secondary school the pupil is qualified to enter the following year. Math subject, besides Science, English and mother tongue (Chinese or Malay or Tamil) are tested in PSLE.

[Answer] Try before you scroll down below ….






























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The Universal Pattern Popping Up in Math, Physics and Biology

Math Online Tom Circle

Key Points:

  • Bus Waiting Time Pattern
  • Biology Chicken eyes
  • Physics: Random matrix / Eigenvalues / Riemann Zeta-function for Prime Numbers
  • Universal Pattern: Normal Distribution Curve

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Nearest Neigbour Problem – Universal Method to Sort Complex Information Found

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Category Theory III for Programmers (Parts 1 & 2)

Math Online Tom Circle

The most interesting “Category Theory” (范畴论) for Programmers course III by Dr. Bartosz Milewski , a follow-up of last year’s course II.


  1. Fundamental of Category Theory: Functor, Natural Transformation, etc. (Course II Series)
  2. (Nice to have) : Basic Haskell Functional Programming Language. (Quick Haskell Tutorial)

1.1: Overview Part 1

Category Theory (CT) = Summary ofALL Mathematics

Functional Programming = Application of CT

Philosophical Background:

  • Math originated 3,000 years ago in Geometry by Greek Euclid with Axioms and deductive (演译) Proof-drivenLogic.
  • Geometry = Geo (Earth) + Metry (Measurement).
  • Math evolved from 2-dimensional Euclidean Geometry through 17 CE French Descartes’s Cartesian Geometry using the 13CE Arabic invention “Algebra” in Equations of n dimensions: $latex (x_1, x_2,…, x_n) $, $latex (y_1, y_2,…, y_n) $
  • Use of Algebra: 1) Evaluation of algebraic equations (in CT: “Functor”) ; 2) Manipulation. eg. Substitution (in CT :…

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Took special needs son to Australia; he graduated from uni at 17

Very motivational story. Suitable for parents to read; sometimes a change of environment is what it takes for your child to reach his/her full potential. Though the Singapore education system is quite good on the whole, there are some gifted children who are unsuited to such an education.

Note that the financial costs are very high to study in Australia: It costs at least $262,000 for an Australian degree, according to Straits Times. The mother in the story below has 4 children studying in Australia, so one can imagine the heavy financial burden.

Also see our previous post on: School System Video (Do not make a fish climb trees).

Source: Facebook of Pamela Liu

(There is also a forum discussion at Kiasuparents.)

This is just a piece of paper, but a paper that is full of sweat, tears and stories.

Just not too long ago, in 2011, Sean was labeled with multiple learning disabilities. Even though he was selected to be in the gifted education program (GEP) in Singapore, we were told we have to withdraw him from the program because they didn’t want him after spending a year there. Instead, they wanted me to put him into a school for special needs children.

Sean did not want to go to the special needs school, because he felt that he did not belong there. The psychologist we hired told us that the place was not suitable for him. MOE and the school were not happy we did not heed their advice, some are not happy that I refused to put him on ritalin. So the only solution they gave me was to exclude Sean in all school activities if I were to send him to school.

They would put him in the principal’s office. The school, out of the goodwill of the principal, will assign a Math teacher to him.

What about other subjects? And what if you just allow him to take PE and recess with his peers? I asked. It was a straight no.

I couldn’t send my son to school to sit in the principal’s office all day long, he would never understand why he was not allowed to mingle with his friends. So I took him home.

I had no solution, but I was determined to find one. I will educate him myself, I thought.

The psychologist told me that homeschooling Sean will endanger me, I had no clue what that meant when she first told me that, but I did not have an alternative. So I brought him together with the rest of the 4 kids to Australia, determined to find a solution for each kid.

The older two kids were attending university but Sean and the other two younger ones had no school to go to, since they were not residents, no public school could take them, the private schools were full.

Out of the container that I rented, I taught Jo and Sean daily for two hours. He was 10, and we moved quickly from Year 4 work to Year 12 work. All within six months. He was attentive and a quick learner. He even won some medals for his SAT exams for being a top scorer. Jo moved from Year 8 to Year 12 in that time period too.

Jo became the youngest the university matriculated at 13, outdone only by Sean. By 11, he enrolled in UQ, and became the youngest they matriculated in history. The condition for him to attend university at this age was that I must accompany him for every class.

