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.

URL: https://getlantern.org/

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.

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.

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: www.facebook.com/liupam

2018 Fields Medallists

URL: https://www.quantamagazine.org/tag/2018-fields-medal-and-nevanlinna-prize-winners/

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.

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.

Source: https://www.nbcnews.com/health/health-news/parasite-cat-poop-could-be-reducing-our-fear-failure-study-n894221

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.

The 17 best universities in the world to study math

Source: https://www.businessinsider.com/the-17-best-universities-in-the-world-to-study-math-2018-7/?IR=T/#17-kyoto-university-japan-2189-1

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

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

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

Source: https://www.futurity.org/approximate-number-system-math-1819602-2/

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.

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

Gov.sg 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

Chinese Tuition HCL O Level

Chinese Tuition Singapore
新加坡华文补习老师
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.

Contact:

HP: 8339 6353

Email: chinesetuition88@gmail.com

Website : https://chinesetuition88.com/
(Preferably looking for students staying in the West side of Singapore)

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.

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.

Hello!

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!

Regards,
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.)

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

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.

Read more at https://www.channelnewsasia.com/news/cnainsider/schizophrenia-imh-sim-kah-lim-artist-singapore-mental-health-10530970

Sim Kah Lim 2019 Update

Found 2 more excellent updated videos on Mr Sim Kah Lim, the artist:

This video also features Mr Sim Kah Lim and his sister Cindy (including two other guests). Very enlightening interview.

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

Source: https://sg.style.yahoo.com/went-elite-school-privileged-024122633.html

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.

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)

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

Results:

Joint 1st: Hong Kong and Singapore (108)

2nd: South Korea (106)

Joint 3rd: Japan and China (105)

Source: https://iq-research.info/en/average-iq-by-country

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.

Source: https://www.forbes.com/sites/kionasmith/2018/06/30/sundays-google-doodle-celebrates-mathematician-gottfried-wilhelm-leibniz/#3d748c371398

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.

Quote:

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.

Singapore universities should look beyond international rankings: Panel

Singapore universities should look beyond international rankings: Panel
Read more at https://www.channelnewsasia.com/news/singapore/singapore-universities-should-look-beyond-international-rankings-10484568.


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.

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

Carbon Dioxide Levels in Closed Bedroom (Students should read this)

Just read this article by a researcher at MIT. Students and parents especially should read this as it affects cognition and alertness levels. Students in Singapore typically have preciously little time (usually less than 8 hours) to sleep, hence the quality of sleep is very important.

Basically to summarize, sleeping in a closed bedroom (without ventilation, with windows and door closed) leads to high carbon dioxide levels that can possibly affect the brain in negative ways (decreased cognitive function). Switching on air conditioner should be fine as essentially fresh air is introduced from the outside.

The solution can be as easy as opening the door/window. Open window is said to be better than open door. However in Singapore, light pollution is another potential problem, most likely there is some form of light shining through the window at night. Singapore’s doors and windows are not as airtight as those in winter countries, but it seems there is still some cause for concern.

A scientific paper for those who want to read in greater detail: https://onlinelibrary.wiley.com/doi/pdf/10.1111/ina.12254.

Korg G1 Air Digital Piano Review

I was searching for digital piano brands when I stumbled upon the Korg G1 Air. Korg is relatively unknown compared to Yamaha/Kawai etc, but it makes excellent digital pianos. Do check out the video above, it features Fantaisie-Impromptu by Chopin, one of my favorite piano pieces.

According to many reviews (see AZ Piano Reviews, Pianodreamers), Korg G1 Air is one of the best digital pianos in its price range. I went to the showroom and tested it out, it is indeed good. The weighted keys do feel like an actual acoustic piano. Touch of keys is very important for classical pianists. The 3 piano sounds are supposedly sampled from Steinway, Bosendorfer and Yamaha respectively. It also has bluetooth audio, so you can stream your music from your phone through the piano’s speaker systems.

The price is surprisingly affordable too, it is around S$1800 (Singapore dollars). According to many reviews online, it is equal or better than many other digital pianos in a much higher price range! I do agree, I have tried Yamaha’s Clavinova (higher priced than Korg G1), the Korg does not lose out to it in terms of sound and touch. Korg is fully made in Japan. Richard Clayderman endorses the Korg digital pianos:

There is another even cheaper model Korg C1 Air (priced at around S$1400), which many also say that it is quite good.

International buyers may want to check the Korg G1 out on Amazon:


Korg G1 AIR Digital Piano Black

For Singapore, the Korg G1 is available on Qoo10: Korg G1 Air. (comes with bench and headphone)

I think in Singapore especially, having a digital piano is a good idea if you want to practice at night (e.g. after 10pm) without disturbing the neighbors. Its design is quite space-saving too, it can fit into the smallest of homes without any problem.

Experts suspect ancient Stonehenge was built using the Pythagorean theorem

Interesting news. It seems that the ancient builders are wiser and more mathematically advanced than previously thought.

Source: Aleteia

A new book suggests that the Neolithic builders of these ancient monuments were more learned than previously thought.

At every great ancient monument visitors often marvel at the ingenuity of our early ancestors. The most common question when it comes to Stonehenge is how they raised such large pillars without modern tools. Those with engineering know-how, however, may ponder the precision of design achieved by its Neolithic builders.

A new book, Megalith, suggests that the builders of Stonehenge and other such Neolithic sites may have known more about construction than we ever could have guessed. In Megalith, Robin Heath, a megalithic expert, claims that the presence of Pythagorean triangles found in the sites are evidence that these builders had discovered the Pythagorean theorem 2,000 years before the birth of Pythagoras.


Megalith: Studies in Stone

What is it like to study at Raffles Junior College?

Quora: https://www.quora.com/What-is-it-like-to-study-at-Raffles-Junior-College

Quite a few interesting answers can be found there. It is highly recommended that students read it before choosing to study at Raffles Junior College.

Also check out: Which JC is the best in Singapore?

Selected Quotes:

  1. “Not pleasant,” would be my answer.Like some other posters, I wasn’t from the Raffles family in any capacity before JC, though I had a few (distant) friends who were Rafflesians. Being in the GEP also served as an insulating factor- gifted kids hung out with other gifted kids, and mainstream kids saw us as aloof. It was a self-fulfilling prophecy that turned itself into a vicious cycle, like a snake swallowing its own tail. Singapore society tends to be stratified like that.So when I got there, there was no in-built friend base waiting for me as a safety net. JC was a pretty shallow place, as far as I can remember.
  2. Honestly? Nothing special.Resources aside (or perhaps more importantly, even with the Resources), Raffles is very much a stereotypical high school. Even though students are touted as the “cream of the cream” in a detestably common turn of phrase or the “top 3% of Singapore“, and everyone probably achieved above 265/300 in their examinations at the age of 12, or topped their secondary schools…it doesn’t mean that everyone is a genius, or a notoriously self-disciplined hard worker. In the words of Mean Girls, there are “preps, jocks, Asian nerds, cool Asians, varsity jocks…” so on and so forth. Everyone’s human, and no one’s flawless. I expected cutthroat competition at every turn, and impossibly well-put-together teenagers, but I’m glad I was wrong.
  3. Academic Rigour
    The archetypal RJC student will not score above D in common tests right up to prelims – but, come A levels, he/she will score straight As. It will be drilled into you for 2 years that you only possess a modicum on intelligence. You get frustrated, then you study hard and you study smart. When you get your result slip, your first instinct would be to walk up to your GP teacher and tell her,”You told me for 2 years straight I wouldn’t make it in life with my current grades. I got all As… including GP. Take that lah.”  Then she knowingly smiles and congratulates you, like that was part of the plan all along. That’s how ‘cutthroat’ the teachers in RJC are.
  4. Leader. Leadership is emphasized and celebrated in the institution. Student leaders are mostly hand-picked by peers and are then trained by the school to hone their leadership skills. Based on high levels of self-motivation, these leaders end up organizing events that demand a high level of coordination and huge amounts of time and effort. They provide tremendous inspiration to their juniors, especially those aspiring to be student leaders as well.

