Python Online Courses for Teenagers/Adults

If your child is interested in a Computer Science/Data Science career in the future, do consider learning Python beforehand. Computer Science is getting very popular in Singapore again. To see how popular it is, just check out the latest cut-off point for NUS computer science, it is close to perfect score (AAA/B) for A-levels.

According to many sources, the Singapore job market (including government sector) is very interested in skills like Machine Learning/ Deep Learning/Data Science. It seems that Machine Learning can be used to do almost anything and everything, from playing chess to data analytics. Majors such as accountancy and even law are in danger of being replaced by Machine Learning. Python is the key language for such applications.

I just completed a short course on Python: Python A-Z™: Python For Data Science With Real Exercises! The course fee is payable via Skillsfuture for Singaporeans, i.e. you don’t have to pay a single cent. (You have to purchase it first, then get a reimbursement from Skillsfuture.) At the end, you will get a Udemy certificate which you can put in your LinkedIn profile.

The course includes many things from the basic syntax to advanced visualization of data. It teaches at quite a basic level, I am sure most JC students (or even talented secondary students) with some very basic programming background can understand it.

The best programming language for data science is currently Python. Try not to learn “old” languages like C++ as it can become obsolete soon. Anyway the focus is on the programming structure, it is more or less universal across different languages.icon

Udemy URL: Python A-Z™: Python For Data Science With Real Exercises!

Related posts on Python:

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Superposition Principle of Linear Algebra

Superposition Principle

If \mathbf{u} is a solution to \bf{A}\mathbf{x}=\mathbf{b}, and \mathbf{v} is a solution to \bf{A}\mathbf{x}=\mathbf{c}, then \mathbf{u}+\mathbf{v} is a solution to \bf{A}\mathbf{x}=\mathbf{b}+\mathbf{c}.

Proof:
\mathbf{A}(\mathbf{u}+\mathbf{v})=\mathbf{A}\mathbf{u}+\bf{A}\mathbf{v}=\mathbf{b}+\mathbf{c}

Properties of Matrix Transpose

1) (A^T)^T=A
2) (A+B)^T=A^T+B^T
3) (kA)^T=kA^T
4) (AB)^T=B^T A^T

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Hangout @ Chinatown

Includes a review on “The Coconut Club”, which serves one of the best Nasi Lemak in Singapore.

Cooking For Fun

Well, today I have one day off and my husband also has time. We planned to go to Chinatown and have lunch there. He wanted to try a nasi lemak restaurant there. It’s the first time for us to go to Chinatown and hunt for non-Chinese food.

Chinatown of Singapore is really close to to the CBD. You can actually walk from Chinatown to CBD and also see blocks of tall buildings from Chinatown.

There are many places to have nice food in Chinatown, such as Amoy Street and Chinatown Food Street.

Chinatown has many traditional buildings of Nanyang style.

The restaurant we went is at Ann Siang Rd.

There are many bars, restaurants and cafes there.

The blue restaurant is the one we were going.

The Coconut Club.

It is not a very big restaurant. Their signature dish is nasi lemak, which can be told from the menu.

Actually…

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To those starting JC life in today’s Singapore

Excellent post by top GP tutor Mr Steven Ooi. This post sums up the current competitiveness of the Singaporean education system. Similarly for Math, there is a knowledge “arms-race” to the extent that a typical Primary 3 student should know how to calculate 1+2+3+…+100 in case this question pops up in the exam. The textbook syllabus remains just as easy as in the past, but what is tested has become 10 times more difficult.

GP & English Tutor with First Class Honours, NUS

jc singapore

[Writer’s note: While this article is addressed specifically to Singapore-based students, it may hold some truth for students in many other places as well.]

Dear young friend,

I’m writing this to share some thoughts that I used to convey to every one of my students when I was still a full-time tutor in Singapore (I retired in 2016). It is just my personal opinion, formed through years of experience as a student in the 1980s and 1990s, then as a tutor in the 2000s and 2010s.

Observing student life in the 90s and then in the 2010s, I can only conclude that the school system in Singapore has become 10 times more competitive than during my time. At least 10 times. During the 90s, most of my junior college classmates didn’t even attend private tuition. We could hang out at the bowling alley, the arcade or the hawker centre most…

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Malayan Aqua Fern

This “Malayan Aqua Fern” is a very mysterious plant, there is very little information on Google about it.

There are two views on it, based on online writings.

First viewpoint on Malayan Aqua Fern:

The “Malayan Aqua Fern” is none other than Peacock Fern, or Selaginella willdenowii. It is NOT an aquatic plant, and will die if fully submerged under water. This is quite reasonable, based on the pictures of Peacock Fern online, it does look like the pictures of the “Malayan Aqua Fern”. Nonetheless, it can be planted in a crab/terrapin tank where it is not fully submerged under water.

The “Malayan Aqua Fern” may give the illusion of surviving under water when it may be slowly dying (takes around a month to die).

Websites that support this view:

Second view:

The “Malayan Aqua Fern” is an amphibious plant, able to live both submerged or in moist conditions. If this is true, then “Malayan Aqua Fern” would be an incredible aquarium plant as it looks very good in a fish tank.

Websites that support this view:

Is Malayan Aqua Fern Aquatic or Not?

The main question is whether the Malayan Aqua Fern is aquatic or not? Can it grow fully submerged under water? If you have experience with the Malayan Aqua Fern, please leave your comments below!

Malayan Aqua Fern and Betta

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Chromatic Fingering for Moonlight Sonata 3rd Movement

In Beethoven’s Moonlight Sonata 3rd movement, there is a very fast stretch of chromatic notes in bar 187.

I was wondering if the most basic fingering is good, or a more advanced fingering involving the 4th or even 5th finger would be better. (Read more on advanced chromatic fingering here: http://www.pianisttopianist.com/?p=486)

Some people on Reddit suggest some very fanciful fingerings, including “using LH (Left Hand!!) (faster playing up)4321,4312,4321,4321. So, groups of 4321 with the exception starting on the C. That part goes 4312. Just play all the way up with the LH and smack that top A (was it?) with yer Right Hand”! This fingering is apparently attributed to Alfred Brendel.

It turns out that at least 2 professional pianists seem to use the basic chromatic fingering: 2 13 123 13 123 … etc. They do not use the fourth finger at all. The starting fingering of the first note (G#) may vary.