I gladly did. Every class, every day, every moment. 30 to 40 hours a week, plus having to bring up 3 other teenagers and a younger son, and all by myself.

Half way through the degree, he started to fail everything. He told me he really did not like that he had no age peers. So we stopped university and got him enrolled in high school.

In high school, he felt out of place, he found kids noisy and boisterous. After 18 months in high school, we decided to dual enroll him, both in the university and high school.

When it got too noisy in school, he would hide in the toilet, sometimes for the whole day. It became so bad, the tutor wanted me to bring to see a psychologist. The psychologist, to my surprise, told me that Sean is way ahead of his peers socially. All these years, I was told he is autistic, in that he is socially poor, and all these years, I was told to send him to therapies so he could catch up and learn social skills. Five years of doing all these later, I was told he is the opposite. His problem is that he cannot endure the childish behaviour of his age peers.

Sean turned 16, he could attend classes in the university alone finally. After sitting in for 2 years full-time and 2 years part-time, I finally bought some time for myself (except that Youngest One started university on the same terms, and so I have to sit his classes).

Sean started to skip many many classes. In the end, we found out that he was sleeping in the library. It is also then we found out that he has a sleeping disorder, narcolepsy. The university made some provisions for him, so that his exams are never in difficult hours of the day.

That was just last year. And with that, he finally graduated with his degree, and is into his second semester on his masters program.

What a journey. This piece of paper is probably the most hard earned one for me this lifetime. It is also the most precious.

Sean is now 18, he is officially an adult (in Australia), and looking back, I will never do it any other way. I think, journeying this with him has made me a much better person than otherwise. I am thankful for all that we had to go through, and I am thankful he was put into my life. I learned so much.

Well done, Sunshine Boy.

*Even though Sean started university the earliest, he did not
graduate the youngest at 17 because of his multiple anxiety problems. Jo graduated at 16 and the Youngest One will graduate at 16 as well. It really does not matter. We took the time to adjust and ensure each child is comfortable in the education path. Education is about finding our kids’ potential and bringing that to the fullest. Isn’t it? Time and age should not determine what we do with them.

**If you want to know about the costs of doing this, I have made some videos and in the midst of editing them. They will be available in two weeks. Go to this link and watch for it:

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2018 Fields Medallists


I find that the above link by Quanta Magazine has the most detailed and educational write up about the 4 new Fields Medallists:

  1. Akshay Venkatesh, a former prodigy who struggled with the genius stereotype
  2. The 30-year-old math sensation Peter Scholze is now one of the youngest Fields medalists
  3. The mathematician Caucher Birkar was born on a subsistence farm and raised in the middle of the brutal war between Iran and Iraq.
  4. he mathematician Alessio Figalli is rarely in one place for very long. But his work has established the stability of everything from crystals to weather fronts by using concepts derived from Napoleonic fortifications.
  5. Also included is the theoretical computer scientist Constantinos Daskalakis, who has won the Rolf Nevanlinna Prize for explicating core questions in game theory and machine learning.
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Programming is Math Proof: Structured Programming

Math Online Tom Circle


  • Dijkstra, Edge Wyber (born 1930 Rotterdam)
  • Goto is harmful
  • Structures: sequence, selection, iteration

Three Programming Paradigms:

1. Structured Programming (1968 Dijkstra)

  • Impose discipline on direct transfer of control aka “Goto“.
  • “If/ then /else, do/while” control structures are structured.

2. Object-Oriented ‘OO’ (1966 Ole Johan Dahl & Kristen Nygaard)

  • Impose discipline on Indirect transfer of control (polymorphism, ‘constructor‘ function of class, it’s local variables = instance variables).

OO = Combination of Data & Function.

3. Functional Programming (1958 John McCarthy’s LISP language, based on Math “Lambda Calculus” from Alonzo Church 1936).

  • Impose discipline upon assignment (side effect, immutability of data, Referential Transparency).

4. Any more ?

All Programs can be constructed from just 3 structures (Böhm and Jacopini, 1966):

Sequence / Selection / Iteration.

Dijkstra’s Math Proofs for:

1. Sequence – by simple enumeration.

  • Math Technique: trace the inputs…

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Parasite in cat poop could be reducing our fear of failure, study finds

This news sounds bizarre, but is true. I have been “researching” on this topic sometime ago, it is a true scientific research topic, not bogus or fake. Basically the parasite “Toxoplasma gondii” affects human brains in some subtle ways that can affect one’s personality.