Chinese Tutor (has experience in tutoring NYGH/RGS/RI students)

Chinese Tuition Singapore
新加坡华文补习老师
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 Girls’ High (NYGH), RGS, RI, and other schools.

Contact:

Email: chinesetuition88@gmail.com

Website : https://chinesetuition88.com/
(Preferably looking for students staying in the West side of Singapore)

1 Million Views (Education and Math Website)

Thank you all readers of mathtuition88.com!

Mathtuition88.com has achieved 1 million views (currently 1,002,090 views)!

I find that the Pareto principle is quite true, even for blog views. The Pareto principle states that roughly 80% of the effects come from 20% of the causes.

For 2017, Mathtuition88.com had 267,859 views. The top 10 posts (out of around 2000 posts) alone accounted for 136,587 views, or around 50% of the views!

Check out the below catchy song about “1 Million”:

Various Benefits of Math Tutor

If you feel that your little child is spending more time watching TV or other electronic gaming devices, then you have a number of reasons to find something interesting and exciting over the next few lines. As the child starts going to school, he or she will have to spend some time doing the home tasks or learning what has been taught in the school. While it is applicable to all subjects, there are reasons to believe that math is a subject in which many students struggle a lot. You could even think of putting your child into the neighborhood tuition center to brush up his or her knowledge of math.

While there are reasons to believe that such tuition centers may not be the best thing going forward though it could help the skill sets of the child to a certain extent. It will not be long before you find that boredom creeping into the child. Should that happen it is just a matter of time before he or she starts developing a hatred for subject and once this happens things could be very difficult to mend and put back on track. Hence, as parents we need to find out a more interesting and enticing way in which math can be taught to the students. It is here that have a math tutor app perhaps could be useful in more ways than one. There are obviously a number of advantages and benefits and we will look at a few of them over the next few lines. Experts in teaching methods and child psychology believe that this could be the way forward and therefore as parents you must know something more about it.

They Are Very Convenient

 In today’s world where time could be a constraint for many, having these math tutors could be convenient both for you as a parent and also for the child. Instead of putting your child in the math tuition center and perhaps waiting outside as the child goes through the grind, would it not be better to use this tutor app and teach what the child wants. It is fun to learn while on the move and this is what makes it quite different from other options.

They Support Better Engagement

 While some students love doing math, there are others who are not very favorably inclined towards the subject. We also have many children who outright detest being with math subject and they are allergic to it. In such cases when you spend some time and choose the right app for math you can be sure that you will be giving them something which they will be happy with and something which will help them to be more engaged and interested in the subject.

Immediate Feedback Is Possible

 Getting the right instruction and feedback as the child learns is something which makes it much more engaging and interesting for the child. There is no denying the fact that when you choose the right math apps you will be in a position to get immediate and meaningful feedback which will be helpful in more ways than one.

It Has A Rewarding And Points System

When you choose an app based tutoring and learning system, you can be sure that it will come with some of the best rewarding and points systems and this certainly makes it very interesting and exciting for children. This is often referred to as massaging the ego of the child and psychologically it has been found out to be extremely interesting for the children who have a special dislike and allergy towards math. This positive reinforcement will certainly encourage students to find quite a bit of interest towards math and even those who are allergic to the subject will certainly fall in line over a period of time.

Portability Is A Big Advantage

 Since many parents and their wards are always on the move it is quite possible that you may not have time to teach their wards in their homes. Hence, having a math app for tutoring could be the best solutions for teaching the children while on the move. The app is something which can be downloaded on your computer and then you can start teaching your child even when you are traveling in a car or any other means of transport.

Improve Your Grades to Perfection: 5 Benefits of a College GPA Calculator

Improve Your Grades to Perfection: 5 Benefits of a College GPA Calculator

If you’re hoping to improve your grades, you can do this by using a college GPA calculator. There are a few different ways to do this. This can leave you with a handful of benefits and help you out with your college success. Let’s look at a few of the benefits that you can get from using a GPA calculator.

1.   You Always Know Your Results

When you use a GPA calculator, you will be able to figure out your expected GPA at all times. You won’t need to wait until the end of the semester to calculate your academic standing. You also won’t have to get in touch with your professor or advisor in order to check in on your grades.

This can be helpful in making sure that you are able to stay in your selected program as some majors have GPA requirements. Additionally, you will know if you need to raise your grade at all. It’s better to be aware of your GPA before it’s too late to make a change in your study habits.

2.   You Can Calculate the Final Grade

You can use a GPA calculator to determine your final grade. This is helpful at all points in the semester so that you can see how you’re doing. This can be applied to multiple classes so you can see your overall GPA too.

As mentioned before, it’s important to know exactly where you stand as you move through the semester. If there is a problem with your grades or your GPA, you should resolve these issues immediately.

Calculating your final grade will show you whether or not you need to seek out a tutor or get additional help. This can give a peace of mind if you are a little bit worried as well.

3.   You Don’t Have to Calculate the Grade by Yourself

There are formulas for calculating your GPA or grade on your own. These work, of course, but they can be time-consuming. It’s much easier to plug the information into a GPA calculator.

If you’re not skilled at math or get lost easily, even simple formulas can be confusing. This can be frustrating and can cause minor errors. In addition, you will be less likely to make a mistake by using a calculator. We can all mess up while working out formulas by hand.

A GPA calculator can save you time and energy! Plus, the results will be instant.

4.   You Can Get Help with Your Grades

If you decide to use a GPA calculator, you will be able to see your GPA right away. You will also be able to calculate it and view it at any time. You don’t have to wait until the end of the semester.

By calculating your GPA, you can see if you will need any help with your grades. If you notice that one of your grades is bringing your GPA down, you can get help.

Some universities have tutoring centers where you can get free study help. You can also meet with your professor to go over any confusing content. Making these efforts to raise your grades can be effective long-term!

5.   GPA Calculators Are Easy to Use

GPA calculators have very straightforward directions. Nearly anyone can figure out how to use them. They are definitely easier to use than formulas!

There are also countless GPA calculators that you can use online, so you should be able to access them. You don’t have to spend a lot of time searching for them.

As you can see, there are plenty of easy ways to raise your grade by using a GPA calculator. Take a few minutes to figure out your GPA before it’s too late to get help and get better grades in your classes!

The GPA Calculator: What? Why? How?

The GPA Calculator: What? Why? How?