The first pianist is Valentina Lisitsa. Watch at 0.25 speed to see the fingering at around 6:07 time. Lisitsa seems to use a “special trick” by using her left hand to play the lowest G# in the chromatic range.

The second pianist is Rousseau. You can see his fingering clearly, it is the basic chromatic fingering at around 6:34 time.

Hence, it seems that for Moonlight sonata it is not needed to use the advanced chromatic fingering. Using the pedal during the chromatic (both pianists use it to some extent) gives the illusion of a fast chromatic.

For other pieces like Fantasie Impromptu, the advanced chromatic fingering works well for greater speed.

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BTS Fan Products

BTS is one of the most popular Korean bands. Previously, we wrote on how Scientists Use Math To Discover Why BTS Jin Is The Most Handsome. Their dance steps are also amazing, hence it is no question why they are so popular worldwide. Basically, nowadays top artistes need to be good at dance + singing in order to be popular.

BTS seems very popular locally in Singapore, their concert tickets are often sold out within an hour. By the way, if a youth says that they are in “the Army”, it may not mean that they are soldiers/National Cadet Corps. BTS fans are also known as “the Army”. I once conversed with a taxi driver who told me that his daughter is in RGS, and most of her classmates are fans of K-pop including BTS. Korea is also now a top tourist destination for Singaporeans.

Both Qoo10 and Amazon have BTS fan paraphernalia, with Amazon having a more extensive collection. Most of the items ship to Singapore, with the delivery charge being quite affordable considering the huge distance from America to Singapore.

An example of a BTS cosmetic set from Qoo10.

[S$64.90](▼36%)[VT Cosmetic]【VT X BTS】★THE SWEET SPECIAL EDITION SET(Cushion(Choice 21 or 23 Tint 2 pcs included) /TTBEAUTY

WWW.QOO10.SG

From Amazon, there are collections of BTS jackets, sweaters, and more. We only showcase those that are at least 4 stars out of 5 for the Amazon rating. Basically, any product with substantial ratings of above 4/5 stars on Amazon are quality products. Especially, if they have the “Amazon’s choice” label, they are personally curated and approved by Amazon’s team.


babyHealthy Kpop BTS Love Yourself Hoodie Suga Jimin V Rap-Monster Sweater Jacket Pullover (4.1/5 stars)


BTS Kpop Socks 7 Pairs (Jungkuk, J-Hope, Suga, V, Jin, Jimin, Rap Mon) (4.8/5 stars, Amazon’s choice)


babyHealthy BTS Baseball Jacket Uniform Bangtan Boys Suga Jin Jimin Jung Kook Sweater Coat (4.3/5 stars)


KPOP BTS New Logo Hoodie Bangtan Boys Unisex Sweatershirt JIN SUGA JIMIN V (4.1/5 stars)


BTS – 2018 SEASON’S GREETINGS Set (4.6/5 stars, Amazon’s choice)


BTS 1st Album [Dark and Wild] CD + PhotoCard + PhotoBook K-POP BANGTAN (4.5/5 stars, Amazon’s choice)

Most of BTS videos have 100 million views or more:

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Free American Tourister 25” Luggage (Dumex)

Very good deal here, free 25 inch luggage (American Tourister brand) with purchase of Dumex milk powder!

This is the official Dumex Qoo-10 store, by the way.

[S$325.90](▼23%)[Dumex]Free 25 luggage(worth $220)【Bundle of 6】Dumex Mamil Gold Stage 2/ 3 / 4 / 5 Milk Formula 1.6kg

WWW.QOO10.SG

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Mathematician Couple’s Wedding Math Questions

Math Online Tom Circle

https://m.facebook.com/nikita.nikolaev.752/posts/2208321356091587

It is fun for the guests who are also mathematicians like the wedding couple…

Why don’t the IT couples do the same with computer questions (eg. private cloud, serverless, containers, DevOps,… ) , lawyers with legal cases, doctors with medical questions …

Example 1 is obvious to this guest whose PhD research topic is in Differential Geometry “Chern Class” invented by Prof S. S. Chern (陈省身) :

Example 2 is obvious to this guest unless he/she can’t count the number of sides (8):

Example 3 is to the guest with some background in secondary school organic chemistry but forgotten, definitely not linear…

Example 4 to the hobbyist of Rubik’s cube, but the answer can be guessed easily by elimination: definitely not 2019 (this year), or π.

Answer in Multiple choices(Only 1answer is correct, the other 2 answers are obviously wrong) :

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The Best Way to Take Online Exams

Today the technology has changed a lot and the way the exams are being taken is changing too with the changing times. Gone are the days when people used to take the paper and pen test. This was time consuming. But today people go for the online tests that not only help them to save their money but also help them as these tests are convenient. There are many advantages of this type of exam and we have mentioned a few of them for your understanding.

Advantages of the online exams

  • Can be taken as per the convenience

These exams can be taken as per the convenience of the higher authority and the higher authority and the candidates can decide a suitable time. This is the way both can save their time. This is a suitable method for all. You will not have to worry as this can be taken as per the ease of both.

  • Helps to save money as well as time

This exam is taken online and hence money will be saved. This is very accurate way of test as it does not involve paper and pen. This will also help to save the money for transportation. As the candidates will write the exam from their place, the transportation money will be saved. This is the most accurate way to take an exam as the results will be there in no time. There is no need to take the print out of results and this is the way we can also say that this is an eco-friendly approach to the examination. Many people go for this as this does not need paper and this helps save paper.

  • The convenient way to take a test

This is the easy and simple way to take an exam. There will be auto grade and there will be multiple answers pattern. The candidate will be given four options for each of the question asked on this online exam platform and there will be negative marking for the wrong answers given. The candidates need to be very careful while they are giving answers. This is a completely automated way of exam and hence this is more perfect in nature. There will be no wasting of time for the distribution of paper and the paper will be uploaded in no time. There is also no need to have a moderator to keep a watch on the candidates as there will be online monitoring. The tests are set up in such a manner that no student can get the answers in a book or anywhere else.

  • It will be an economical way, just go for it

This is the economical manner to take an exam. There is no paper involved, and everything will be done online only. The candidates will only need to have an internet connection and a device. They can also give the exam on their phone and this is a simple and easy manner. There is no need to rent a class and this is the way the higher authority as well as candidates can save their money. Also, there is no need to appoint a moderator to keep a watch on the students.