A mind-controlling parasite found in cat feces may give people the courage they need to become entrepreneurs, researchers reported Tuesday.

They found that people who have been infected with the Toxoplasma gondii parasite are more likely to major in business and to have started their own businesses than non-infected people.

The parasite, which makes rodents unafraid of cats, may be reducing the fear of failure in people, Stefanie Johnson of the University of Colorado and colleagues said.

They haven’t actually shown that. But toxoplasma does get into the brain, and it’s been linked to a variety of mental effects in mice and people alike. And fear of failure could be a good thing, Johnson said.

Toxoplasmosis has been linked to a greater risk of “car accidents, mental illness, neuroticism, drug abuse and suicide,” Johnson and her colleagues wrote in their paper, published in the Proceedings of the Royal Society B.

It might be affecting message-carrying chemicals in the brain called neurotransmitters, or hormones such as testosterone, they wrote.

In particular, scientists have studied whether the parasite might increase risk-taking behavior.

Johnson is an associate professor of management at the University of Colorado and often told her students about the odd effects of the parasite, which travels to the brains of rodents and causes them to lose their innate fear of the smell of cat urine.

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The 17 best universities in the world to study math


According to the above source, the best 17 universities to study Math are:

  1. Princeton, United States
  2. University of Paris-Sud, France
  3. Stanford University, United States
  4. Oxford University, United Kingdom
  5. New York University, United States.
  6. 6-17 are listed in the website.

The above ranking is a little strange, Cambridge (7th) and Harvard (12th) are both outside the top 5. Most typical rankings will have these 2 universities in the top 10.The ranking “looked at factors including how many Field Medalists had studied at each institution”.

See also: Singapore universities should look beyond international rankings: Panel

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Math shapes our primal ‘number system,’ not vice-versa

Interesting article on the “power of education in modeling the brain”.


Scientists have long believed that our ability to solve symbolic math problems such as 3+2=5 depends on an imprecise, primal brain function called the Approximate Number System. A new study suggests otherwise.

“Our study shows that gaining expertise with symbolic math, which is a human cultural invention, actually refines this evolutionarily ancient system of quantity representation, not the other way around,” says lead author Macarena Suárez Pellicioni, an educational neuroscience postdoctoral researcher at Vanderbilt University’s Peabody College of education and human development.

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Free Limited Edition National Geographic (Singapore Edition)

Students / parents do take note of this once-in-a-lifetime opportunity to get the free limited edition National Geographic magazine. Need to be quick since anything free in Singapore is snapped up almost instantaneously.

Share to your friends via Facebook!

Source: Yahoo

To celebrate Singapore’s 53rd birthday, we’ve got a special Singapore edition of a little magazine you may have heard of called National Geographic. Dropping islandwide at community centers and libraries, the limited edition publication will see 250,000 copies distributed for free from Aug 1 onwards.

Of course, this being a collaboration with the Ministry of Communications and Information, the mag will feature an interview with Prime Minister Lee Hsien Loong about his thoughts on the future of Singapore, alongside a series of local stories about individuals contributing to “shaping our future home through their pursuits.”

Source: PM Lee’s Facebook has partnered National Geographic to do a special Singapore edition of the magazine titled “Singapore – City of Tomorrow”!

Read about the people shaping the future Singapore – they are active in design, sports, sustainable urban farming, volunteerism and other unexpected areas. The articles are accompanied by great photos, of course.

You can pick up your complimentary copy at Suntec City, West Atrium from today till 29 Jul, and at Community Centres and libraries from 1 Aug.

In conjunction with the magazine launch, the #WhatMakesSG photo exhibition is currently on at Suntec City till 29 Jul. It features Nat Geo photojournalist Michael Yamashita’s photos taken during his visit here in May, as well as the winning entries of the #WhatMakesSG photo contest. Do drop by if you’re nearby. – LHL

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Chinese Tuition HCL O Level

Chinese Tuition Singapore
Tutor: Ms Gao (高老师)

Ms Gao is a patient tutor, and also effectively bilingual in both Chinese and English.

A native speaker of Mandarin, she speaks clearly with perfect accent and pronunciation. She is also well-versed in Chinese history, idioms and proverbs.