As a student, having a high GPA (grade point average) is pretty important. It’s based on a student’s letter grade and the number of credit hours each course is. The final answer is the GPA, which has a lot of weight tied to it. A high or low GPA can be very meaningful to a student’s status at a university.

What Is a GPA?

Many colleges will not allow students to be at their school if they do not maintain a high enough GPA. Certain majors require a specific GPA in order to be a part of that program. This can be scary for a student who doesn’t know exactly what their GPA is.

Why Do We Need to Know the GPA?

If a student is not keeping track of their GPA, they could be falling behind without even noticing it. This could lead to the student being removed from their program or being dismissed from the college. This is why students must be monitoring their GPA at all times. If a student isn’t aware of how low their GPA is, they could suffer the consequences.

How to Calculate the GPA?

Students can take advantage of a GPA calculator as they work through their courses. A GPA calculator allows students to plug in their grades and the number of credit hours for each course. The calculator then gives them their GPA. There are many different GPA calculators available online.

These GPA calculators are essential for students. They help students to keep track of their GPA before the end of the semester. When students monitor their GPA, they can see how their GPA might turn out at the end of the semester. This can show the student if they might need additional help in certain subjects in order to bring their GPA up.

Many colleges will have an online system set up where students can view their grades and their GPA. This usually isn’t updated throughout the semester though. It’s only changed at the end of the term. While it’s useful to see a GPA at the end of the semester, it’s better to know what it is earlier than that. Students can actually make a change when it counts if they know what their GPA is as they progress.

If students use GPA calculators, they can see their current grades. This can show them if they are doing enough or not. It can also help them see If they can keep putting in the same efforts that they have been and maintain a good academic standing. Some students will need to seek out tutoring or additional assistance from a professor if they are concerned about their GPA.

What Are the Benefits?

Aside from being able to stay in the school or the particular program, students can also receive scholarships for high GPAs. If a student knows what their GPA is, they can be applying for additional scholarships. Keep in mind that a low GPA can mean losing a scholarship that has already been received.

As students move through college, they need to be knowledgeable about the GPA requirements for their university, major, any scholarships, and financial aid they might be receiving. GPA calculators are a quick and easy way to check on a GPA at any time.

By knowing their GPA, students can seek out additional help or try to raise their grades. Raising their marks would then increase their final grade, which is the goal. It’s important for students to know what’s going on with their GPA and academic standing at all times! This will help them to be the most successful that they can be throughout their college career!

Should PSLE be Scrapped? 四不能除

According to this article by Channel News Asia, there are four “constraints” for why the PSLE cannot be scrapped. I call it the “四不能除“, named after a saying “四不能战” regarding a general Feng Zicai which I recently learnt about after watching the movie “The War Of Loong“.

  1. Compromise education standards;
  2. Hamper students’ preparation for the future economy;
  3. Unduly increase levels of stress and competition; or
  4. Unnecessarily disrupt the system

It is quite logical actually, I encourage readers to read the article, which is written by a student yet to enter university.

Point 1 and 2 are sort of self-explanatory; just think realistically how many kids will study hard if there is no PSLE exam? Even if there is an internal school exam, if its importance is not high, it may not cause students to study.

Point 3 needs some explanation on why scrapping the PSLE may actually increase stress:

Earlier this year, during the Ministry of Education’s Committee of Supply debate, then- Minister for Education (Schools) Ng Chee Meng remarked that “removing the PSLE and having a through train will only transfer the stress on parents and students elsewhere, such as at the P1 registration”.

He also emphasised that “it will make the O-Level and N-Level exams most stressful – a single exam in the whole career of a child’s life.”

Basically, if PSLE were to be scrapped, the focus and stress will be shifted to P1 registration and O Levels. P1 registration is based on where you stay and your parent’s alumni, in this respect PSLE is actually fairer and more meritocratic as it is based more on the child’s academic ability.

Nonetheless, despite the four reasons not to scrap PSLE, one thing that strikes me is the example of Finland. Despite Finland having no exams until the age of 16, it is well known that Finland’s education system is top in the world. There must be some secret to Finland’s education system, but the question is whether it can work and be applicable to other countries.

General Feng Zicai actually said something that is very wise and applicable to PSLE: “光绪二十九年(1903年)临终前,冯子材为子孙留下遗训:“读书不求官,服官不要钱,违者不孝。” (http://www.qzlz.gov.cn/Item/251.aspx)

Translated: “The main goal for studying is not for becoming an official; Becoming an official is not for gaining money for oneself; Whoever disobeys is unfilial (he said this to his descendants).”


Also read our previous post on PSLE:

Free Water Saving Kit (Singapore)

I believe this is not new, but it is the first time I heard of it. Anyway, it is free, so do feel free to request for a sample at the PUB Official Website.


PUB has revamped the packaging of its popular water saving kits featuring its mascot Water Wally. A set of thimbles with three and four holes allows residents to have greater flexibility in regulating their tap’s and showerhead’s flow rates. Water Wally stickers with specific messages are also included in the kit to act as reminders of good water saving habits in homes. ​

URL: https://www.pub.gov.sg/savewater/requestforwatersavingkit

So You Want To Be a Doctor?

This workshop should be useful to students aiming to be a medical doctor. (Note the ticket prices, this event requires ticket for admission.)


Interested students may also check out our previous blog post on BMAT Book Recommendations for NTU Medicine.


Source: https://www.facebook.com/events/1714853475261989/

Date: 21 July 2018 (Saturday)
Time: 9:30am to 12:30pm (F&B at tea break)
Venue: NUS Shaw Foundation Alumni House, 11 Kent Ridge Drive, Singapore 119244

Calling all IP, JC, polytechnic and university students!

Join us at So You Want To Be a Doctor?, a half-day medical seminar on Saturday, 21 July 2018, from 9:30am to 12:30pm, featuring panel discussions, inspiring keynotes and networking opportunities.

Our seminar provides a unique opportunity for prospective medical students to hear from clinical professors, network with doctors who’ve gone onto diverse careers, and learn about the many job options available in healthcare.

This seminar is targeted at IP, JC, polytechnic and university students, as well as anyone interested in pursuing careers in healthcare, such as biomedical research, allied health, entrepreneurship, technology in medicine, public health and humanitarian projects.

So You Want To Be a Doctor? covers topics such as:
– How will doctors practice in the future?
– Is medicine for me?
– Is clinical research for me?
– The path less wandered: A chat with Dr. Benjamin Seet

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Agenda
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09:30 AM: Keynote – “How will doctors practice in the future?”
Professor Wong Tien Yin, Medical Director, Singapore National Eye Centre

09:50 AM: Panel #1 – “Is medicine for me?”
Assistant Professor Isaac Liu Desheng, National University of Singapore
Dr. Tiah Ling, Emergency Medicine Physician, Changi General Hospital
Dr. Kumaran Rasappan, Senior Orthopedic Surgical Resident, Tan Tock Seng Hospital

10:30 AM: Panel #2 – “Is clinical research for me?”
Assistant Professor Swaine Chen, National University of Singapore
Assistant Professor Chester Drum, National University of Singapore

11:10 AM: Tea break

11:40 AM: The path less wandered: A chat with Dr. Benjamin Seet
Dr. Benjamin Seet, Executive Director, Biomedical Research Council, Agency for Science, Technology and Research

12:20 PM: Closing note

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Speakers
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Professor Wong Tien Yin (keynote talk)

Prof. Wong Tien Yin is medical director of the Singapore National Eye Centre (SNEC). He is also deputy group CEO (Research & Education) of SingHealth and academic chair of the Ophthalmology and Visual Sciences Academic Clinical Programme at Duke-NUS Medical School. Prof. Wong completed medical school at the National University of Singapore as a 1987 President’s Scholar. He studied on fellowships at the University of Wisconsin-Madison, US, and the University of Sydney, Australia. He obtained his MPH and PhD degrees from the Johns Hopkins University, US.