  • Safe, secure and accurate way that is

This is the safe and accurate way to take an exam. You only need to create a big question bank that has many questions. The student will have to select the question sets. This is the way there is a variety and safety too at the same time.

Though there are many advantages, there are a few things that you need to keep in mind while the exam is going on. We have mentioned a few points for you to keep in mind.

  • It is free way of exam

There will be no check on the students and to see if they are copying from some book. This is the reason there is a need to alter the questions from time to time. The questions should not be very simple, and they must be asked in such a manner that the candidates will not be able to find them from books easily.

  • The results will be out instantly and there will be no time waste

The results will be there immediately after the exam is over. There will be no time waste and waiting over.

Why to go for an online examination and how does that work

There are many advantages as well as disadvantages of the online exam system. There are many reasons for which you need to go for this option. One needs to create a test with the help of generator. The candidates can easily get started with the exam. They need to search through the various sites and see which test they are fine with. As you set exam you need to write a description in which you need to mention what you expect from the candidates at the time of examination. You can add some questions there. You can also add some audios or videos for a better effect.

Easy to share

These tests are easy to share, and the candidates will be able to share the tests with ease. You need to create your own timetable and set a date and time for the exam. After the exam is created you can put that online. You can upload thee exam and the students can find that. You will be able to have a look at the progress of the students. You can also make sue of the statistics and graphs so that you will be able to measure the growth of the candidates.

The easy and simple it works

This is the easy way to take the exam. You need to create an exam and upload that. This is the way you save your energy as well as time. Just go for this type of test and have a good time.

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Cheap Portable Aircon

How to stay Cool in Singapore

Singapore’s heat and humidity makes it quite unbearable to live without an air-conditioner. Especially for students who study, a hot and humid environment makes it harder to concentrate.

For long term purposes, most families will install a split aircon system like Mitsubishi Starmex.

[S$1,898.00](▼58%)[MITSUBISHI ELECTRIC]Mitsubishi Inverter Multi Split AirCon FN Series – SYS. 2 – 4 [5 Ticks]

WWW.QOO10.SG

However, for short term purposes (e.g. rental, or do not want the hassle of installing a permanent air-con), a portable aircon is the solution. A portable aircon will be enough to cool a small room (i.e. most HDB rooms and small Condo rooms).

Whatever you do, DO NOT buy those mist fans, they are close to useless since Singapore’s humidity is already close to 90%. Those mist fans work well in hot and dry desert-like environments, possible like Saudi Arabia or Australia. They work by making the mist evaporate, which does not work well in Singapore due to the high humidity. Not to mention, the constant mist may lead to some mold problems.

You might as well buy a powerful fan with vortex action:

[S$58.80](▼41%)[PULLMAN][XMAS SALE] PULLMAN AIR CIRCULATOR FAN TURBO FORCE With Remote Control

WWW.QOO10.SG

Cheap Portable Aircon Singapore

A good brand for cheap portable aircon is Europace. The last Europace portable aircon I bought lasted close to 10 years, and counting.

[S$399.00](▼51%)[Europace][LAST 5 SETS] EuropAce Portable AirCon (10KBTU / 12KBTU) (EPAC 12T8/10Q/10P/12P) – 5 YEARS WARRANTY*

WWW.QOO10.SG

This is another newer model of Europace:

[S$399.00](▼64%)[Europace]EuropAce Portable Air Conditioner with HepaCarbon filter 10K/12K/14K BTU- (EPAC 10T6/12T6/14T6)

WWW.QOO10.SG

A cheaper brand would be Trentios. This price is probably the cheapest for a brand new portable aircon.

[S$288.00](▼68%)[TRENTIOS]Trentios/Avolta Portable Aircon 10000/12000/14000 BTU / (Include Air Freshener/Dehumidifying)

WWW.QOO10.SG

Bonus Cooling Tip

Another good way of staying cool at home is to wear Uniqlo DRY-EX T-Shirts. They are much more cooling than cotton shirts. Wearing one of these can be equivalent to a drop of 1-2 degrees Celcius. Sometimes the online Uniqlo stores do have 50% discount, do grab them during the discount if possible.

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Cute Graph Cheatsheet

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Sir Michael Atiyah obituary

Math Online Tom Circle

Atiyah is so-called the “2nd Newton” in being both a Mathematics & a Physics Grandmaster, his life achievement extends the ancient Greek Geometry to Topology and Algebra since Euclid till now, providing useful application to Quantum Physics.

https://amp.theguardian.com/science/2019/jan/15/sir-michael-atiyah-obituary

Vector Bundle 向量丛

K-Theory : Vector Bundle invariant

In Sept 2018, Atiyah claimed in a seminar of his astonishingly simplest proof of the Riemann Hypothesis (one of the 6 outstanding millenian problems with US$1 million Clay Prize) – but sadly nobody believes him even after his death 3 months later !

https://tomcircle.wordpress.com/2018/09/28/what-is-riemanns-hypothesis/

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China Education Documentary

Similar to Singapore, China has different tiers of universities. The top tier in China is Tier 1 (一本). Within Tier 1, there is a further differentiation of “Project 985” and “Project 211” universities, the former being more selective. That is, Project 985 universities is a subset of Project 211 universities.  “Project 985” universities consists of 39 top universities, including Peking University and Tsinghua University.

The above documentary exposes some fraudulent private universities that are out to con money from simple, rural folk. It also shows the hardship experienced by the young people in China, where salaries are low but living expenses can be quite high.

Summary from IMDB:

In ancient times in China, education was the only way out of poverty; in recent times it has been the best way. China’s economic boom and talk of the merits of hard work have created an expectation that to study is to escape poverty. Many Chinese parents see getting a degree as a way of ensuring their children have better, less impoverished lives than their own. But in 1997, the Chinese government privatized universities and education became a commodity. It’s a money-making business where there’s a profit to be made – The University Entrance Exams Day – the day students receive their results – often determines the future of one’s whole life. If you get good results, you get into the state-subsidized universities. If you don’t, there are other universities you can get into but they are more costly, often substandard, and run as lucrative businesses. Some unscrupulous colleges employ marketing techniques to target poor, rural families who are often less streetwise to their tactics. More often than not, these families can’t afford the tuition fees and some end up selling livestock and even their homes to cover the cost of their child’s education. But many colleges can’t live up to their promises and each year, more than two million graduates in China do not find work. For students and families who incurred debt while studying, education is no longer a way out of poverty but a cause of it along with unemployment and despair.