Ms Gao is able to teach Chinese at the Secondary school level (Chinese and Higher Chinese). She will teach in an exam-oriented style, but will also try her best to make the lesson interesting for the student.

Ms Gao has taught students from: Nanyang Girl’s High (NYGH), RGS, RI, and other schools.


HP: 8339 6353


Website :
(Preferably looking for students staying in the West side of Singapore)

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NUS High School DSA Selection Test Results Out

The first round results of NUS High School DSA Selection Test are apparently out since yesterday July 24. (Source: Kiasuparents)

Those who are successful will receive the following email:

Thank you for attending NUS High School DSA Selection Test and Camp. Candidates who passed the selection will be invited to our DSA School Preview to gain a sneak peek into the unique learning experience at NUS High School.

The outcome of the DSA Selection Exercise will be announced by the 3 August 2018 via the registered e-mail.

We would like to notify you early that the DSA School Preview would be on 8 August 2018. The shift is made after the consideration of the PSLE oral examination which will happen on the 16 August 2018 as well as to provide you and your family an uninterrupted 4-day long weekend break from 9 – 12 August 2018. We hope that the shift of date will allow you to have more family time with your parents during weekend as well as sufficient time for you to prepare for the coming PSLE oral examinations.

We seek your understanding and patience in this matter.

Congratulations to those who have passed this round! Do check out our tips for DSA interview.

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Tip for SST Selection Camp

SST (School of Science and Technology) is a relatively new secondary school (established in 2010) that offers an alternative approach to the usual MOE secondary schools. It is not very well known at the moment and I wouldn’t be surprised if majority of Singaporeans did not hear of it or know its existence. It does seem like a good school though.

According to Kiasuparents, majority of parents (53%) are concerned that SST does not have a good track record yet. However, there are students who are very keen to enter SST, and it is not that easy given its limited enrollment. They have to attend some selection camp similar to NUS High School. (SST admits 100% of the students through DSA exercise, so there is no way to get in via PSLE score alone.)

Also check out: NUS High Selection Test (DSA). Most probably students applying for SST are also considering NUS High School as their alternative choice.

SST Selection Camp Review

Came across an “insider tip” for the School of Science and Technology selection camp at Kiasuparents. Quite impressive actually that a secondary student can write so well.


I’m a student is currently studying in SST, while the teachers do look for prospective students, they look out for those with the ability to think on the spot, work well with others and conquer unexpected challenges. The school wants those with the passion for science and technology, but also those who have the desire to do well. In my personal experience, just be yourself, do not try to “fake” your way through, because our teachers can see through the smoke… Erm, let’s say, they deal with it a lot, especially during humanities. Be yourself; the teachers do look for one thing, the most important thing, which is respect and honesty.

The DSA Phase II for our school will have the students split up into groups of 4/5, in which group interviews are carried out, but do note, in these interviews, respect your other interviewees, or they usually won’t accept you. After the group interviews, they would have you go through a challenge. In 2015 they had my team design and built a parachute, which had various requirements and restrictions, which will hinder prospective students, in a right way. This is a part of the process to see what prospective students can achieve via creative and critical thinking.

For those going for the Phase 2 next week, CONGRATULATIONS AND GOOD LUCK!
I hope to see you for the “A Day @ SST” and/or in school next year!

An SST Student

Basically, I think SST is looking for a creative student that is genuinely interested in science and technology (i.e. not being forced by their parents). Personality traits matter too, at the minimum the student should be able to coexist peacefully with his/her fellow students. Good teamwork is definitely a plus point.

According to the official Selection Criteria, these are the factors that will give you better admission chances to SST:

Selection Criteria

Academic and Cognitive Abilities

Applicants are assessed on both academic achievements and cognitive abilities based on academic track records and other accomplishments, as well as the outcome of the General Ability Test (GAT) and Comprehension Reasoning Test (CRT).

Aptitude for Applied Learning

SST aims to engage our students through Applied Learning approaches. Shortlisted candidates will thus have to participate in a selection activity and be assessed for their suitability  to work and learn in the fast-paced and rigorous environment of the school.

Interests and Motivation

Candidates’ proclivity and passion for areas related to mathematics, science and technology may be gauged through their CCA involvement, student portfolios, teachers’ recommendations and personal statements. Students who have done well in Science, Technology, Engineering and Mathematics (STEM) competitions may be considered favourably for admission.

Hint: Math Olympiad may be useful here. Check out our post on Math Olympiad.