Dr. Benjamin Seet (keynote talk)

Dr. Benjamin Seet is executive director of the Biomedical Research Council (BMRC) at the Agency for Science, Technology and Research (A*STAR). Prior to joining A*STAR, he served as chief medical officer of the United Nations (UN) Department of Peacekeeping Operations in New York. He oversaw medical support for UN personnel in 16 post-conflict countries. Dr. Seet also served with the Singapore Armed Forces (SAF) for more than 20 years before retiring as chief of the SAF Medical Corps at the rank of Brigadier-General.

Assistant Professor Isaac Liu Desheng (panel #1)

Asst. Prof. Isaac Liu Desheng is a pediatric nephrologist who specializes in dialysis and renal transplantation. In addition to his research on kidney disease, Asst. Prof. Liu is the chief doctor of the Shaw-National Kidney Foundation Children’s Kidney Centre Annual Camp. He is currently an assistant professor (clinician investigator) at the Yong Loo Lin School of Medicine. For his achievements, he was awarded the 2017 Singapore Youth Award, the nation’s highest accolade for youth.

Dr. Tiah Ling (panel #1)

Dr. Tiah Ling is an emergency medical physician consultant in the accident and emergency department at Changi General Hospital. Prior to joining Changi General Hospital, Dr. Tiah participated in the METASHARP project, where she provided technical support, monitoring and evaluation of health facilities in Afghanistan. In 2009, she spent three months in Ghana as a program coordinator in the ‘Systems Improvement at District Hospitals and Regional Training of Emergency Care’ program (sidHARTe). Dr. Tiah received her Masters in Public Health (MPH) degree from the Johns Hopkins University, US.

Dr. Kumaran Rasappan (panel #1)

Dr. Kumaran Rasappan is a senior orthopedic surgical resident with Tan Tock Seng Hospital. In 2012, he became the first Singaporean to scale the summit of Mount Everest for a charitable cause, raising over S$40,000 for needy patients. Since then, Dr. Kumaran has scaled the heights of K2 and Makalu, the second and fifth highest peaks in the world respectively, in an effort to raise funds for the Home Nursing Foundation’s program which aims to address the psycho-social and emotional needs of caregivers. His fundraising effort is titled “No Mountain Too High.”

Assistant Professor Swaine Chen (panel #2)

Asst. Prof. Swaine Chen is an assistant professor of medicine at the National University of Singapore and a senior research scientist at the Genome Institute of Singapore. His research interests include the application of genomics to understanding molecular mechanisms of urinary tract infection, particularly those caused by Escherichia coli. He received a Bachelor’s degree in chemistry and mathematics from Harvard University, US, and an MD-PhD degree from the Stanford University School of Medicine, US.

Assistant Professor Chester Drum (panel #2)

Asst. Prof. Chester Drum is an assistant professor at the National University of Singapore, a consultant cardiologist at the National University Hospital and director of the Clinical Trial Innovation Lab at the Agency for Science, Technology and Research. He received his MD-PhD degree from the University of Chicago, US, and trained at the University of California, San Diego, US, and Harvard Medical School, US. Asst. Prof. Drum has over 20 years of clinical experience in managed care, private, public and academic healthcare settings and holds multiple patents.

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About the organizer
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Combining savvy communication with technical rigor, Wildtype Media Group is Asia’s leading STEM-focused media company, spanning digital, print, custom publishing and events.

Brands under Wildtype Media Group include the flagship Asian Scientist Magazine and Supercomputing Asia, award-winning titles available in print and online. Through its Asian Scientist Intelligence consulting division, Wildtype Media Group provides a full suite of marketing and communication services to industry and academic clients hoping to engage Asia.

Facebook page: https://www.facebook.com/events/1714853475261989/

Peatix page: https://doctalks.peatix.com/

Cultivating Confidence in Students to Excel Academically

Cultivating Confidence in Students to Excel Academically

Students who struggle academically may lack the self-confidence to continue to learn actively and get their point across during lesson. Educators have a huge influence on their students and hence there is an onus on them to instil confidence in the students and help them to feel confident enough to overcome any obstacles in their path to success despite any initial struggles.

When students possess more confidence in their ability, they will be more willing and ready to study and will put in more efforts to work harder as compared to when they doubt their academic ability due to struggles faced. Hence, self-confidence is extremely important in motivating students to excel academically.

Here are some tips that should be taught to students who struggle with their studies so as to provide them with a proper structure to follow when they are at a loss and also to enable them to regain confidence and guide them to the path of success. The tips can also be used by educators who use them to guide and encourage their students.

  1. Set the right goals

As students, be sure to set goals that are realistic and attainable and this is one way where you will be able to see growth and improvement as compared to setting an unrealistic goal that is too hard to reach. As educators, remember to guide your students in their goal settings and do not impose too high expectations on them, as it will only cause them to falter. Ensure that the goals are what the student wants to attain while also making sure that they are realistic. When learning is goal-oriented, there is more intrinsic motivation to be able to want to attain their goals and hence more confidence in pursuing the academics.

  1. Practice

Practice makes perfect and that is often the case. When studying for quantitative subjects like mathematics, remember that practice is the key to success! But of course you practice when you understand the concepts behind questions and not blindly do questions without any understanding. For more qualitative subjects, one way to practice is to come up with a skeletal / point form answer for the question so as to test your understanding of the subject. For educators, remember to remind your students to practice for topics that they are unfamiliar with in order to familiarise themselves with the chapter.

  1. Use visual aids

If long chunky words don’t interest you and deter you from studying, use visual aids to help you study better! Research has shown that students study better with visual aids such as mind maps and flow charts. So students, sketch those mind maps out to better understand difficult concepts! Similarly when teaching, it is better for educators to use visual aids which capture the attention of their students. Do not include large chunks of works on your notes and presentation slides when teaching, as such chunks deter students from reading and understanding the content.

  1. Seek help

When in doubt, do not hesitate to seek help! It is better to clarify a misunderstanding or something that you do not know at the start. Your teachers and tutors will definitely make themselves available whenever possible. Educators, do not chide your students who seek help from you and instead help them to the best of your abilities when they approach you with questions! Questions are a sign that one is learning.

  1. Do not be afraid to make mistakes

A Japanese proverb goes, “fall down seven times and get up eight”. The meaning behind this is to not be discouraged by any mistakes and failures as it is bound to happen. Remember to always pick yourself after making a mistake and that making mistakes are normal and fine as no one is perfect. Educators should always remind their students of this and be there for students to reach to when students face a failure or a mistake.