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中国历法

Math Online Tom Circle

Chinese calandre is both solar and lunar, unlike western (pure solar) and Muslim (pure lunar):

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Byrne’s Euclid

Math Online Tom Circle

https://www.c82.net/euclid/

My Modern Met: Geometry Lovers Will Enjoy This Interactive Version of Byrne’s Euclid.

https://mymodernmet.com/byrnes-euclid-nicholas-rougeux/

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Modern Mathematics and the Langlands Program | Institute for Advanced Study

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The Error Function & The Integral of e^(-x^2)

Math Online Tom Circle

$latex boxed{ displaystyle erf(x) =
frac{2}{sqrt{pi}} int_{0}^{x} {e^{-{t}^2}dt}}&fg=aa0000&s=3
$

The Bell Curve:

$latex boxed{displaystyle y = e^{-x^2}}&fg=0000aa&s=3$

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Delete Jetbrains toolbox Mac (Solved)

Jetbrains toolbox is a software that manages programs from the Jetbrains company, including the popular PyCharm interpreter.

However, it did not work for me on Mac, and I was trying to remove it. The system did not let me remove it as it claimed that Jetbrains toolbox was open and running.

The way to remove it completely is to first force quit it from Activity Monitor on Mac. Then, you can simply delete Jetbrains toolbox from the Applications folder.

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Which JC is the best in Singapore?

Do vote for your favorite JC! Currently our poll seems to be quite “accurate”, the top 3 JCs are:

Hwa Chong Institution 15.48% (13 votes)
Raffles Institution 15.48% (13 votes)
Nanyang Junior College 13.1% (11 votes)

Singapore Maths Tuition

Which JC is the best in Singapore?

Feel free to leave any comments as to why you think your JC is the best in Singapore 🙂

Also, check out: Which Secondary school is the best in Singapore

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Unable to view DBS/POSB Consolidated Statement

Recently, when I click the “View PDF” button, either I am led to a page “about:blank” or the DBS Welcome page itself.

Hence, I am unable to view the DBS / POSB Consolidated E-statement.

Upon waiting for a while on the DBS Welcome page, an error message pops up:

“Our site is currently unavailable. We expect to be back soon. Thanks for your patience.”

The only solution seems to wait for a day or two for them to repair the site.

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O Level Results 2019

Congratulations to all who did well in the ‘O’ Levels!

Do check out our post on Latest JC Cut-off points COP, to see the trend of JC cut-off points to help you choose your desired school. (Remark: I am curious to see how Nanyang JC Cut-off point is like, it seems that NYJC is now one of the bona fide top JCs in Singapore.)

For those who did not do well, check out our post on What to do if fail O level Singapore, there are still available routes, do not give up!

For this year, again there is a loss of 32 A-Math scripts in the UK. See also:

Sincere condolences to those affected.

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Benefits of hiring Private Math Tutors

Being city-state of just 5.5 million people, Singapore is constantly ranked as one of the top countries that harbors great mathematic talents and has one of the most admired education systems in the world. Based on test scores from 76 countries published by the OECD, Singapore came first, followed by Hong Kong, South Korea, Japan and Taiwan. The ranking reiterated that Asian children are ahead of the curve indeed, all thanks to the kind of education systems that they have.

Source: Google.com

Though the education system produces many great young talents, it is undeniable that the system is highly demanding and it’s all about producing a generation of “21st century competencies”. Unfortunately, many students find this to be a chokehold and they feel deprived of a much-needed breathing space internalise and understand everything that happens around them.

It is a known fact that in order to survive and conquer math, what is being taught in schools is insufficient. There is a need for the extra help and hence many are turning towards the option of tuition. There are many types, but the most famous one of all is private tuition. By hiring a private math tutor, students will notice a huge change, a huge transformation in the way they learn and it will be reflected in their grades.

So, let’s take a look at the benefits of hiring a private math tutor!

 #1: PERSONALISED APPROACH

Teaching a group of 10 children, as compared to tutoring one child is at either ends of the spectrum. Tutoring one child requires the tutor to study, analyse and comprehend the student’s learning pace, learning methods, memory retention process and the areas of the student’s strengths and weaknesses. All this analysation then translates into a more customised teaching which will help the student to excel at a faster rate.

This is crucial when teaching math, especially because it is a challenging subject which not everyone is innately good. Some students grasp concepts quickly while others lag behind and require extra coaching and visual representations for them to comprehend those same concepts.

It is also important to note that private tutors are not there to be their student’s confidante, to molly-coddle them and console them all the time. Instead, they will be a source of motivation, a pillar of strength and they will guide them (but never reveal the answers).

#2: INTERESTING AND EFFECTIVE LESSONS

Schools have an almost ritualistic way of teaching this subject, that is, to flash answer keys of practice papers on the visualiser and hand out more practice papers for students to complete. This ineffective and boring teaching method is of stark contrast to how private tutors handle this rather complex subject.

The reason why such a lesson is interesting is because there is a form of given-and-take; an interaction, making the lesson engaging and spontaneous. It does not lull the students to sleep. Private tutors also have a way of simplifying abstract concepts and turning them into something less intimidating for students.

ALL IN ALL, children may not comprehend how useful math private tuition could possibly be for them. As parents, you need to make them understand the benefits of tuition. Do not wait for problems to snowball and take action quickly!

 

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RIP Sir Michael Atiyah

Rest in peace, Sir Michael Atiyah. Many scientists have called Atiyah the best mathematician in Britain since Isaac Newton.

Read also our previous posts:

Source: New York Times

Michael Atiyah, a British mathematician who united mathematics and physics during the 1960s in a way not seen since the days of Isaac Newton, died on Friday. He was 89.

The Royal Society in London, of which he was president in the 1990s, confirmed the death but gave no details. Dr. Atiyah, who was retired, had been an honorary professor in the School of Mathematics at the University of Edinburgh.

Dr. Atiyah, who spent many years at Oxford and Cambridge universities, revealed an unforeseen connection between mathematics and physics through a theorem he proved in collaboration with Isadore Singer, one of the most important mathematicians of the last half of the 20th century.

His work with Dr. Singer, of the Massachusetts Institute of Technology, led to the flowering of string theory and gauge theory as ways to understand the structure and dynamics of the universe, and has provided powerful tools for both mathematicians and theoretical physicists.