(For admission into Secondary 3, particular emphasis will be placed on personal leadership, academic strength and consistent performance.)

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What Knitting Can Teach You About Math | Innovation | Smithsonian

One snowy January day, I asked a classroom of college students to tell me the first word that came to mind when they thought about mathematics. The top two words were “calculation” and “equation.”

When I asked a room of professional mathematicians the same question, neither of those words were mentioned; instead, they offered phrases like “critical thinking” and “problem-solving.”

This is unfortunately common. What professional mathematicians think of as mathematics is entirely different from what the general population thinks of as mathematics. When so many describe mathematics as synonymous with calculation, it’s no wonder we hear “I hate math” so often.

So I set out to solve this problem in a somewhat unconventional way. I decided to offer a class called “The Mathematics of Knitting” at my institution, Carthage College. In it, I chose to eliminate pencil, paper, calculator (gasp) and textbook from the classroom completely. Instead, we talked, used our hands, drew pictures and played with everything from beach balls to measuring tapes. For homework, we reflected by blogging. And of course, we knit.

via What Knitting Can Teach You About Math | Innovation | Smithsonian

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Singaporean van Gogh – Mr Sim Kah Lim

This is an amazing story of an amazing artist. His passion for painting is so great, according to his therapist he wants to paint 24/7 without eating or sleeping. I find his paintings of Singapore River very good.

“Bumboats on Old Singapore River”

“Singapore River of a Previous Era”

SINGAPORE: For nearly 35 years, Mr Sim Kah Lim’s world has been the walls of his ward at the Institute of Mental Health (IMH).

Outside, changes have swept the landscape, old buildings falling and new ones rising – skylines and shorelines of a 21st-century nation transformed.

But in his mind’s eye – and in his bold-stroked acrylic and watercolour paintings – Mr Sim’s homeland is one where bumboats still crowd the Singapore River, ferrying goods and passengers; and where Chinatown’s open-air markets thrive and its five-foot ways are bustling with locals, not tourists.

They are pictures, frozen in time and memory, from early childhood when his father used to take him to these places.

“My father brought me outdoors (for) painting. I saw the Singapore River and all the artists,” the 50-year-old said, words spilling out without pause in a torrent of English and Mandarin, sometimes incoherent and muddied, like the river of his paintings during monsoon season.

It’s through his art that he finds order, focus and clarity in expressing himself.


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Experience in Elite School (Hwa Chong aka Chinese High)

Check out this interesting article about the experience and “privileges” of elite schools in Singapore. Also covered are the competitiveness and academic pressure in such schools. Finally, the author shares his experience of studying overseas in New York.

Also see: Hwa Chong IP Sec 2 Maths Question: Equation of Parabola


My heart sank when I received my PSLE results. Falling a few points short of qualifying for Raffles Institution, 12-year-old me broke down in the school hall, my elitist dreams crushed.

Qualifying for Chinese High was the next best thing, although I hated the idea of attending a “communist” school. At least, that was my impression. You can’t blame me for believing what people told me when I was 12.

A number of us (including myself) were RI rejects. However, for some, Chinese High was their first choice for its focus on Chinese language and character education.

From the moment I entered the school, the principal and school leaders were unabashed about informing us of our elite status. The principal would do so during school assemblies, only to be echoed later by teachers in a classroom setting.

Whenever we misbehaved, as boys often do, a good chunk of each lecture revolved around how we took our place in the school for granted. Being there was a privilege, and it lay on our shoulders to continue the prestigious legacy of the school.

We were also reminded that we should be thankful for the resources and the very upscale school facilities that we had.

And so from the very beginning, we were told that we were different and maybe better. No surprise that many of us grew up believing it.

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Challenging P6 Math Question (Cycling)

One afternoon, 5 friends rented 3 bicycles from 5.00 p.m. to 6.30 p.m. and took turns to ride on them. At any time, 3 of them cycled while the other 2 friends rested.

If each of them had the same amount of cycling time, how many minutes did each person ride on a bicycle?

Hint: There is an “easy” way and also a “complicated” way to do this question. The “easy” way involves calculating total cycling time, while the “complicated” way involves working out a timetable to determine exactly who is cycling at which time.

(Source: Hardwarezone)

(Ans: 54)

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Thd World’s first 18-Qbit Quantum Computing by the young Chinese scientist Prof Pan (潘).