  1. Encourage

More for the educators, remember to be a source of encouragement to your students and constantly praise them for whatever progress or good work that has been done! If constructive feedback or criticism needs to be given, it might be better to do it when one on one with the student so that he or she does not feel embarrassed in front of the class. Research about people management has also shown that the “Sandwich Method” works best when one wants to give constructive feedback. How the “Sandwich Method” works is that you begin your feedback with something good as the bread before going into the criticisms and finally ending with encouragement again. These various layers form the “sandwich”.

  1. Enthusiasm

Enthusiasm is extremely important in facilitating interest and confidence in the subject. Try your best to be enthusiastic when learning and it really makes a difference rather than looking at the subject as one that is dreary and boring. The enthusiasm of the educators also matters as an enthusiastic teacher helps students to model after the teacher’s enthusiasm for the subject and hence gain confidence.

  1. Positive learning environment

Last but not least, a positive learning environment is extremely important! Find friends who are willing to help and not those who hate studying and form a study group! Such friends will definitely motivate you to work harder and can also be of aid when help is needed to understand a concept. For educator, a classroom that has a positive environment is one where students feel safe to express themselves and have the desire to learn. These develop confidence in the students.

Hopefully with all these tips, educators will be able to help students to cultivate confidence in order to excel academically and that students themselves will be able to orientate themselves into a structure, which enables them to gain confidence.

“Self-confidence is like a super power, once you believe in yourself, magic starts happening.”

Making Sense Chemistry Tuition instils confidence in students. To find out more about Making Sense Chemistry tuition, click here: https://www.makingsense-sg.com/free-trial/

Story of Yunhao Fu, 2-time IMO Perfect Scorer

Those who are acquainted with IMO (International Math Olympiad) would know that it is extremely tough to get a gold medal (in fact any medal at all) in the IMO. Fu Yunhao, from China, scored 42/42 perfect score twice in a row. His record can be viewed here. IMO’s difficulty varies from year to year. Fu Yunhao’s two attempts were during “difficult” years, hence he may be one of the best Math Olympians in the history.

However, his life story is quite unique in the sense that after his IMO triumph, things did not go quite smoothly. The below interview (unfortunately only in Chinese) describes it: http://news.ifeng.com/a/20180504/58096549_0.shtml.

Google Translate of interview: English Translation

Excerpt:

“The two-time Olympic champion” – although not accurate enough, it also summed up the highest achievements in the first 33 years of Fu Yunsheng’s life: he was the IMO (International Mathematical Olympiad) 2002 and 2003 two consecutive years of full-time gold medalist . In the 30-year history of the Chinese national team, only three players have achieved this result. IMO has the difficulty of being “relatively difficult” and “relatively simple.” Fu Yunyi is the only Chinese player who has competed for two “relatively difficult” matches. The Education Authority of China, Zhu Huawei, commented on Fu Yunxi: “He is a symbol of the Chinese mathematical community.”

To some extent, young people who are qualified to embark on the battlefield of IMO can represent the most outstanding mathematics mind of the generation. Professor Yakovlev, a former communications academy of the Soviet Academy of Sciences and a former chairman of the two-year IMO, made famous assertions: “Now the participating students will become the laborers who hold the golden key of knowledge and wisdom in the world 10 years later. they.”

Most of the IMO contestants will continue to engage in mathematics research in their adulthood. Among the 14 winners of the Fields Prize (recognized as the “Nobel Prize in mathematics”) since 2000, at least 8 of them have IMO’s record. But Fu Yunjun, the much-anticipated Olympic genius who once occupied the high point of IMO, unexpectedly disappeared in academia for the next fifteen years.

Some netizens came up with an old post titled “Fu Yunyi, First Class Cowman”, and asked for advice on the status quo of Fu Yunyi. Like igniting curiosity, those who have heard of their reputation have asked each other in the bottom: where is Fu Yunyi going?

(“Cowman” 牛人 means someone who is really good and excels in doing something.)

(Due to some translational errors, different spelling versions of Fu Yunhao’s name appear. They are all the same person, Fu Yunhao.)

However, the published interview does not reflect the full story. Fu himself posted a follow-up post here: http://news.ifeng.com/a/20180504/58096623_0.shtml. Basically, Fu argues that not following the traditional path of becoming a top mathematician does not mean that it is a failure; on the contrary his chosen path (lecturer at teacher’s college) benefits society by producing more good teachers to teach more students.

Google Translate of Fu’s follow-up post: English Translation

Excerpt: The third reaction: Incomprehension of the values ​​conveyed by the report. According to the author of the article, the point is: Excellent people are engaged in basic work and it is a very shameful thing. Those who have won the imo championship are, if nothing else, their journey must be the sea of ​​higher mathematics instead of teaching a group of “second normal school students” to teach junior high school mathematics knowledge. Two of the normal students who lectured said that the genius had fallen. Although I denied that I was a genius, I still thanked Wu for collecting my example of genius. He is very hardworking and commendable. However, the negative energy brought by his values ​​has forced me to vocalize. I didn’t speak for self-explanatory innocence. I just sang for the positive energy development. First of all, for the Wu students who wrote such values, I expressed my understanding that the author, as a senior student who has not completely taken the ivory tower, has such an idea that it is normal. In his cognitive system, academic research is the top grade, ordinary work is relatively low, and lectures are given to two normal students, and it is even closer to the center of the earth. If a once successful genius did not make achievements in heaven and earth, but lived aliciously, it was failure! In Wu’s report to me, this tendency was obvious during the interview. In an interview on April 1st, I even put forward an example of Mr. Zhang Yitang to mention him. At the same time, I mentioned that many researchers have strong academic abilities, but they always go the wrong way, and they have never been able to conquer their life. Want to overcome the problem, but they are still happy and fulfilling. Those things that I spent 10 days and a half wanting to understand may not be of great value, but how many are some interesting conclusions. Moreover, aside from the results of the research, the process of research itself is a happy thing. Although the author did not ignore this paragraph, I mentioned it slightly at the end of the article, but in his eyes, I would like to give this example in order to balance my talent from the genius champion to the teacher of the “Second Normal School” in front of the interviewer. Heart drop it. However, I do not have such a psychological gap. Young people experienced academic crackdowns, and there were some gaps during the very decadent period, but these have been resolved. For so many years of work and life, I learned that there is a vast world beyond the University’s ivory tower and there are so many things waiting for people to practice. If you have a halo above your head and you are in a high tower, you may be able to refer to the country and spur words, but only if your feet are implemented and everything is done well, you can accumulate less and contribute more to the community. Two of my teammates who were with me in 2003, two of them are still swimming in the sea of ​​mathematics, and the other three are involved in the financial industry, which I mentioned in the interview. Each of them did not regret his choice, nor did I.


If you are interested in Olympiad books, check out Recommended Maths Olympiad Books for Self Learning / Domain Test.

Book Review: Topology, James R. Munkres

Just updated the book review on Munkres’ Topology book.

mathtuition88's avatarMathtuition88

Topology (2nd Edition)

This book is the best introductory book on Topology, an upper undergraduate/graduate course taken in university. I have written a short book review on it.

Excerpt:

Book Review: Topology
Book’s Author: James R. Munkres
Title: Topology
Prentice Hall, Second Edition, 2000

It is often said that one must not judge a book by its cover. The book with a plain cover, simply titled “Topology”, is truly a rare gem and in a class of its own among Topology books.