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Betta Community Tank

My betta in a 5 Gallon tank, together with 2 Amano shrimp (I think that’s the breed though I am not 100% sure) and 1 Zebra Snail. Anyone knows the names of the aquatic plants? I know one of them is “guppy grass”, the other two I have no idea. Please comment below if you know!

A more detailed view of the Zebra snail:

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The most beautiful and important mathematical equations

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From Polynomial to Modern Algebra

Math Online Tom Circle

Examples Polynomial with degree > 5

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13 classic mathematics books for lifelong learners

Math Online Tom Circle

View at Medium.com

Out of 13 must-read Popular Math books, our Singapore National Library NLB has 6 which I borrowed and read: eg. “Prime Obsession” , “What is Mathematics” , etc.

Popular math books are better than the boring textbooks (Axiom – Theorem – Proof – Exercise). They are motivational, more concrete instead of abstract, philosophical analogy with the Nature (afterall, the math ideas derived from the universe, eg. Pi, e, golden ratio, infinity, limit, …), plus the historical background in which these math ideas were first discovered, and the beauty of these inter-connected ideas such as the Euler’s Identity:

$latex boxed{e^{i. pi} + 1 = 0}&fg=aa0000&s=3 $

Proof from the Book” – the name “Book” (God’s Theorem Proof Book) is coined by Paul Erdos the Hungarian ‘vagabond’ (homeless, single, no nationality) mathematician, who had proven 1000+ theorems (some co-operated with his students). He said…

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Logic & Math (Set Theory)

Math Online Tom Circle

Cambridge Prof Peter Smith:

You can download the book at the bottom link from the below web site.

https://boingboing.net/2018/12/26/beyond-a-equals-a.html/amp?from=singlemessage

Philosophy using Math – that is cool!

Set Theory is Philosophy, see this “Set Proofing Technique” taught in French Baccalaureate high school but Cambridge GCE A level ignores :

Prove : A = B
You need to prove 2 ways:
A ⊂ B
and
B ⊂ A
=> A = B

In the Bible 《John 14:11》
Jesus said to his disciples:
“Believe me when I say that I am in the Father and the Father is in me”.

Proof: Father (God) = Jesus

“Father in Me” :
<=>
Father ⊂ Jesus
and
“I am in the Father” :
<=>
Jesus ⊂ Father
Hence,
Jesus = Father (God)
[QED. ]

Merry Xmas! 圣诞快乐!

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How Singapore Data Scientists caught the subway MRT “Circle line” rogue train

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Quara: Strategy to teach yourself math from basic algebra to high level mathematics

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Betta Fish Tank

Betta, also known as Siamese Fighting Fish, are ideal pets for Singaporeans since they require relatively less equipment. Firstly, they are labyrinth fish and can gulp oxygen from the air. Hence, theoretically they can survive without a filter. Filter is still good to purify the water from excessive nitrates.

However, to put them in a small fishbowl is too extreme (though they may still live) and will lead to shortened lifespan and an unhappy Betta fish.

Online, many sources say that a 5 gallon tank will be a good fit for Betta. 5 gallon is roughly 18.9 litres.

Where to buy Betta Fish Tank

Hence, this “Ripples Premium Aquarium Glass Fish Tank (with Filter and LED Lights) 18.9L” is a perfect fit for a Betta fish. Buying from Qoo10 is also convenient for those without a car, as taking a fish tank around in public transport is highly inconvenient.

This Qoo10 aquarium shop Fins and Paws is very good; I experienced the fastest ever delivery time with them (ordered and delivered the next day).

[S$54.90](▼22%)[Resun Aquarium]Ripples Premium Aquarium Glass Fish Tank (with FilterLED Lights) 18.9L/56.7L

WWW.QOO10.SG

For those who want an even bigger tank, you can try out the Classica ECO 60 Aquarium Fish Tank. Your Betta fish will definitely feel like a king in this fish tank, and you can add more fish to keep the Betta fish company. (Note that there can only be a maximum of 1 Male Betta fish in the tank, as they will fight each other to the death if put in the same tank.) For suitable Betta tank mates, check out this website: ModestFish.

[S$95.00][Classica]ECO 60 Aquarium Glass Tank – 60 x 30 x 35cm Fish Tank with LEDFilter

WWW.QOO10.SG

It is good to have some substrate on the floor of the tank (e.g. sand, gravel, soil). This is especially so if you want to grow some real aquatic plants. For a 18.9 litre tank, 3L of Aqua Gro Aquarium Soil will cover the base nicely to a suitable depth.

[S$17.00](▼6%)[Ocean Free]Aqua Gro Aquarium Soil (PlantsShrimp)

WWW.QOO10.SG

A nice Betta 5 Gallon tank can look like this:

Where to buy Betta Fish

To buy the Betta Fish itself, you can check out Iven Betta. They have won many awards for Betta Fish breeding, currently they are located at KAP Mall, 9 King Albert Park #02-15. (Note: do call/message them before going if you live very far. The last time I went on Saturday 7pm, they were closed though their official hours states that they should be open from 1pm-8pm.)

For a cheaper option, check out Polyart Clementi (open 24 hours!). While not exactly show-quality, the Male Bettas there are decent quality and cost only $4 (correct as of Jan 2019). They even have Nemo Betta and Crowntails selling for $4!

My Betta Community Tank

My personal 5 Gallon Betta Community Tank consists of: 1 Male Betta (Delta/Super Delta), 2 Amano Shrimp, and 1 Zebra Snail. Currently, the Betta is quite friendly/indifferent to the shrimp, they are coexisting peacefully for the time being. I do have a few aquatic plants for the shrimp to hide if necessary. The Betta is bought from Polyart Clementi at just $4.

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Indian Scientist: Albert Einstein was wrong and that gravitational waves should be renamed “Narendra Modi Waves”

Source: BBC

According to BBC World News,

Some academics at the annual Indian Science Congress dismissed the findings of Isaac Newton and Albert Einstein.

Hindu mythology and religion-based theories have increasingly become part of the Indian Science Congress agenda.

But experts said remarks at this year’s summit were especially ludicrous.

The 106th Indian Science Congress, which was inaugurated by Prime Minister Narendra Modi, runs from 3-7 January.

The head of a southern Indian university cited an old Hindu text as proof that stem cell research was discovered in India thousands of years ago.

G Nageshwar Rao, vice chancellor of Andhra University, also said a demon king from the Hindu religious epic, Ramayana, had 24 types of aircraft and a network of landing strips in modern day Sri Lanka.