Math Online Tom Circle

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Lambda Calculus – The Math Behind Functional Programming

Math Online Tom Circle

Functional Programming (FP) Languages : Lisp, Haskell, Scala, Kotlin, etc.

Other non-FP influenced by Lambda Calculus: Python, Ruby, Javascript, Java 8, C++

Inventor of Lambda Calculus : Alonzo Church (1903 – 1995), whose student in Princeton University (1936-1938) was Alan Turing (The Father of Artificial Intelligence).

Lambda Calculus is not : another Differential Calculus !

Note: Calculus has a meaning of manipulating symbolic expressions : either in functions (differentiation, integration) or computations.

Lambda Calculus is almost programming!

I. Syntax of Lambda Calculus: $latex boxed {lambda text { param . body }}&fg=aa0000&s=3$

eg. $latex lambda : x : . : x + 1 $

Notice: it has only one parameter “x”.

  1. Function definition: $latex lambda $
  2. Identifier reference: $latex x $
  3. Function application: $latex x + 1 $

II. Currying 柯里化 : (named after Haskell Curry ) for multiple parameters.

eg. $latex lambda : x : …

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Hong Kong and Singapore have highest average IQ

Just saw this news online. Note that top 3 are all Asian countries. Probably one factor is that IQ test is after all still a paper-based test that rewards good test-taking skills. IQ test does not really cover all forms of creative and intellectual ability. Also, most likely the effect of early-age tuition has boosted the IQ scores. Since IQ is defined as the ratio of mental age over actual age, if a child learns material (be it math or vocabulary) beyond his age, by definition his/her IQ would be increased, though this does not mean that he is “smarter”.

In Singapore it is now common that a child by age 6 has already mastered the Primary 1 (age 7) syllabus. This achievement alone will give a mental age of 7, versus a actual age of 6, giving an estimated IQ of 7/6×100%=117.

For those gifted students that pass the GEP test (age 9), it is common that they already possess knowledge of Primary 5 (age 11) syllabus, or even Primary 6 (age 12). This translates to an IQ of around 11/9×100=122 to 12/9×100=133.

See also:

Recommended Books for GEP Selection Test and How to Get Into GEP


Joint 1st: Hong Kong and Singapore (108)

2nd: South Korea (106)

Joint 3rd: Japan and China (105)


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How Piano Lessons May Improve Language Learning for Kids | Time

Music => Language => Abstractness (Abstract Mathematics, Advanced Physics), these 3 faculties reside on the same (right) part of our brain., the earlier a kid develops it through music education (piano, violin or any instrument) the better.

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Infinite Cake

Math Online Tom Circle

The Big Internet Math-Off, Round 1 – James Tanton v Nira Chamberlain | The Aperiodical

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Celebrates Mathematician Gottfried Wilhelm Leibniz’s 372nd Birthday

Math Online Tom Circle

My favorite mathematician is German Leibniz, who co-invented Calculus with Newton.

Today we thank Leibniz for his elegant Calculus symbols:

$latex boxed {frac{dy}{dx}}&s=3&fg=aa0000$

$latex boxed{int_{0}^{infty}x^{n}e^{-x}dx}&s=3&fg=aa0000$

Leibniz also invented 01 binary algebra, which he later found it was already in the 3,000-year-old Chinese “Yin-Yang” (阴阳 八卦), so impressed that he recommended to the most powerful western (French) king Louis XIV (14th) to use Chinese as the Universal Language of the world.

The rich Newton sued Leibniz for plagiarism of Calculus, until Leibniz died poor in bankruptcy, buried in a common unknown grave.

The war between Newton & Leibniz extended & lasted 100 years between UK Math Community and Continental Europe Math Community. As a result UK lost its math leadership after Newton, France (Lagrange, Fourier, Cauchy, Galois… ) followed by Germany (Felix Klein, Gauss, Hilbert, Riemann …) took over as the world…

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Sunday’s Google Doodle Celebrates Mathematician Gottfried Wilhelm Leibniz

If you log in to Google today, you will see a doodle of binary numbers that celebrates Leibniz’s development of the binary system. Leibniz is very honest and generous to credit Chinese books for his inspiration behind developing the binary numbers.

See also:

Leibniz was a universal genius, but why is Isaac Newton more known? Does it have to do with Newton being British and Leibniz being German?