One striking aspect of the book is that it is almost entirely self-contained. As stated in the preface, there are no formal subject matter prerequisites for studying most of the book. The author begins with a chapter on Set Theory and Logic which covers necessary concepts like DeMorgan’s laws, Countable and Uncountable Sets, and the Axiom of Choice.

The first part of the book is on General…

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Change traffic light rules to prevent further casualties (Singapore)

This petition is important to save future lives. The traffic rules should be machine controlled, i.e. clearly dictated by traffic lights whether to turn or not. In this way, there will be less error due to human judgement.

URL: https://www.change.org/p/land-transport-authority-change-traffic-light-rules-to-prevent-further-casualties-singapore

Quote: “Two accidents involving fatalities this week have prompted this petition. Roads have been widened significantly in recent years, with new lanes added and as such it is difficult to have field of vision of so many lanes, pedestrians, mobility devices, and fast moving oncoming cars all at once to make an informed and safe judgement.

Requesting LTA to determine if it is still safe to keep to discretionary turning on green given the growth in sizes of junctions (such as the Commonwealth Ave West/Clementi Road and Upper Bukit Timah/Jln Anak Bukit junctions) and to work on improving the safety of all road users.

Thank you”

School System Video (Do not make a fish climb trees)

Singapore is being mentioned around 4:54. Very nice video. The truth is that the classroom of today is still nearly the same as the classroom of 150 years ago. There needs to be a “Educational Revolution” parallel to that of the Industrial Revolution. Many children cannot fit into the single classroom model, leading to growth in diagnosis of behavioral “problems” such as ADHD in developed nations.

Americans who are tired of “Common Core” may want to check out Singapore Math for their kids, which is highly acclaimed in the educational realm.

11-year old math and chess prodigy in Singapore

Source: Channel News Asia

Aarushi Maheshwari solved the famous “Cheryl’s Birthday Problem” when she was only 9. She is also a chess champion and can play blindfold chess.

Watch the video below to learn more!

Also read our previous post on The Most Accomplished 10-Year-Old (Gifted pupil).

For those who want to learn more about Olympiad Math and International Chess, check out the previous two links. Math and Chess are two of the most intellectually challenging activities that can develop the intelligence of kids.

Basics of Partial Differential Equations Summary

PDE: Separation of Variables

1) Let u(x,y)=X(x)Y(y).
2) Note that u_x=X'Y, u_y=XY', u_{xx}=X''Y, u_{yy}=XY'', u_{xy}=u_{yx}=X'Y'.
3) Rearrange the equation such that LHS is a function of x only, RHS is a function of y only.
4) Thus, LHS=RHS=some constant k.
5) Solve the two separate ODEs.

Wave Equation
\displaystyle c^2y_{xx}=y_{tt}, where y(t,0)=y(t,\pi)=0, y(0,x)=f(x), y_t(0,x)=0.

Solution of Wave Equation (with Fourier sine coefficients)
\displaystyle y(t,x)=\sum_{n=1}^\infty b_n\sin(nx)\cos(nct) where \displaystyle b_n=\frac{2}{\pi}\int_0^\pi f(x)\sin(nx)\,dx.

d’Alembert’s solution of Wave Equation
\displaystyle y(t,x)=\frac{1}{2}[f(x+ct)+f(x-ct)].

Heat Equation
\displaystyle u_t=c^2u_{xx},
u(0,t)=u(L,t)=0, u(x,0)=f(x).

Solution of Heat Equation
\displaystyle u(x,t)=\sum_{n=1}^\infty b_n\sin\left(\frac{n\pi x}{L}\right)\exp\left(-\frac{\pi^2n^2c^2}{L^2}t\right), where \displaystyle b_n=\frac{2}{\pi}\int_0^\pi f(x)\sin(nx)\,dx are Fourier sine coefficients of f(x).

5 Good Habits to Develop for College

As soon as you start your freshman year in the university, you’ll be faced with countless challenges. Getting accepted into college is an accomplishment, but it is only one of the many steps you’ll need to take in order to succeed.

The good news is: there are habits you can develop and continue to practice in preparation for the challenges of college life.

The value of pre-college preps

But first: Before you can develop good habits that will serve you during your college years, it is essential that you establish a strong foundation for success in advance.

The best way to achieve your goals in college is to prepare for college way before you enter the university. While in high school, you can get help from the experts who can help you make smarter decisions about your higher education plans.

By working with college application consultants, you can get expert help every step of the way, including:

  • Assessing your current situation and future academic goals.
  • Establishing an organized system to identify and plan the schools that suit your skills and preferences.
  • Preparing and submitting winning applications on time.
  • Acing your college admissions interview.
  • Finding the best college options, from the institution to the course to study, that matches your goals and capabilities.

Once you find the right college for you, college goals such as developing good habits become easier to achieve.

Habits to achieve your college #goals

It’s important for you to develop good habits early on to have a successful college experience. As an incoming freshman, here are five good habits you should develop.

1. Establish your priorities

When you’re so accustomed to high school life, it may become hard for you to really visualize what college life will be like. The independence needed to cope with different class requirements and strictly following your personal study schedule are some of the things you need to consider.

College is a process of preparing for your future career. You should make it a habit to set priorities, and create and follow a schedule to manage your school workload. Make a list of your priorities from the most urgent projects to those that are due later.

This way, you can tackle them one at a time and reduce stress arising from the pressure of wanting to finish them all at once.

  • Plan ahead. The brain can’t handle things all at once. Overloading your mind with things to remember will only trigger stress. And before you know it, your stress may become unmanageable so you end up making mistakes, and missing assignments and projects.
  • Have a planner. Have a checklist of things you should bring to college. Create or buy an academic planner to help you stay organized. List down due dates for projects, assignments and many others. Make sure to stick to your planner and finish your work before the deadline. While you’re at it, you can also create backup alarms using your smartphone calendar app.
  • Break down big tasks into smaller ones. Writing a 12-page research paper and preparing for a huge exam at the same time can be difficult. Planning ahead means you have time to break down these huge tasks into smaller, manageable chunks so that they seem less daunting.

You can also follow these valuable tips on how to adjust to college life.

2. Participate, get involved

Don’t show up in class just to get your attendance checked. Involve yourself by participating in class discussions.

When you go to college, large lecture halls may appear intimidating to you. Practice the habit of engaging yourself during lectures. This will help you get a better grasp of learning. If there’s a vacant seat in front, occupy it.

Grab the opportunity to sit close to the professor for you to feel more present. You shouldn’t take part just because you want to dominate discussions or to help you get a better grade. Choose to speak out for the sake of engaging yourself.

Foster relationships with professors. A close mentoring relationship with a professor is advantageous as he or she can provide you some guidance as you go about your college education.

3. Challenge yourself

When you get into college, be on the lookout for opportunities. Take some challenging classes to expose yourself to new fields. Be open to new things. The world is too big for you to confine yourself to the things you already know.

Branch out and try everything you can. The more you explore your interests, the earlier you’ll discover your college major. Develop the habit of constantly challenging yourself; it will teach you about the value of hard work and discipline.

4. Build your portfolio

In connection to the third tip, pick activities that’ll advance your knowledge and experience. Make it a habit to save great pieces or project works you’ve done during high school. These will work to your advantage the moment you apply for college.