Another scientist from a university in the southern state of Tamil Nadu told conference attendees that Isaac Newton and Albert Einstein were both wrong and that gravitational waves should be renamed “Narendra Modi Waves”.

Read more at: https://www.bbc.com/news/world-asia-india-46778879

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American Health Concerns that many are unaware of

America (and prosperous European countries like UK and France), being 1st world countries, are sometimes concerned about “First World Problems” that most other countries do not have time/energy/money to care about.

Two health concerns that are very popular in America, but virtually unknown in most Southeast Asian countries are:

Vaccines Health Concerns

Although the main research linking MMR Vaccines to Autism has been retracted, many Americans, including President Donald Trump, have expressed their concern about vaccines. There are many anecdotal stories from parents whose children are doing well developmentally, until the day they took the vaccine where strange effects happened, including autistic regression.

Read here about a Nature article on “The real issues in vaccine safety”. By the way, Nature is the top science journal in the world, it is considered a tremendous achievement for any professor to publish in Nature.

The main author behind the MMR-Autism link, Andrew Wakefield, has published his version of the story in his book called “Callous Disregard”. He has been called a fraud, but yet many people do believe in his theory. Notably, in his retracted paper Wakefield did not claim that vaccines cause autism, he just investigated the link and basically said that more research needs to be done. His punishment was very severe (lost his UK doctor’s licence; he spent a decade earning his Gastroenterologist specialist degree), and some people believe it to be a conspiracy theory backed by the billion-dollar vaccine pharmaceutical giants.

“We have identified a chronic enterocolitis in children that may be related to neuropsychiatric dysfunction. In most cases, onset of symptoms was after measles, mumps, and rubella immunisation. Further investigations are needed to examine this syndrome and its possible relation to this vaccine.” (Andrew Wakefield’s paper’s final conclusion.)


Callous Disregard: Autism and Vaccines–The Truth Behind a Tragedy

Basically, vaccinations rely on a phenomenon called “herd immunity”, it requires at least 90-95% of the population to be vaccinated in order for it to be successful. Hence, many people dropping out of the vaccinations can cause the “herd immunity” to be lost, which may be dangerous. On the other hand, vaccines contain dangerous ingredients like preservatives and viruses, and even used to contain a mercury compound called thimerosal, which no doubt is something unnatural that you wouldn’t want to put in your body. Due to the vaccine controversy, thimerosal has now been discontinued in most vaccines.

Gluten


The Gluten Connection: How Gluten Sensitivity May Be Sabotaging Your Health–And What You Can Do to Take Control Now

In Southeast Asia, I would say that more than 90% of people do not know what gluten is (though they eat it everyday). In Laymen’s terms, it is a type of protein that is found in wheat, barley, rye, etc. In America, many people have been tested to have gluten sensitivity, causing digestive problems such as Crohn’s disease or Celiac disease. Again, similar to vaccines, most people have no problem at all eating gluten, but in a selected minority of the population, it can cause severe problems.

The digestive system is said to be a “second brain”, (see The Strange Location of Your Second Brain). It contains a lot of neurotransmitters. Hence, many scientists have started to notice the gut-brain connection. Read this Harvard article that links anxiety and depression to digestive (gut) problems. Hence, for people with gluten sensitivity or allergy, gluten can be the starting trigger for their other problems like depression/anxiety. It has also been linked to ADHD and even schizophrenia.

Check out this book (1,001 positive reviews) on the connection between the gut (digestive system) and the brain:


Brain Maker: The Power of Gut Microbes to Heal and Protect Your Brain–for Life

Watch what Donald Trump has to say about vaccines:

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Egg Stuffed Mushroom

Cooking For Fun

Since last time I cooked portobello mushroom last time, my husband had deeply fallen in love with this giant brown mushroom. He required to buy some portobello mushroom when we went out for shopping.

One of my hobbies is to explore the different cooking method for different ingredient. So I decided to try this dish with this mushroom. It’s quite easy.

  1. preheat oven to 180 Degree c.
  2. wash portobello mushroom gently in water. Then wipe them dry with kitchen towels.
  3. remove the stem. Also use a spoon to scratch off the black gills to save more room for egg.
  4. brush mushroom with butter.
  5. sprinkle a little salt over the mushroom. Only a very little is enough.
  6. place mushroom in baking try, better with a parchment paper underneath. crack an egg onto the gill of each mushroom.
  7. sprinkle cheese, black gills scratched off  and chopped spring onion on egg. Avoid egg…

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清朝妃子的“薪水”

For those who enjoy Chinese Dramas, do check out “Yanxi Palace”.

Chinese Tuition Singapore

前一段时间,一部中国古装剧播得十分火——《延禧攻略》(Story of Yanxi Palace)。我经常在巴士上看到有人在手机或者平板电脑上观看,而在我家附近的购物商场卖家用电器的地方也在播这部电视剧。包括之前也十分火爆的《甄嬛传》都是在讲述清朝时期,皇帝后宫嫔妃之间的勾心斗角,恩恩怨怨。

之前,我在网上看到一个数字:紫禁城(皇帝以前住的地方,也就是现在的故宫)有8707间房子。由此可见,紫禁城里的人数庞大,从小小的宫女太监,到皇室贵族,形成了一个等级分明,制度严格的小社会。

后宫当中有严格的等级划分,清朝时每个皇帝拥有皇后一人、皇贵妃一人、贵妃二人、妃四人、嫔六人、贵人不定、常在不定、答应不定。

皇太后——后宫地位最高的当然是皇帝的母亲,薪水俸禄一应之物也是最多最好的。太后每年俸禄是黄金20两、白银2000两,换算成现在的人民币约是年薪44万。(以下均是RMB)

皇后——白银1000两,年薪20万元。

皇贵妃——白银800两,年薪16万元。

贵妃——白银600两,年薪12万元。

——白银300两,年薪10万元。

——白银200两,年薪4万元。

贵人——白银100两,年薪2万元。

常在——白银50两,年薪1万元。

答应——白银30两,年薪0.6万元。

还有别的补贴。比如,每年到了各自的生日、节庆赏赐、生孩子赏赐、孩子满月赏赐、冬夏季节有冰敬碳敬、一年四季的衣料绸缎等等,如果哪个人平日里与皇帝走的近,受宠多,那皇帝随意一赏就不得了。