Leibniz Integral Rule (Differentiating under Integral) + Proof

Quote: Leibniz also developed the binary system, whose notation of zeroes and ones is the basis of modern computer languages. His book, Explication de l’Arithmétique Binaire, credited the ancient Chinese divination manual, the I Ching, with inspiring the binary system of zeroes and ones, since the I Ching’s hexagrams use a very similar notation to record numbers. In an age of European ethnocentrism, Leibniz still recognized China’s long-standing mathematical advancement.


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Singapore Families with Many Children

In Singapore, having 5 kids is so rare that even the newspaper reports it!

Another related video is about raising 7 kids in modern Singapore:

This YouTube video is only a short excerpt, for those who want to watch the full series, it is available on Toggle, under the title of “Full House”.

Source 1: Starting a family of 7 in Singapore at the age of 21 (Family of 7 in this case means 5 kids and 2 adults apparently, not 7 kids.)

Source 2: Raising 7 children on under S$3,000 a month in Singapore

(These are two separate stories, the first is about a family with 5 kids, the second is with 7 children.)

It seems that the biggest worry for most families (be it big or small) is still their children’s education.


Her husband’s absence or his relationship with their children, however, is not her biggest concern. “My greatest worry is Bryan. His PSLE,” she declared.

Her Primary 6 son seems to be more interested in playing – or fighting – with his siblings than in his coming examinations.

Said his mother: “He doesn’t really bother about his studies, but I can’t push him … because the more you push him, the more he doesn’t want (to listen).”

Growing up dyslexic and recently diagnosed with hearing difficulties, Bryan has been struggling in school. And in a family of seven, it has been hard to devote attention and resources to just one child.

We did try giving them tuition. It did help, but it’s quite costly, so we cut down,” Mrs Lim said. “Nick and I are still … working out with teachers – taking (their) advice – how to handle him.

“But he’s a very stubborn boy, and he keeps everything to himself, so it’s kind of hard to get him to open up.”

His parents only want him to pass his subjects, but in his recent report card, he passed only his English out of three subjects.

“I did try, but … I always end up with only a few more marks (needed) to pass,” said the 12-year-old, who had to then promise his parents that he would do better or else they would take away his phone.

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困扰了人类358年 费马大定理 Fermat’s Last Theorem

Math Online Tom Circle


  1. Fermat’s Last Theorem (FLT):$latex boxed {x^{n} +y^{n} = z^{n} ; ; forall n >2 }&s=3&fg=aa0000$
  2. Pierre de Fermat (France 17CE): FLT Conjecture or Prank ?
  3. Euler (n= 3)
  4. Taniyama-Shimura-Weil Conjecture: Modular Form = Elliptic Curve
  5. Galois Group Symmetry
  6. Andrew Wiles (UK Cambridge 1994): (Modular Form = Elliptic Curve) = FLT (q.e.d.)

Notes: Do not confuse Prof Andrew Wiles (proved FLT) with (French/American) Prof André Weil (Founder of Bourbaki School of Modern Math in POST-WW2 universities worldwide) who proved (4) laying the ground work for FLT.

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Singapore universities should look beyond international rankings: Panel

Singapore universities should look beyond international rankings: Panel

Singaporean students are quite lucky that 2 of Asia’s top universities NUS, NTU are located here. I think that there should be room for even more universities to be built here, to cater to those students whose grades are decent but not good enough to enter NUS, NTU, SMU.

Ranking wise, I think maintaining current ranking should be good enough. In practice, there should not be any big difference in say a Top 5 or Top 20 university in the world. (Currently NUS is around 12th in the world, compared to say Yale which is 25th in the world, for Natural Sciences.) There should not be a need for a deliberate push to be top in the world, at expense of other factors.

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World Cup Soccer Maths

Do check out the following books on the Math (and Economics) of the World Cup Soccer Match. The second book “Soccernomics” has a very interesting title, it predicts that one day Japan, Iraq, and the United States will become World Cup Soccer champions?

Soccermatics: Mathematical Adventures in the Beautiful Game Pro-Edition (Bloomsbury Sigma)

Soccernomics (2018 World Cup Edition): Why England Loses; Why Germany, Spain, and France Win; and Why One Day Japan, Iraq, and the United States Will Become Kings of the World’s Most Popular Sport

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How Abstract Math Can Analyze Social Injustice

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