Your portfolio will serve as a proof of how adept you are in the course you’re applying for. This will also increase your chances of getting in a university that you want.

5. Understand how you learn

Each student has different learning abilities. While some are visual learners, others may be auditory learners. It’s important to consider what type of learner you are.

  • Kinesthetic Learner – gains knowledge through feelings or experience
  • Visual Learner – gains knowledge by seeing
  • Auditory Learner – gains knowledge by hearing

Knowing how you learn will be beneficial to you once you start college. There will be no more spoon-feeding in college so you have to be quicker in learning new things. If you know that you are an auditory learner, grab the chance to sit in front to hear each lecture clearly.

To sum up

Every student is unique, so there really is no one-size-fits-all formula for achieving college success. But by getting expert help in finding the right college and excelling in your chosen institution by building good habits, college can be one of the best years of your life.

AUTHOR BIO

Brian Giroux is an experienced college admissions advisor and co-founder of Capital College Consulting. Brian is a Professional Member of Independent Educational Consulting Association (IECA). Brian has worked with students from over 30 countries to help provide guidance through the US admissions process.

Brian’s experience includes 18+ years in education serving multiple roles as educator, athletic director, and college admissions consultant.

The Most Accomplished 10-Year-Old (Gifted pupil)

Pan Annan is probably the most accomplished 10 Year-old student in Singapore, or perhaps even in the world.

Her list of accomplishments:

  • International rhythmic gymnastics champion
  • Youngest member of the Singapore National Youth Chinese Orchestra (SNYCO), where she plays the Pipa
  • Gifted Education Programme (GEP)
  • Math Olympiad trainee
  • Raffles Girls’ Primary pupil

Any one of the above accomplishments is enough to stand out among 10 year-olds, and she has all of them! The most amazing is how she manages her time. I am familiar with Chinese Orchestra trainings, that alone is enough to account for quite a significant amount of time after school, since there is group practicing, sectional practicing, not to mention practicing alone. Possibly Chinese Orchestra alone adds up to a minimum of 5-10 hours per week.

Also, the workload from RGPS GEP is very demanding. Her schedule and timetable can only be achieved with 100% efficiency and focus. (She even does her homework in the car to maximize efficiency and save time.)

Parents may want to read my previous blog post on Book by Truly Gifted Kid (GEP Book), where a similarly prodigious child genius Moshe Kai Cavalin outlines his secret, with input from his mom on parenting. Also, as you can see, the standard for GEP students nowadays is very high, you may read Recommended Books for GEP Selection Test and How to Get Into GEP for some tips on how to do some foundational preparation for the GEP.

Sincerely all the best to Pan Annan for achieving her dreams of being a gymnastic champion.

Read more at: Channel News Asia

Population Differential Equations and Laplace Transform

Malthus Model
\displaystyle \frac{dN}{dt}=BN-DN=kN

N: Total population

B: Birth-rate per capita

D: Death-rate per capita

k=B-D

Solution to D.E.:
\displaystyle \boxed{N(t)=\widehat{N}e^{kt}},

where \widehat{N}=N(0).

Logistic Equation
\begin{aligned}  D&=sN\\  \frac{dN}{dt}&=BN-sN^2\\  \widehat{N}&=N(0)\\  N_\infty&=B/s  \end{aligned}

Logistic Case 1: Increasing population (\widehat{N}<N_\infty)
\begin{aligned}  N(t)&=\frac{B}{s+(\frac{B}{\widehat{N}}-s)e^{-Bt}}\\  &=\frac{N_\infty}{1+(\frac{N_\infty}{\widehat{N}}-1)e^{-Bt}}  \end{aligned}

The second expression can be derived from the first: divide by s in both the numerator and denominator.

Logistic Case 2: Decreasing population (\widehat{N}>N_\infty)
\begin{aligned}  N(t)&=\frac{B}{s-(s-\frac{B}{\widehat{N}})e^{-Bt}}\\  &=\frac{N_\infty}{1-(1-\frac{N_\infty}{\widehat{N}})e^{-Bt}}  \end{aligned}

Logistic Case 3: Constant population (\widehat{N}=N_\infty)
\displaystyle N(t)=N_\infty

Harvesting
Basic Harvesting Model: \displaystyle \boxed{\frac{dN}{dt}=(B-sN)N-E}.

E: Harvest rate (Amount harvested per unit time)

Maximum harvest rate without causing extinction: \boxed{\dfrac{B^2}{4s}}.

\displaystyle \boxed{\beta_1,\beta_2=\frac{B\mp\sqrt{B^2-4Es}}{2s}}.

\beta_1: Unstable equilibrium population

\beta_2: Stable equilibrium population

Extinction Time: \displaystyle \boxed{T=\int_{\widehat{N}}^0\frac{dN}{N(B-sN)-E}}.

Laplace transform of f
\displaystyle F(s)=L(f)=\int_0^\infty e^{-st}f(t)\,dt

Tip: Use this equation when the questions contains the words “show from the definition”.

Inverse transform of F(s)
\displaystyle f(t)=L^{-1}(F(s))

Linearity
\begin{aligned}  L(af(t)+bg(t))&=aL(f)+bL(g)\\  L^{-1}(aF(s)+bG(s))&=aL^{-1}(F)+bL^{-1}(g)  \end{aligned}

List of common Laplace Transforms

\begin{aligned}  L(e^{at})&=\frac{1}{s-a}\\  L(1)&=\frac{1}{s}\\  L(\cos wt)&=\frac{s}{s^2+w^2}\\  L(\sin wt)&=\frac{w}{s^2+w^2}\\  L(t^n)&=\frac{n!}{s^{n+1}}\\  L(f')&=sL(f)-f(0)\\  L(f'')&=s^2L(f)-sf(0)-f'(0)\\  L(f^{(n)})&=s^nL(f)-s^{n-1}f(0)\\  &\quad -s^{n-2}f'(0)-\dots-f^{(n-1)}(0)\\  L\left(\int_0^t f(\tau)\,d\tau\right)&=\frac{1}{s}L(f)  \end{aligned}

s-shifting
If L(f)=F(s), s>a, then \displaystyle \boxed{L(e^{ct}f(t))=F(s-c)},
s-c>a.

Tip: Use this when doing Laplace Transform of a function with an exponential factor e^{ct}. Note that the reverse direction can sometimes be used as well: \displaystyle L^{-1}[F(s-c)]=e^{ct}f(t).

t-shifting
If L(f(t))=F(s), then \displaystyle \boxed{L(f(t-a)u(t-a))=e^{-as}F(s)}.

Tip: Frequently, we use the reverse direction \displaystyle L^{-1}[e^{-as}F(s)]=f(t-a)u(t-a).

Delta function
\delta(t): infinitely tall and narrow spike at t=0.

\delta(t-a): infinitely tall and narrow spike at t=a.

\boxed{L[\delta(t-a)]=e^{-as}}

Two properties of delta function
\begin{aligned}  \int_0^\infty\delta(t-a)\,dt&=1\\  \int_0^\infty \delta(t-a)g(t)\,dt&=g(a)  \end{aligned}
for a\geq 0.

Tip: Use delta function when the keywords “suddenly”, “burst”, etc. appear.