除了固定年奉外,每个等级的后妃每年还能得到固定的衣料。

生日的时候也有按等级发放的 “例钱”。比如每年皇后的生日,皇帝要恩赐:黄金90两、白银900两、缎纱45匹、蟒缎9匹、缎9匹、宁绸9匹、宫绸9匹、纱9匹、春绸9匹、绫9匹。其他等级的后宫嫔妃,按地位高低逐级加减。

生孩子,孩子满月时也会有红包。

因为“员工”数量众多,皇上又很少“裁员”,因此皇宫里仅是后妃们“工资”的支出,就已经是个非常庞大的数字。

在这些妃子的等级中,答应的地位最低,而且其地位仅次于宫女。住房方面,至于嫔以上才有自己的专房。无论时衣食住行,不同等级之间差距非常大,这也大概是为什么很多妃子不择手段要往上爬的原因吧

https://kknews.cc/zh-sg/history/eoz2byy.html

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Beef Wellington

Cooking For Fun

It just came to me that there was still a piece of beef fillet in my fridge last night, so I decided to cook beef wellington today.

Main Ingredients:

beef, chopped shiitake mushroom & carrot (of course you can use the help of a blender), puff crust, salt, and pepper.

1, Sprinkle salt and pepper over the fillet. Rub a bit with hands.

2, Heat a pan, add in some oil. Fry beef fillet till each side turns brownish.

3, Beef fillet in a plate and rest for a while. Use the same pan to fry mushroom and carrot. When the juice comes out, drizzle in a little red wine. (I just want to add a little flavor, if you don’t have red wine, you can just skip this step.) Add in a little dried thyme. Turn to low heat and simmer for a little while. Season with salt.

4…

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Maths Tuition Blog

We have revamped our Maths Tuition Blog at: https://mathtuition88.blogspot.com/.

It now features a “sticky” Home Page that showcases some useful JavaScript Apps. We have also increased the font size for easier reading.

For instance, our most popular App is the App to calculate JC Ranking Points: https://mathtuition88.blogspot.com/2015/03/calculate-uas-points.html.

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Nalgene Bottle Singapore

Since Singapore is such a hot country, it is important for students and adults to keep hydrated to avoid heatstroke. One of the most popular and best brands of water bottles is Nalgene, which is made in the USA.

It is BPA free, which is very important to avoid drinking toxic plastic particles that may leach into your water. (I think by now Singaporeans know it is not good to reuse Coca Cola bottles as your water bottle; 10 years ago it was very common to do that.)

It is quite hard to find Nalgene bottles in supermarkets. NTUC Fairprice, Giant does not seem to carry them in their stock.

Interested buyers may purchase Nalgene bottles from Qoo10 (see image link below). Do choose this store as it has many positive reviews, it has an actual store in Pasir Ris, but buying online would be much more convenient.

[S$12.00](▼74%)[GHSGIFTS]Nalgene Water Bottle / WIDENARROW mouth/BPA Free / Small water Bottle – 500ml / 1000ml / 1500ml

WWW.QOO10.SG


For our international readers, Nalgene is also available on Amazon:


Nalgene Wide Mouth Bottle – 32 oz., Clear w/ White Cap

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Students about to major in Biology / Lifescience, read this first

Many countries (including Singapore) promote Biology/Lifescience as a very good major with plenty of jobs after graduation. However, students may want to read some opinions from multiple sources to get a balanced viewpoint.

According to most of the answers, it is recommended that students truly love biology to pursue it in university. Also, many answers comment that a Bachelor Degree is usually insufficient for a good job in Biology/Life Science, and even people with advanced degrees can face problems finding relevant jobs.

Quora: https://www.quora.com/I-want-to-major-in-biology-Can-I-get-a-brutally-honest-opinion-on-this-major

You asked so I will give you an honest answer. I am a 64y old career biologist. I can speak freely. I could not with a clear conscience recommend biology as a career. It might sober you up that I got tenure one month after I turned 60y old. I am not being a snob. I am a first generation graduate. I do admit I have had a long and interesting career but at the cost of no wife, no children, no family and no job security before becoming too old for such domestic things.

  • One of the answers at Quora
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Corn Soup

Cooking For Fun

1. Cut all the kernels from a fresh corn.

2. Put corn in a pot. Add in 1/2 cup milk. Bring to boil then turn to low heat and simmer till corn is cooked.

3. Pour all the corn with milk into a blender. Blend till smooth.

4. Pour back to pot. Turn to low heat. Keep stirring while heating. Bring soup to boil again.

5. Season with salt and pepper.

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What is 20+C+M+B+19? (Epiphany)

This looks like a Math question, actually it is an Epiphany tradition called Chalking the door.

20 and 19 stands for the year 2019. C, M, B stands for the names of the three magi, CasparMelchior and Balthasar. The plus sign is actually a symbol for the cross †.

Some variations also put “20*C+M+B+19”, where the star stands for the star of Bethlehem.

CMB can also be the abbreviated form of the Latin blessing “Christus mansionem benedicat“, which means, “May Christ bless this house”.

The LaTeX code for it can be:

20\dagger C\dagger M \dagger B\dagger 19

\displaystyle\Huge\boxed{20\dagger C\dagger M \dagger B\dagger 19}

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Korea’s Education System

Check out this interesting video highlighting Korea’s academic system. Seems at least thrice as stressful as Singapore, no? Recently, I do see quite a few Koreans studying in Singapore, possibly to them it is less stressful in Singapore compared to Korea.

One comment in the video summarized it: “How sad, all that for a spot in university that isn’t ranked high internationally, an average job with average pay and a crappy personal life that barely exists.”

Video features:

  • Hagwons (Korea tuition centres)
  • Superstar Tutors
  • Plastic Surgery
  • University Admissions
  • Alternative New Schools in Korea

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Official Website: Migrating to New Zealand from Singapore

Source: https://www.newzealandnow.govt.nz/why-choose-nz/compare-new-zealand/singapore

New Zealand Government has set up an official website targeting Singaporeans to migrate to New Zealand. Check out the website here.

Natural environment wise, New Zealand is fantastic, with great landscapes and low population density. Due to its faraway proximity and buffer in the form of Australia, it is the least likely country to be affected in World Wars.

Only potential downsides are natural disasters (earthquakes), and possible employment difficulties. I have heard anecdotal stories about people migrating to Canada (another low population density country) and then having a hard time finding jobs.

 

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Centrum Vitamin Review

I used to think that with a balanced diet, there is no need to take vitamins. However, recently I read several articles that due to soil depletion, there is lack of minerals in the soil that is used to plant the crops. According to the Bible, the soil is supposed to rest every 7 years for the Sabbath, but I doubt many countries practice this as it will lead to total loss of income for that year.

By the way, Northern China has a type of rice called Dong Bei Rice that is considered one of the best type of rice, certainly superior to Thai rice. I have tasted Dong Bei Rice in Liaoning Province, it is absolutely delicious. The reason it is so good is because due to the harsh winter, the soil there is forced to rest once a year during the winter. Hence, the soil is rich in minerals.

As a result of soil depletion, the plants that you eat may lack certain trace minerals like Magnesium, Molybdenum, Zinc, etc. The animals (cow/pig/lamb) eat plants that lack the minerals, hence the animals themselves lack the mineral too. Basically, the entire food chain, including humans, lack the mineral. Magnesium deficiency is especially serious, even in 1st world countries like America, 57% of the US population lack Magnesium.

Centrum Men’s and Women’s Vitamin Review

Centrum is the number one selling vitamin in the US. And it is very affordable. For its price range, it is probably the best multivitamin. There are two types for Men and Women. (Women need more iron due to the monthly loss of blood; Men need less iron. There are some other differences too, like Men need more Zinc.)

After just one day, I can feel the difference, more energetic and alert. My wife feels it too, and also experienced less hair dropping. Possibly people in Singapore and 1st world countries do not need to eat it everyday, since our diet is relatively nutritious (but still lacking certain minerals due to soil depletion). One can eat it every other day, or up to your own schedule.

Amazon sells it quite cheaply (different packaging from the Singapore version):


Centrum Men (250 Count) Multivitamin / Multimineral Supplement Tablet, Vitamin D3


Centrum Women (250 Count) Multivitamin / Multimineral Supplement Tablet, Vitamin D3

For faster delivery in Singapore, one can purchase in Qoo10:

[S$23.90](▼53%)[Centrum]★Centrum★ 40% OFF SALE! Silver / MultiVitamin / MultiMineral Supplement For Adults / Women / Men

WWW.QOO10.SG

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How to Study in Extreme Noisy Environment (+ Math of Decibel System)

Singapore Maths Tuition

[S$54.90][3M][STOCK IN SG] 3M Peltor H10A Optime 105 Earmuff Ear Muff Ear Protection Head Set. Noise Reduction Rating of 30dB

WWW.QOO10.SG

The exams are coming, but your neighbor decides to do a major renovation? Neighbor has loud music blasting/ very noisy children? An urgent and drastic measure must be taken, as scientific research has shown that loud background noises reduce children’s test scores!  Recent research in London (UK) has shown that high levels of environmental noise outside schools reduce children’s scores in standardised nationwide academic tests.

This is hardly surprising, as it is very hard to do any studying in the presence of very loud noises. The source of noises, in Singapore context, may come from the following:

  • Neighbor’s heavy renovation (Drilling, Hammering, etc.) Singaporeans are big fans of renovation and like to renovate their houses every couple of years! Unfortunately, as long as the neighbors stay within the…

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Probably the Best Yong Tau Foo I’ve Ever Had

Cooking For Fun

Yong Tau Foo is a Hakka Chinese cuisine. Yet, I have never tried it in China before. Yong Tau Foo stall is quite similar to Chinese spicy hot pot (malatang). All the meat, vegetables and seafood are displayed on shelves. Customers can choose whatever they want to add in their Yong Tau Foo. The main difference I guess lies in cooking method. Malatang (麻辣烫) includes 3 Chinese words. 麻 (ma)means numb, it refers to the feeling caused by pungent spices like Sichuan pepper corn. 辣(la)means spicy, it refers to chili, chili powder and chili oil. 烫(tang)means hot. Because malatang is always served very hot. I still remember when I had social linguistic class, my teacher taught us malatang could be translated as “3 hots”: hot, hot, hot. 🙂

I have tried Yong Tau Foo several times after I came here. Since I really missed malatang and I couldn’t find it…

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import matplotlib on PyCharm: Quick 3 min solution

Students trying to import the package “matplotlib” on PyCharm will soon face the cryptic error message: “Python is not installed as a framework. The Mac OS X backend will not be able to function correctly if Python is not installed as a framework.”

It is extremely puzzling what to do. I have researched the steps that you can follow to solve it in 3 minutes:

First you need to install the “matplotlib” on PyCharm following the instructions here: https://stackoverflow.com/questions/21883768/pycharm-and-external-libraries

Then, to import matplotlib, you need the following lines:

import matplotlib as mpl
mpl.use('TkAgg')
import matplotlib.pyplot as plt

Done! You are ready to use matplotlib on PyCharm interpreter, by using:

plt.plot(...)
plt.show()
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Steak & Portobello Mushroom

Cooking For Fun

This is the first time for me to cook Portobello mushroom. They are really big and look like a giant brown umbrella.

For steak:

1. Season both sides with salt and black pepper.

2. Heat a pan. A little oil in. Sear the steak for about 3 mins.

3. Flip the steak over. Cut in a cube of butter. And add in 2 cloves of garlic and dried thyme (fresh thyme will be better, but I didn’t have any at that time).

4. Fry for about 3 mins. Use a spoon, to scoop better and spread over steak. Sear the edge side too.

Steak in the plate and rest.

To cook Portobello mushroom:

Remove the Portobello mushroom’s stem first and wash clean.

1. Heat a pan. Cut in a small cube of butter.

2. When butter melts, add the mushroom in with cap side down. Sear for 3 mins. If…

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Cod Fish Fillet

Cooking For Fun

My husband loves fish, especially fish from the deep sea. We often buy salmon. We don’t buy cod fish that often. Last time when we went out shopping for groceries, he saw the frozen cod fish fillet. He asked if he could buy some. I was a bit hesitant because I didn’t cook cod that much. He told me just to cook it in the same way of cooking salmon. OK, then. My husband always tells me to cook seafood in a simple way with less condiments, even though he almost never cooks.

As he said, I just pretend I am cooking a salmon fillet.

1. Season cod fillet with salt and pepper.

2. Heat a pan, drizzle in a little oil. When pan is hot, place cod fillet in.

3. Sear the cod fillet for 3-4 mins. Then flip over. Sear for another 3-4 mins. I also added in…

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