Unit step function
\displaystyle u(t-a)=\begin{cases}  0, &t<a\\  1, &t>a.  \end{cases}

For 0<a<b, \displaystyle u(t-a)-u(t-b)=\begin{cases}  0, &t<a\\  1, &a<t<b\\  0, &t>b.  \end{cases}

Tip: Use unit step function for questions that require a force to “switch on / switch off” at certain times.

\displaystyle \boxed{L(u(t-a))=\frac{e^{-as}}{s}}

Free Money from PayLah (Quick! Before it is fully redeemed)

Last call to redeem the offer by PayLah! $5 just for downloading the app is pretty worth it.

mathtuition88's avatarMathtuition88

Hey! You can get S$5 when you register for PayLah! with my Referral Code WILDOF087 (last 3 digits are numbers zero-eight-seven) by 31 December 2018. Download PayLah! from http://www.dbs.com.sg/paylah now and enter the above Code during sign-up before this offer is fully redeemed. T&Cs apply.–

PayLah! can be downloaded from Apple Store or Android store (Singapore). Getting your $5 should be instantaneous. Be sure to redeem it today since there is a cap of 40000 people who can redeem. (The offer is still available now, but who knows next week it may be fully redeemed.)

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NTUC Fairprice Receipt Number

For those participating in lucky draws, often it requires you to SMS the NTUC Fairprice Receipt Number. However, the latest version of NTUC receipts, upon closer inspection contains many numbers but none that are explicitly specified as “receipt number”.

In the old NTUC receipt, the receipt number is clearly stated.

What is NTUC Receipt Number?

It is extremely confusing to find the NTUC Receipt Number (out of the many numbers in the receipt). After some “research”, I come to the conclusion is that the receipt number is the same as the transaction number, labelled by Tr!

How I came to this conclusion: Look at the image above. The receipt number is 65539, the transaction number is Tr: 65539. It matches, right? Hence, it is logical that the NTUC Fairprice receipt number is precisely the Tr (transaction) number.

Similarly, I believe that this logic applies to Giant, Sheng Siong, Cold Storage receipt numbers too, it should be the transaction number, in the event that the receipt number is not clearly stated in the receipt. Same for NTUC Finest, NTUC Extra and all other types of NTUC Fairprice receipts.

I hope this helps those who are desperately searching for the receipt number!


Money Saving “Lobang” (Tips):

Free Money from PayLah (Quick! Before it is fully redeemed)

Hey! You can get S$5 when you register for PayLah! with my Referral Code WILDOF087 (last 3 digits are numbers zero-eight-seven) by 31 December 2018. Download PayLah! from http://www.dbs.com.sg/paylah now and enter the above Code during sign-up before this offer is fully redeemed. T&Cs apply.–

PayLah! can be downloaded from Apple Store or Android store (Singapore). Getting your $5 should be instantaneous. Be sure to redeem it today since there is a cap of 40000 people who can redeem. (The offer is still available now, but who knows next week it may be fully redeemed.)

110 Nanyang Girls’ High students fall sick during boarding school programme

Quite worrying. Based on my personal experience and online research, food in Singapore cannot be left in room temperature for more than 4 hours, due to our hot and humid temperature. To be safe, food needs to be put in the refrigerator as soon as possible if not consumed immediately.

Hope all affected students get well soon.

Source: 110 Nanyang Girls’ High students fall sick during boarding school programme
Read more at https://www.channelnewsasia.com/news/singapore/110-nanyang-girls-high-students-sick-boarding-school-programme-10097196

Second Order Linear ODE Summary

Second Order Linear D.E. Summary

Homogenous D.E.
y''+ay'+by=0.

Solve the Characteristic Equation: \lambda^2+a\lambda+b=0.
Case 1) Two real roots \lambda_1,\lambda_2: \implies \boxed{y=c_1e^{\lambda_1x}+c_2e^{\lambda_2x}}

Case 2) Real double root \lambda: \implies \boxed{y=c_1e^{\lambda x}+c_2xe^{\lambda x}}

Case 3) Complex Conjugate root \lambda_1,\lambda_2=-\frac{a}{2}\pm iw, where w=\sqrt{b-\frac{a^2}{4}}: \implies \boxed{y=e^{-\frac{a}{2}x}(c_1\cos wx+c_2\sin wx)}

Non-homogenous D.E.
General solution of non-homogenous D.E.: \displaystyle y=y_h+y_p, where y_h is the general solution of the homogenous equation, and y_p is the particular solution (with no arbitrary constants).

Method of Undetermined Coefficients (Guess and try method)
y''+p(x)y'+q(x)y=r(x).

Only works if r(x) is polynomial, exponential, sine or cosine (or sum/product of these).

Polynomial: Try y=Polynomial (e.g. y=Ax^2+Bx+C or y=Bx+C.)

Exponential (e^{kx}): Try y=ue^{kx}, where u is a function of x.

Trigonometric (\sin kx or \cos kx): Convert to complex differential equation by replacing y with z, replace \sin kx/\cos kx by e^{ikx}.

Try z=ue^{ikx}, where u is a function of x. After solving for z, take real/imaginary part of z for cosine/sine respectively.

Method of variation of parameters
y''+p(x)y'+q(x)y=r(x).

[Step 1)] Solve the homogenous D.E. y''+p(x)y'+q(x)y=0.

Get solution of the form y_h=c_1y_1+c_2y_2.

[Step 2)]
Let \displaystyle u=-\int\frac{y_2r}{W}\,dx and \displaystyle v=\int\frac{y_1r}{W}\,dx where W is the Wronskian \displaystyle W=y_1y_2'-y_1'y_2.

Particular solution: y_p=uy_1+vy_2.

General solution: y=y_h+y_p.

Forced Oscillations
Let F_0 be the amplitude of the driving (external) force. If F_0=0, by Newton’s Second Law, m\ddot{x}=-kx, hence \displaystyle \boxed{\ddot{x}=-\omega^2 x},
where \omega=\sqrt{k/m}. The value \omega is called the natural frequency.

If F_0\neq 0, then \displaystyle \boxed{m\ddot{x}+kx=F_0\cos\alpha t},
where \alpha is the driving (external) frequency.

At resonance (when \alpha=\omega), \displaystyle \boxed{x=\frac{F_0t}{2m\omega}\sin(\omega t)}.

10 Things You Don’t Know About Albert Einstein

Source: Thoughtco

Some of the 10 facts are:

  • He Loved to Sail
  • Einstein’s Brain
  • Einstein and the Violin
  • Presidency of Israel

For those interested in the theory of relativity (special and general), which is the main core of Einstein’s research, do check out this book Relativity: The Special and the General Theory, 100th Anniversary Edition. Highly rated on Amazon, it is one of the few books that tells the story of Einstein and also includes real scientific content.

Drawing Chemistry Diagrams in LaTeX

The web application “mol2chemfig” is very amazing. (http://py-chemist.com/mol_2_chemfig).

Especially the search function, where one can just type the name of the chemical and out comes the chemfig code where it can be pasted to LaTeX. The mol2chemfig package needs to be imported in LaTeX before the code can be compiled. Alternatively, one can just save the PDF image (vector graphics) generated by the web app.

Below is a screenshot of what is happening: