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Tessellations of Pentagons

Tessellation is a cool topic in primary level to PSLE math. Most students will enjoy it even if they hate other types of Math. It is a natural human instinct to be amazed at how different shapes can fit together perfectly to tile the plane.

Apparently, tessellation is going to be removed from the entire PSLE syllabus soon (see http://schoolplus.com.sg/primary-math-syllabus-2017/). That is certainly quite sad for many reasons.

Triangles and quadrilaterals (even irregularly shaped ones) can be easily tessellated. However for pentagons, it is less clear and some pentagons (including the regular pentagon) cannot be tessellated!

For more information read the article here at: https://www.quantamagazine.org/the-math-problem-with-pentagons-20171211/

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50 Life Lessons from an 80 Year Old

Quite interesting list. Wonder who is the 80 year old?

Source: http://www.familyfriendlyhq.ie/family-blog/50-life-lessons-from-80-year-old-everyone-should-know

We absolutely love these pieces of advice from an 80 year old man. 

  1. Have a firm handshake.
  2. Look people in the eye.
  3. Sing in the shower.
  4. Own a great stereo system.
  5. If in a fight, hit first and hit hard.
  6. Keep secrets.
  7. Never give up on anybody. Miracles happen everyday.
  8. Always accept an outstretched hand.
  9. Be brave. Even if you’re not, pretend to be. No one can tell the difference.
  10. Whistle.
  11. Avoid sarcastic remarks.
  12. Choose your life’s mate carefully. From this one decision will come 90 per cent of all your happiness or misery.
  13. Make it a habit to do nice things for people who will never find out.
  14. Lend only those books you never care to see again.
  15. Never deprive someone of hope; it might be all that they have.
  16. When playing games with children, let them win.
  17. Give people a second chance, but not a third.
  18. Be romantic.
  19. Become the most positive and enthusiastic person you know.
  20. Loosen up. Relax. Except for rare life-and-death matters, nothing is as important as it first seems.
  21. Don’t allow the phone to interrupt important moments. It’s there for our convenience, not the caller’s.
  22. Be a good loser..
  23. Be a good winner.
  24. Think twice before burdening a friend with a secret.
  25. When someone hugs you, let them be the first to let go.
  26. Be modest. A lot was accomplished before you were born.
  27. Keep it simple.
  28. Beware of the person who has nothing to lose.
  29. Don’t burn bridges. You’ll be surprised how many times you have to cross the same river.
  30. Live your life so that your epitaph could read, No Regrets
  31. Be bold and courageous. When you look back on life, you’ll regret the things you didn’t do more than the ones you did.
  32. Never waste an opportunity to tell someone you love them.
  33. Remember no one makes it alone. Have a grateful heart and be quick to acknowledge those who helped you.
  34. Take charge of your attitude. Don’t let someone else choose it for you.
  35. Visit friends and relatives when they are in hospital; you need only stay a few minutes.
  36. Begin each day with some of your favourite music.
  37. Once in a while, take the scenic route.
  38. Send a lot of Valentine cards. Sign them, ‘Someone who thinks you’re terrific.’
  39. Answer the phone with enthusiasm and energy in your voice.
  40. Keep a note pad and pencil on your bed-side table. Million-dollar ideas sometimes strike at 3 .
  41. Show respect for everyone who works for a living, regardless of how trivial their job.
  42. Send your loved ones flowers. Think of a reason later.
  43. Make someone’s day by paying the toll for the person in the car behind you.
  44. Become someone’s hero.
  45. Marry only for love.
  46. Count your blessings.
  47. Compliment the meal when you’re a guest in someone’s home.
  48. Wave at the children on a school bus.
  49. Remember that 80 per cent of the success in any job is based on your ability to deal with people.
  50. Don’t expect life to be fair.
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Biological evidence that Jesus actually was born in December

The type of sheep in Israel is the “Awassi” sheep, a type of desert sheep. In Israel, the principal lambing season is December through January. It makes sense, since the winter in Israel is around 8 degrees Celsius, which is not too freezing cold. Something interesting to know!

Source: Aleteia

Long ago, I accepted the idea that December 25 was probably not the actual date of Christ’s birth, that the real date was unknown but probably in the spring. Knowing the exact date doesn’t really impact the liturgical celebration, after all. It was just one more sad thing about being an adult, one more little bit of wonder gone from life.

Since then, I’ve become well acquainted with the historical evidence in favor of a date of December 25. The date can be derived historically from the dating of Zechariah’s entry into the temple to burn incense. It can also be derived theologically from the ancient tradition that a great prophet entered and left the world on the same calendar day. Thus, the Annunciation was determined to have occurred on the same day as the crucifixion, March 25. December 25 naturally follows nine months later. They are good arguments, held to strict standards of historical research and logic, within their own fields.

But neither ever quite satisfied my desire for something really concrete. One continual objection was that the shepherds in the fields at night were presumed to be attending to the dropping of lambs. And lambs didn’t drop in December. Lambs dropped in the spring, not the winter.

So, when yet another person asked “Why do we celebrate Christmas in December if lambs are born in the spring?” instead of explaining the significance of March 25, I suddenly wondered: ARE lambs actually born in the spring in Israel? Can I find out?

The Awassi sheep is a desert sheep, a fat-tailed breed that has existed in the Middle East for an estimated 5,000 years. It is the only indigenous breed of sheep in Israel. They are raised for wool, meat, and milk. Awassi sheep breed in the summer and drop lambs in the winter, when there is sufficient pasture for the ewes in milk. In Israel, the principal lambing season is December through January.

This is practical, I thought. This is fact. This is biology.

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$1 (Bid) R2-D2 Droid for kids interested in Robotics

For $1, you can bid on this R2-D2 Droid inventor kit at Hachi.Tech (https://www.hachi.tech/auction/RHOTFI). This is a very reliable online site that is owned by Challenger.

The Droid is perfect for those kids who want to learn more about robotics during their holidays. You may also purchase it from Amazon:


Star Wars Droid Inventor Kit

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America’s Lost Einsteins

Source: https://www.theatlantic.com/business/archive/2017/12/innovation-income-chetty/547202/

Millions of children from poor families who excel in math and science rarely live up to their potential—and that hurts everyone.

Consider two American children, one rich and one poor, both brilliant. The rich one is much more likely to become an inventor, creating products that help improve America’s quality of life. The poor child probably will not.

That’s the conclusion of a new study by the Equality of Opportunity project, a team of researchers led by the Stanford economist Raj Chetty. Chetty and his team look at who becomes inventors in the United States, a career path that can contribute to vast improvements in Americans’ standard of living. They find that children from families in the the top 1 percent of income distribution are 10 times as likely to have filed for a patent as those from below-median-income families, and that white children are three times as likely to have filed a patent as black children. This means, they say, that there could be millions of “lost Einsteins”—individuals who might have become inventors and changed the course of American life, had they grown up in different neighborhoods. “There are very large gaps in innovation by income, race, and gender,” Chetty told me. “These gaps don’t seem to be about differences in ability to innovate—they seem directly related to environment.”

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Appeal from RGS to NYGH (Success)

Just read that appealing to transfer from RGS (Raffles Girls School) to NYGH (Nanyang Girls High) is possible:

dd moved out of rgs to nygh. she got 262+2. she appealed to nygh and was granted interview on Thursday. was given the good news after her interview.

nygh her first choice. she probably missed by decimal points. thus tried to appeal. was telling her both schools are equally good thus if not successful for nygh in her appeal, just move on 🙂

https://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=48&t=7127&start=3940

NYGH cut off point has been higher than RGS for the recent past years. It is the opposite situation of their boy school counterparts: RI cut off point is usually higher than Hwa Chong (Chinese High).

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From Medical Doctor to Math Professor

Just read about this rather amazing biography: https://today.duke.edu/2017/10/hau-tieng-wu-vital-signs. From a medical doctor, Hau-tieng Wu pursued a Ph.D. in math, and is now a math professor at Duke. Quite an interesting transition, that is quite rare, possibly less than 100 such cases in the world. Most mathematicians know little about medicine, and most medical doctors know little about math. It is rare to have someone know both fields.

Listen to your heartbeat with a stethoscope and you’ll hear a rhythmic lub-dub, lub-dub that repeats roughly 60 to 100 times a minute, 100,000 times a day.

But the normal rhythm of a healthy heart isn’t as steady as you might think, says Hau-tieng Wu, M.D., Ph.D., an associate professor of mathematics and statistical science who joined the Duke University faculty this year.

Rather than beating like a metronome, heart rhythm varies depending on whether you’re asleep or awake, sitting or jogging, calm or driving in rush hour. Breathing rate, brain activity and other physiological signals vary in much the same way, Wu says.

He should know. Before becoming a professor, Wu trained as a medical doctor in Taiwan. In his fifth year of medical school he was doing clinical rotations in the hospital when he was struck by the complex fluctuations in heart rhythm during anesthesia and surgery.

Where some saw noisy patterns — such as the spikes and dips on an electrocardiogram, or ECG — Wu saw hidden information and mathematical problems. “I realized there are so many interesting medical data that aren’t fully analyzed,” Wu said.

When a patient is in the hospital, sensors continuously monitor their heart rate and rhythm, breathing, oxygen saturation, blood pressure, brain activity and other vital signs.

The signals are sent to computers, which analyze and display the results and sound an alarm if anything veers outside normal ranges.

An ECG, for example, translates the heart’s electrical activity into a squiggly line of peaks and valleys whose frequency, size and shape can change from one moment to the next.

Wu is using techniques from differential geometry and harmonic analysis to detect patterns hidden in these oscillating signals and quantify how they change over time.

His methods have been applied to issues in cardiology, obstetrics, anesthesiology, sleep research and intensive care.

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Why do Americans have such trouble with fractions—and what can be done?

Fractions indeed are challenging for kids from ages 7-12. Probably the mental picture of a pie/pizza helps. Also, making fractions to the same denominator is a technique that once mastered will make addition/subtraction of fractions much easier.

Source: Scientific American

Many children never master fractions. When asked whether 12/13 + 7/8 was closest to 1, 2, 19, or 21, only 24% of a nationally representative sample of more than 20,000 US 8th graders answered correctly. This test was given almost 40 years ago, which gave Hugo Lortie-Forgues and me hope that the work of innumerable teachers, mathematics coaches, researchers, and government commissions had made a positive difference. Our hopes were dashed by the data, though; we found that in all of those years, accuracy on the same problem improved only from 24% to 27% correct.

Such difficulties are not limited to fraction estimation problems nor do they end in 8th grade. On standard fraction addition, subtraction, multiplication, and division problems with equal denominators (e.g., 3/5+4/5) and unequal denominators (e.g., 3/5+2/3), 6th and 8th graders tend to answer correctly only about 50% of items. Studies of community college students have revealed similarly poor fraction arithmetic performance. Children in the US do much worse on such problems than their peers in European countries, such as Belgium and Germany, and in Asian countries such as China and Korea.

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Very nice introduction to Cohomology (8 min)

This is a very nice and concise 8 minute introduction to cohomology. Very clear and tells you the gist of cohomology.

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Kids struggling in math? Try this “magic” method from Japan (VIDEO)

URL: Aleteia

It’s an Asian-style mathematics similar to Common Core that’s actually fun to do.

Confession time: I’m terrible at math. I don’t just mean like “struggled with calculus” bad, I mean like “had to watch YouTube videos to relearn long division in order to help my 4th grader with her homework” bad. I don’t know my times tables, except the easy ones. I can’t do fractions or percentages. I count on my fingers. 

It’s sad and shameful, and I was determined that my children would not share my fate. So when my oldest daughter was 5, I bought the insanely expensive starter package from Right Start Math and set about teaching her how to do math the right way.

It did not go well, nor did it last long. I found even the very simple activities baffling because I couldn’t grasp the intention. It was like trying to teach my daughter a foreign language I didn’t know.

However, my abject failure to understand it did not diminish my enthusiasm for the Asian method of mathematics. One of the reasons I like Common Core math is because there are lots of similarities. If you’ve never been exposed to the wonder of Asian-style mathematics, allow me to remedy that for you:

Check out the video on the page, it is quite amazing. (Japanese method of multiplying with lines).

URL: Aleteia

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Asus VivoBook E12 Review (Singapore)

[$369.00](▼27%)[ASUS]ASUS VivoBook E12 E203NA / lightweight 11.6-inch laptop /1 Years International warranty

WWW.QOO10.SG

I think currently this is the best budget laptop below $400. Size wise it is about the size of an iPad (around A4 size). The 4GB RAM makes it better and faster than those budget laptops with only 2GB RAM.

From the reviews on Qoo10, it is good for everyday uses such as YouTube, Microsoft Word etc.

Buying from Qoo10 has free shipping, Free Xiaomi Smart Scale and also “Free MS Office 365 Personal 1 Year” Pre-Installed Worth $98. (as of Nov 2017, check the updated terms and conditions to see if it is still valid)

URL: https://www.qoo10.sg/su/415685937/Q100000595

[$369.00](▼27%)[ASUS]ASUS VivoBook E12 E203NA / lightweight 11.6-inch laptop /1 Years International warranty

WWW.QOO10.SG

 

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US students aren’t bad at math—they’re just not motivated

It turns out that US students aren’t that bad at math, they just have no motivation to do the PISA test properly. (The PISA test is an external test that has no bearing on their school academic results.)

Source: https://qz.com/1130505/us-students-arent-bad-at-math-theyre-just-not-motivated/

It’s no secret that young Americans perform poorly on math and science tests, especially compared to their peers in countries like Singapore, Korea and China, where math scores are among the highest in the world. Now, a working paper surfaces a fundamental reason for that weak performance: American students are simply not trying hard enough.

In the latest results of the Programme for International Student Assessment (PISA), US students ranked roughly average among the 75 participating countries. The PISA tests, administered by the OECD every three years, assess 15-year-olds around the world on math, science and reading. Governments and policy makers point to the outcomes when making the case for education reform.

The researchers also ran a simulation, and found that if the 15-year-olds in the US had been given the same cash bonus in 2012 when taking the assessment, America would have ranked 19th in the PISA math test instead of 36th among 65 nations.

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Shepherd Me O God

Very nice and calming Christian music. Composed by Marty Haugen.

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Hokkaido University Photo Gallery and Trip Guide

These photos are from a trip to Hokkaido University in August 2017. Hokkaido University is just walking distance away from Sapporo station, and is worth spending an afternoon there. Admission is free. Even in the hottest summer, Hokkaido has cool weather, ranging from around 17 degrees to 25 degrees.

Some places to visit are the Poplar Avenue, and also the Hokkaido University Museum (check the time, it can close as early as 5pm.) Also, the statue of one of the founders, Dr. William Smith Clark, is also a good place to visit. There is also a monument of the school motto: “Be ambitious!” (少年よ、大志を抱け )

Raven/crows can be spotted all around the campus of Hokkaido University. They are the largest raven I have ever seen, about the size of a small eagle.

A random willow tree in Hokkaido University.

Students can be found reading or just sitting in the field. I even spotted one student practicing violin.

The famous Poplar Avenue of Hokkaido University.

A small stream running through the middle of Hokkaido University.

Hokkaido University Museum: A Town Plan of Hokkaido University.

Poster in Hokkaido University Museum.

Chemical Structure in Hokkaido University Museum.

The Hokkaido University Museum is 3 storeys. It is quite big actually, there should be enough things to see for around one hour or more.

The below are some photos from inside the Hokkaido University Museum.

 

A signboard in a garden.

 

A large raven in Hokkaido University. It is much larger than it looks in the photo.

The famous motto of Hokkaido University: “Be ambitious!” (original words: “boys, be ambitious!”)

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8 Facts About Infinity That Will Blow Your Mind

Nice article on infinity. Also little known is the fact that the symbol of infinity was introduced by clergyman and mathematician John Wallis, hundreds of years ago in 1655. Although not well-known, John Wallis was a talented individual as can be deduced from his biography. His works include integral calculus, analytic geometry, and collision of bodies. He was the one who coined the term “momentum”.

Source: ThoughtCo

Infinity has its own special symbol: ∞. The symbol, sometimes called the lemniscate, was introduced by clergyman and mathematician John Wallis in 1655. The word “lemniscate” comes from the Latin word lemniscus, which means “ribbon,” while the word “infinity” comes from the Latin word infinitas, which means “boundless.”

Wallis may have based the symbol on the Roman numeral for 1000, which the Romans used to indicate “countless” in addition to the number. It’s also possible the symbol is based on omega (Ω or ω), the last letter in the Greek alphabet.

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Fave (previously Groupon) FREE Promo Code

FREE Promo Code discount: http://myfave.com/invite/KJMDZ?city=singapore

Fave (previously known as Groupon) is a fantastic deals site that offers many discounts. It includes discounts to many restaurants/buffets in Singapore.

Quite many famous restaurants are offering discounts there: e.g. Dancing crab, Mouth Restaurant, Ah Yat Abalone, JUMBO Seafood, Charcoal Thai and more.

Here is a free Promo Code, for first-time users who sign up on Fave: KJMDZ

You will get a further first-timer’s discount upon sign-up.

Click here to sign up with the Promo Code: http://myfave.com/invite/KJMDZ?city=singapore

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Increased Tax for US PhD Students

This is very bad news. Graduate students are already poor (stipend is already low to begin with and fixed for the duration of study). A very bad policy for grad students.

The tax overhaul passed Thursday by House Republicans could cost graduate students thousands of dollars, prompting a backlash from students and university leaders who say the proposal could make graduate degrees unaffordable, especially for low-income students.

A provision tucked away in the House’s bill would count the tuition discounts given to many grad students as income, meaning that students would pay taxes on tens of thousands of dollars that they never see. The bill would double or even triple many students’ taxes.

Source: Buzzfeed

Source: PhD Comics

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A Mathematician is Grateful For…

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Free Math Public Lecture at National Library

Interested students may want to attend. It is at the National Library, on 14th December 2017.

The Liar Game: Truths & Proofs from Euclid to Turing

Ng Kong Beng Public Lecture Series

Mark Wildon, Royal Holloway, University of London, UK

(14 Dec 2017, 6.30pm – 7.30pm)

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Union-closed sets conjecture

Just read about this conjecture: Union-closed sets conjecture.

The conjecture states that for any finite union-closed family of finite sets, other than the family consisting only of the empty set, there exists an element that belongs to at least half of the sets in the family. (Wikipedia)

It is quite interesting in the sense that the statement is extremely elementary (just basic set notation knowledge is enough to understand it). But it seems that even the experts can’t prove it.

One basic example is: {{1},{2},{1,2}}. The element 2 belongs to 2/3>1/2 of the sets in the family.

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MRT train collision: Scientifically, where is the safest place to sit in a train?

In light of the recent MRT train collision in Singapore (Joo Koon), where at least 23 passengers were injured, it may be of interest to consider scientifically, where is the safest place to sit/stand in a train?

We sincerely hope the 23 injured passengers are fine and will recover quickly.

Summary:

  • Most safe position is middle of the train.
  • If you are standing, face backwards in opposite direction of the train’s motion, with your back leaned against a solid support.

According to this article on Huffington Post, scientifically the safest place is the middle of the train.

On a passenger train, your safest bet just may be to sit in the middle cars, or one car behind the middle. After all, most collisions happen at the front or rear of a train, and the types of issues that cause derailments, such as broken rails or welds, tend to occur near the front of the train, according to findings cited by Live Science.

It is quite common sense actually, most collisions happen at the front or rear; it is highly unlikely that the collision happen in the middle given the configuration of the tracks. Also, the front/back will absorb most of the impact of the collision.

Also, rear facing seats are the most safe (but they are not present in Singapore MRT).

In other words, “it comes down to basic physics,” as Placencia said. “When something happens, most of the time you have a problem when a train has to stop quickly… If I’m in a forward-facing seat, then I’m going to be pushed out of my seat. But if I’m rearward-facing, what happens is, I would be pushed back into my seat.”

So the next best thing is if you are standing, stand leaning against a support (e.g. the panel near the doors or the metal pole) facing in the opposite direction of the train motion. So that if the train brakes suddenly, you are pushed back onto the support instead of falling down.

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Bid for iPhone 8 at only $1 (real)

[Auction] iPhone 8 64GB [Gold]

Hachi.tech (online website of the Challenger store) is holding an auction. From time to time, the items there are actually quite good and useful. This time the auction is a iPhone 8 64GB. The auction starts at $1.

It is a lucky draw type of auction, meaning that it is not the higher bidder that wins, but rather your chance of winning is proportional to your bid. Also, you only pay if you win the bid, i.e. at no point are you paying anything until you are selected as the lucky winner.

Use the link here to start bidding!: https://www.hachi.tech/auction/67RO6G

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Singapore is in the wrong timezone

Most people who have been living in Singapore all their lives wouldn’t know this: Singapore is in the wrong timezone. To be precise, Singapore should be in the GMT +7 timezone, but we are using the GMT +8 instead. This means that, for instance, 7am in the current time is actually supposed to be 6am.

I only realized it myself after googling, and only after some suspicions after going overseas: Comparatively, why does the sun rise in Singapore so late (around 7am), and why does the sun set in Singapore so late (around 7pm). In Singapore, it is common that the day is still very bright at 7pm. At first I attributed it to the fact that Singapore is in the equator and hence experiences “summer” all year round. It turns out that a bigger reason may be the wrong GMT timezone.

In this article: Singapore’s time zone biggest contributor to sleeplessness problem, it is argued that being in the wrong timezone causes lots of problems, such as sleeplessness. This is because the body’s true time (circadian rhythm) is out of sync of the “fake” GMT +8 time.

The biggest issue may be the time school starts for school going children. In most schools, the morning assembly starts at around 7.30am. Depending on where the children live and their mode of transport, it is common for children to have to wake up at around 5.30am. By the previous logic, this corresponds to the true time of 4.30am!

 

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‘Stemaritans’ help breathe life into maths and science

Quite interesting term “Stemaritans”, referring to people who promote STEM (Science Technology Engineering Math).

‘Stemaritans’ help breathe life into maths and science

“Parents think highly of the Singapore education system and like the fact that the bulk of our teachers had taught in mainstream Singapore schools …

Other interesting educational news from Singapore.

‘Titles culture’ in Singapore stifles entrepreneurial streak, say foreign-born businessmen

Mr Staarman, 60, who is from the Netherlands, added that the results-driven, exam-centric approach in Singapore’s education system does not require …
Tech, the road less travelled by girls

In Singapore, the programme has reached more than 6,500 girls in more … This programme comes amid a push by education institutes to get girls …
Skills portal to guide S’poreans from age 11

… and plan their careers”, said the Ministry of Education (MOE), Workforce Singapore (WSG) and SkillsFuture Singapore (SSG) in a joint statement.
What the rollout of IHL SkillsFuture Series means for workers and highereducation

Given the longstanding policy of heavy state subsidies for higher education in Singapore, the state has a significant influence in determining the main …
Rising school fees for non-S’poreans force rethink among Johoreans

The Singapore government began sharpening the distinction between citizens and non-citizens in education, healthcare and other major policy areas …
Be less ‘uptight’ about times tables, urges Singaporean maths mastery expert

Dr Yeap Ban Har spent 10 years at the National Institute of Education in Singapore, a country that has played a leading role in the development of the …
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He who loves learning is better than he who knows how to learn (Confucius)

From Baidu Baike:

知之者不如好之者,好之者不如乐之者: 对于学习,了解怎么学习的人,不如喜爱学习的人;喜爱学习的人,又不如以学习为乐的人。比喻学习知识或本领,知道它的人不如爱好它的人接受得快,爱好它的人不如以此为乐的人接受得更快。

Translation: He who knows how to learn, is not as good as he who likes learning. He who likes learning, is not as good as he who loves learning. (Confucius)

I guess this applies to mathematics as well. The first step to do well in mathematics is to keep an open mindset and try to get rid of any negative thoughts regarding math. Then, slowly proceed to like and enjoy, and even love math. Only then can one reach his full potential in mathematics.

Like most things, there is a nature and nurture component to this. Some people just naturally love logical things including math. Environment like parents and teachers are very important too, a negative encounter in early childhood can easily give a child a bad impression of learning math.


Learning to Love Math: Teaching Strategies That Change Student Attitudes and Get Results

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It’s mathematically impossible to beat aging, scientists say

According to Math, no one can live forever. So far, the only counterexample that I know of is Turritopsis dohrnii, also known as the “immortal jellyfish”. The article doesn’t seem to address this counterexample though.

Source: Science Daily

Aging is a natural part of life, but that hasn’t stopped people from embarking on efforts to stop the process.

Unfortunately, perhaps, those attempts are futile, according to University of Arizona researchers who have proved that it’s mathematically impossible to halt aging in multicellular organisms like humans.

“Aging is mathematically inevitable — like, seriously inevitable. There’s logically, theoretically, mathematically no way out,” said Joanna Masel, professor of ecology and evolutionary biology and at the UA.

Masel and UA postdoctoral researcher Paul Nelson outline their findings on math and aging in a new study titled “Intercellular Competition and Inevitability of Multicellular Aging,” published in Proceedings of the National Academy of Sciences.

Current understanding of the evolution of aging leaves open the possibility that aging could be stopped if only science could figure out a way to make selection between organisms perfect. One way to do that might be to use competition between cells to eliminate poorly functioning “sluggish” cells linked to aging, while keeping other cells intact.

However, the solution isn’t that simple, Masel and Nelson say.

Two things happen to the body on a cellular level as it ages, Nelson explains. One is that cells slow down and start to lose function, like when your hair cells, for example, stop making pigment. The other thing that happens is that some cells crank up their growth rate, which can cause cancer cells to form. As we get older, we all tend, at some point, to develop cancer cells in the body, even if they’re not causing symptoms, the researchers say.

Read more at: Science Daily

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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?

Answer by Albert Heisenberg, Science Historian M.A. Brown University

Leibniz’s formulation of differential and integral calculus was more refined, elegant, and ‘generalizable’ than Newton’s ‘fluxions.’ Leibniz, the natural genius that he was, became interested in mathematics much later in his life than Newton, and yet was able to generalize Descartes work on analytic geometry into calculus in a way that is so clear that till this day we still use Leibniz’s notation (e.g. dx/dy; his symbolism for time integration/differentiation, etc). Newton’s Principia is a work of incredible genius, but it is riddled with errors and inconsistent notation. As the co-founder of classical physics (along with Galileo) and the culmination of the scientific revolution, his legacy was deeply tied to the spread of natural philosophy as a mathematically rigorous discipline even though Leibniz’s formulation of infinitesimal calculus was superior. Newton achieved greater fame for a few reasons:

Read more at: https://www.quora.com/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

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DSA Interview Questions

Interviews can be intimidating even for adults, let alone 12 year olds. However, the DSA interview is a very important aspect, especially since many would have the same qualifications / test results. Familiarizing with some of the questions can be useful, but not overtraining to the extent of being unnatural or memorizing a script written by mommy or daddy, which can be easily detected by the interviewing committee.

Frankly speaking, at age 12, it is very rare for a child, unprepared, to naturally just perform well in an interview. Most children at that age would be well-versed in games/cartoons but not in current news or social issues. Hence, some preparation, like preparing for PSLE English oral, would be useful and even necessary.

Some DSA Interview questions are compiled below. Clearly, developing good spoken English language is a foundational step that has to be addressed too. Judging from the questions, knowledge of the school history, culture and values would help too. Knowledge of current affairs like basic Singapore news would be of use too.


I Can Ace My College Interview: A step-by-step guide based on an Admissions Officer’s experience evaluating applicants

This book (though in a college context, since in Western countries they don’t interview children as young as 12 years old) provides some tips to ace school admission interviews. DSA interviews do ask very mature questions like “What are your weaknesses” that even adults struggle to answer properly. Hence this book is still very relevant.


Speakers’ Club: Public Speaking for Young People

Another useful book is the above. Public speaking involves the same skills as interview, just that it is delivered to a larger audience.


Different schools asked different DSA interview questions, even within the same school, the questions are different. Some examples of questions, for my DS and his friends are:
(1) Why did you DSA to this school?
(2) Did you DSA to another school? If both offer you a place, which would you choose?
(3) How did you think you can contribute to this school?
(4) If you have the chance to have dinner with a public figure, who will it be and why?
(5) What do you think is the most important colour in the world? Why?
(6) If there is something you can change in your primary school, what will it be and why?

Source: Kiasuparents

1.Tell me about yourself?
2.Why do you want to come to our school?
3.Why did you apply to our school / programme?
4.What are the things you like about our school that other schools do not include?
5.How many schools have you applied to and which school is your first choice?
6.Are you applying to this school because it is a branded/ elite school?
7.What is your definition of a good school?
8.Why should we accept you among all the great candidates /applicants who apply?
9.What are the problems of accepting students to a school based on their exam results?
10.Tell us what you enjoy doing when you are NOT attending school
11.Who is the greatest influence in your life or who do you admire the most?
12.What do you think about Steve Jobs and iPhone?
13.Tell us about an event that is significant in your life?
14.What is your goal for life?
15.What are your strengths?
16.What are your weaknesses? How do you overcome them?
17.What is your favourite subject?
18.How do you think you can help the CCA achieve greater heights?
19.Do you have any question about our school?
20.What questions would you like to ask us?

Source: Kiasuparents

There is even this website www.dsainterview.com dedicated to the DSA Interview. One point that they mentioned seems very important:

10. NEVER ANSWER WITH ‘my mommy said or my daddy said…’  

This is a very common occurrance. The student should always present HIS/HER opinions as his or hers. Even if the student got the opinion from a parent or a teacher, the student should just state his thoughts without mentioning who said it to him​.

Another tip is from http://smartification.net/how-to-handle-dsa-interview-questions/,

“Why do you want to come to our school or how many schools have you applied to and which school is your first choice?”

Interviewers ask these questions to determine how motivated students are about attending the school. The best way to tackle this question is to talk about the academic programs or CCA that the school offers. Visiting the open house and speaking to students, coaches and teachers will help students acquire valuable information. Looking through the school website will also provide more information about the school. Try to avoid common reasons such as ‘Your school is the best school in Singapore” or “My parents want me to attend your school because it can help me get into a top university in the future”. These answers are just too cliché.

As to which school is the first choice, the answer should be the school which the student is interviewing with at the moment. In most cases, schools who ask this question do it as a formality. Answering it with an “I don’t know or I have not decided” will give the impression the student is not serious about attending the school and the interviewers will feel like they have just wasted their time.

RGS DSA Interview Questions

–> In one sentence, introduce yourself.
–> Why do you wish to come to RGS?
–> What are the things you like about RGS that other school does not include?
–> Is it because RGS is a ‘branded’ school, you do not bother checking up on other schools?
–> What is a good school?
–> What are the problems of accepting students to a school only based on their exam results?
–> What are questions you would like to ask us?

Source: https://agirlwhowishestoliveinafantasy.wordpress.com/2013/07/22/rgs-dsa-interview-2/

Certain hot topics (like Singapore Olympic Games, news on Joseph Schooling / Feng Tian Wei) have a high chance to come out:

The application procedures were quite straightforward—online application, followed by GAT tests and interviews.  DD enjoyed the tests and interviews, though those were the very first interviews she ever had.  One of interviews was happened in the week when our table tennis team won first Bronze medal at London Olympic.  there were some questions during the interview:-

What news has she read?” 
She replied “Feng Tian Wei won Bronze medal for Singapore.”
“What is your goal for life?
She replied “To represent Singapore in Olympic.”

I guess she was in Olympic fever then.

Source: http://full-time-mothers.blogspot.sg/2012/08/our-journey-of-dsa.html

 

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Donate to SOSD (very pitiful dog)

Recently chanced upon SOSD Facebook, and saw this dog, with a very serious maggot wound. They have a few other such dogs under medical care too. Just to spread some awareness through my blog, as not many people have heard of SOSD. Do donate any amount (through their Donation page) if you can afford. It is hard to imagine how did they get such wounds, and the pain they must be suffering.


Update (from SOSD Facebook):
Thank you for your generosity and kindness. We have reached our target amount for August. Stay in tune for update on his development coming soon.

August needs your help!

Sweet-natured August was first spotted hiding in the workers’ dormitories with a large maggot-infested wound on the back of his neck.

Being awfully shy and afraid of strangers, August proved to be a challenging rescue to our volunteers. After a few nights of futile attempts, we finally succeeded with the help of a dog trapper.

Clinical examinations revealed that his blood count was very low, and the poor boy was also diagnosed with Babesia Gibsoni, a dangerous strain of tick fever.

Over the past two months, our volunteers have carefully tended to his wound and with medication, his tick fever is resolved. Due to the severity of the wound, he still has not fully recovered and will continue to require medical attention.

Although August is still rather shy and takes a while to warm up to people, he has been very gentle and mild-mannered, allowing our volunteers to clean his wound and carry him without making a fuss.

Newly sterilized, August is well on his way to becoming a healthy and strong doggy. To date, his vet bills total $1,600 so we are appealing to charitable dog lovers to help cover the accumulating costs. Please help us with the bills if you can. Any amount will be most appreciated!

To donate via GivingSg, please click on this link: http://bit.ly/2itG5N2

August is HDB-approved, if you would like to adopt, please fill in this form: http://bit.ly/2gOlYbo

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Lichess to FIDE Elo Rating Conversion

Lichess is a free Chess Server – one of the best out there in fact. It comes with free engine (Stockfish) analysis, and many other nice features. It is well known that Lichess ratings are inflated compared to FIDE / USCF / most other rating systems. The following are some of the best conversion systems to convert Lichess rating to other ratings.

1) Dudeski_robinson’s Formula

FIDE Rating = 187 + Lichess Classical Rating X 0.38 + Lichess Blitz Rating X 0.48

Dudeski_robinson’s formula is pretty scientific, he actually uses linear regression out of real data to produce the above formula.

A rough estimate would be:
Fide ELO = Lichess Classical – 170
or
Fide ELO = Lichess Blitz – 80

Source: Lichess Forum

2) Chess Rating Comparison 2016 (Google Sheets)

This is also pretty scientific, with the added plus that it also compares between USCF and Chess.com, in addition to FIDE.

Chess.com Lichess.org USCF FIDE
Bullet Blitz Rapid Bullet Blitz Classical Regular Regular
860 1100 1160
900 1125 1200
930 1150 1250
960 1175 1290
1000 1200 1330 1370 1530 1590 1270 1260
1030 1225 1360 1390 1550 1620 1290 1280
1060 1250 1400 1410 1570 1640 1320 1310
1090 1275 1430 1440 1590 1670 1340 1330
1130 1300 1460 1460 1610 1690 1360 1350
1160 1325 1490 1480 1630 1720 1390 1370
1190 1350 1520 1510 1650 1740 1410 1390
1230 1375 1550 1530 1670 1770 1430 1410
1260 1400 1570 1550 1690 1790 1460 1430
1290 1425 1590 1580 1710 1810 1480 1460
1320 1450 1610 1600 1730 1830 1500 1480
1360 1475 1630 1620 1750 1860 1530 1500
1390 1500 1650 1650 1770 1880 1550 1520
1420 1525 1670 1670 1790 1900 1570 1540
1460 1550 1680 1690 1810 1920 1600 1560
1490 1575 1700 1720 1830 1940 1620 1580
1520 1600 1710 1740 1850 1960 1640 1610
1550 1625 1730 1760 1870 1980 1670 1630
1590 1650 1740 1790 1890 2000 1690 1650
1620 1675 1750 1810 1910 2010 1710 1670
1650 1700 1760 1840 1930 2030 1740 1690
1690 1725 1770 1860 1950 2050 1760 1710
1720 1750 1780 1880 1970 2070 1780 1730
1750 1775 1790 1910 1990 2080 1810 1760
1790 1800 1800 1930 2010 2100 1830 1780
1820 1825 1810 1950 2030 2110 1850 1800
1850 1850 1820 1980 2050 2130 1880 1820
1880 1875 1820 2000 2070 2150 1900 1840
1920 1900 1830 2020 2090 2160 1920 1860
1950 1925 1840 2050 2120 2180 1950 1880
1980 1950 1850 2070 2140 2190 1970 1910
2020 1975 1860 2090 2160 2210 1990 1930
2050 2000 1870 2120 2180 2220 2020 1950
2080 2025 1880 2140 2200 2230 2040 1970
2110 2050 1890 2160 2220 2240 2060 1990
2150 2075 1900 2190 2240 2250 2090 2010
2180 2100 1910 2210 2260 2270 2110 2030
2210 2125 1930 2230 2280 2280 2130 2060
2250 2150 1940 2260 2300 2290 2160 2080
2280 2175 1950 2280 2320 2300 2180 2100
2310 2200 1970 2300 2340 2300 2200 2120
2340 2225 1980 2330 2360 2310 2230 2140
2380 2250 2000 2350 2380 2320 2250 2160
2410 2275 2020 2370 2400 2330 2270 2180
2440 2300 2040 2400 2420 2340 2300 2210
2480 2325 2420 2440 2340 2320 2230
2510 2350 2440 2460 2350 2340 2250
2540 2375 2470 2480 2360 2370 2270
2580 2400 2490 2500 2360 2390 2290
2610 2425 2510 2520 2370 2410 2310
2640 2450 2540 2540 2370 2440 2330
2670 2475 2560 2560 2380 2460 2360
2710 2500 2580 2580 2380 2480 2380
2740 2525 2610 2600 2380 2500 2400
2770 2550 2630 2620 2390 2530 2420
2810 2575 2650 2640 2390 2550 2440
2840 2600 2680 2660 2390 2570 2460
2870 2625 2700 2680 2390 2600 2480
2900 2650 2720 2700 2400 2620 2510

Source: Google Docs

Discussion: Reddit

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Note on p-divisibility in Bockstein Spectral Sequence

If u\in H_n(X) generates a copy of \mathbb{Z}, then u\notin\ker p^r.

Write u=a+b, where a\in pH_n(X), b\in\ker p^r. Note that since b=u-a\in\ker p^r, hence b=u-a does not generate a copy of \mathbb{Z}. The only way that is possible is when b=u-a=0, i.e u=a.

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Making big data a little smaller

While this result is nice, it also seems to mean that theoretically, we have already reached the limit in dimensional reduction for data compression.

Source: Science Daily

Harvard computer scientist demonstrates 30-year-old theorem still best to reduce data and speed up algorithms

Date:
October 19, 2017
Source:
Harvard John A. Paulson School of Engineering and Applied Sciences
Summary:
Computer scientists have found that the Johnson-Lindenstrauss lemma, a 30-year-old theorem, is the best approach to pre-process large data into a manageably low dimension for algorithmic processing.

When we think about digital information, we often think about size. A daily email newsletter, for example, may be 75 to 100 kilobytes in size. But data also has dimensions, based on the numbers of variables in a piece of data. An email, for example, can be viewed as a high-dimensional vector where there’s one coordinate for each word in the dictionary and the value in that coordinate is the number of times that word is used in the email. So, a 75 Kb email that is 1,000 words long would result in a vector in the millions.

This geometric view on data is useful in some applications, such as learning spam classifiers, but, the more dimensions, the longer it can take for an algorithm to run, and the more memory the algorithm uses.

As data processing got more and more complex in the mid-to-late 1990s, computer scientists turned to pure mathematics to help speed up the algorithmic processing of data. In particular, researchers found a solution in a theorem proved in the 1980s by mathematics William B. Johnson and Joram Lindenstrauss working the area of functional analysis.

Known as the Johnson-Lindenstrauss lemma (JL lemma), computer scientists have used the theorem to reduce the dimensionality of data and help speed up all types of algorithms across many different fields, from streaming and search algorithms, to fast approximation algorithms for statistical and linear algebra and even algorithms for computational biology.

Source:

Harvard John A. Paulson School of Engineering and Applied Sciences. “Making big data a little smaller: Harvard computer scientist demonstrates 30-year-old theorem still best to reduce data and speed up algorithms.” ScienceDaily. ScienceDaily, 19 October 2017. <www.sciencedaily.com/releases/2017/10/171019101026.htm>.

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Free Cooking Recipes Newsletter

https://chewbaccascook.wordpress.com/subscribe/

Feel free to subscribe to this Free Cooking Recipe Newsletter.

Hundreds of Home Cooking Recipes!

recipe

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SOSD Dog Adoption Drive

Just saw this. SOSD (something like SPCA for dogs) is organizing an adoption drive tomorrow 22 Oct Sunday. So if you are interested to see the dogs and perhaps adopt one, you are free to attend (above One-North MRT Station).

I read on their Facebook that they are facing some problems due to too many stray dogs, their “enclosures are all full; we do not even have space in our quarantine unit to house any more dogs”.

They also do have dogs suitable for HDB, under this project called Project ADORE. If more dog lovers adopt instead of buy, the problem of stray dogs in Singapore can be solved humanely.

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New PR Singpass

Googling info on this is quite hard. Just to share what is the procedure. Basically you need to apply for a new Singpass based on your new PR NRIC, as the previous Singpass based on FIN will be invalid.

Also, most would soon encounter this problem: Your mobile phone is tied to the old Singpass account, and the system would not let you use it for the 2FA.

The solution (took quite a while for me to find this): (Source)

Q: I am a FIN holder who has been granted Singapore PR, how can I continue to use SingPass?

Ans: You will need to register for a new account using your NRIC number. Upon successful registration, your account details will be mailed to you within four working days. Click here for more details. Please note that one mobile number can only be registered with one SingPass account. If you have previously registered your mobile number in your existing account, and would like to use the same number for your new account, please email support@singpass.gov.sg with the following details:
Your FIN number
Your new NRIC number
Your mobile number

Source: Singpass FAQ

Disclaimer: This info is dated 21 October 2017. The procedure may or may not change in the future. Also, please double check with the official website before taking any actions.

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Terence Tao Numberphile

Among current mathematicians, many people regard Professor Tao as the world’s finest… Opinions on such things vary, of course. Professor Tao kindly fielded some of our questions, including many submitted by Numberphile viewers. EXTRA FOOTAGE: https://youtu.be/48Hr3CT5Tpk (and more extras to come)

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“Actual” GEP Questions 2017 (from Forum)

Since the actual GEP papers are never released, the next best source is from those who have actually taken it and post on forums like Kiasuparents.

Some Maths questions my girl remembers.

“ In a fishing competition, five kids caught 50 fish in total. A is the winner – she got 12 fish. B and C caught the same number of fish and both are at second place. D is at fourth place. E came in last, got only 6 fish. How many fish did B get?“

( my girl couldn’t solve this one. )

“ The red ribbon is twice as long as the blue ribbon. The green ribbon is 2cm shorter than the blue ribbon. A red ribbon and two green ribbon together measure 16cm. How Long is the blue ribbon? “

( she managed to solve this one- but only after spending a lot of time on it. )

Source: https://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=72&t=89066&start=160

Review by mathtuition88: These two questions are not that hard. Can be solved by either model method or algebra.

Some tips from parents: English and GAT is actually harder to prepare than Maths:

Just sharing based on our experience last year. Of the 6 that were selected for GEP eventually from my child’s class, it seems English and GAT were the determining factors. For maths, a lot of kids are already very advanced and well – prepared nowadays. The majority of the balance 14 who went for round 2 found English harder than maths. According to them, English is somewhat like pitched at sec 1 and sec 2 standard, while maths was like up to P6 and Primary Maths Olympiad standard and more manageable. I think it was also more because anything can come out under the sun for English and you can’t really prepare for it. That’s what I heard last year.

Source: https://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=72&t=89066&start=140

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The State of Being Stuck

Nice story (with drawings) on Andrew Wiles and the Fermat’s Last Theorem.

Math with Bad Drawings

Last year, I got the high school math teacher’s version of a wish on a magic lamp: a chance to ask a question of the world’s most famous mathematician.

20161031143242_00026

Andrew Wiles gained his fame by solving a nearly 400-year-old problem: Fermat’s Last Theorem. The same puzzle had captivated Wiles as a child and inspired him to pursue mathematics. His solution touched off a mathematical craze in a culture where “mathematical craze” is an oxymoron. Wiles found himself the subject of books, radio programs, TV documentaries—the biggest mathematical celebrity of the last half-century.

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Why do people get so anxious about math? – Orly Rubinsten

View full lesson: http://ed.ted.com/lessons/why-do-peop… Have you ever sat down to take a math test and immediately felt your heart beat faster and your palms start to sweat? This is called math anxiety, and if it happens to you, you’re not alone: Researchers think about 20 percent of the population suffers from it. So what’s going on? And can it be fixed? Orly Rubinsten explores the current research and suggests ways to increase math performance. Lesson by Orly Rubinsten, animation by Adriatic Animation.

Also view my previous post on Coping with maths anxiety.

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McCleary User’s Guide to Spectral Sequences (Errata)

(pg 455) When an element u\in H_{n-1}(X) satisfies ru=0, then, by exactness, there is an element \mathbf{\bar{u}\in H_n}(X;\mathbb{Z}/r\mathbb{Z}) with \partial(\bar{u})=u. Should be H_n instead of H_{n+1}.

(pg 458) The first differential is given by d^1=\boxed{{\text{red}_p}_*\circ\partial}=\beta. The order in the printed version is incorrect. Note that the first differential should be d^1=j\circ k for the exact couple.


See also Recommended Books for Spectral Sequences.

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Free Video about GEP

Video URL: https://video.toggle.sg/en/series/talking-point-2017/ep23/540809

Talking Point 2017 – EP23

Thu 5 Oct 2017
23 MINS

By Channel 5 Published: 05 Oct 2017 Audio: English

Each year, only the top 1% of the primary school cohort will enter the Gifted Education Programme. Yet scores of parents send their children to preparatory classes in hopes that their child will ace the GEP Selection Exercise. Authorities frown on such courses. Learning centres say there’s overwhelming demand. Can a child be trained to be gifted? And should he? Talking Point gives you an inside look into how primary school students are being prepped to take a screening test for gifted kids.

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Free Movie about PSLE

There are 2 short films on the subject of PSLE, free on YouTube. Quite accurate about the lives of kids in Singapore currently. Do feel free to watch if you are interested.

It is truly a first-world problem (only kids in middle to high income families will suffer from this, as tuition is not cheap), but it does reflect the stress that children go through nowadays.

Look at the child’s timetable: https://youtu.be/FQB7ritn580?t=116. Completely packed from Monday to Sunday. (Quite realistic as I have seen real life examples of such scenarios.)

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More expat students catch the ‘tuition bug’ and other Educational News

More expat students catch the ‘tuition bug’

Singapore has gained a reputation for being a “tuition nation”, with surveys … Mr Shaun Lim, a partner at Quintessential Education, said the “kiasu” …
SUSS to weave social impact into all courses

The Singapore University of Social Sciences (SUSS) will expand its … It provides an applied education approach that targets fresh school leavers and …
NTU alumni to receive $1600 credits each to take up courses

SINGAPORE – About 222,000 alumni of Nanyang Technological University (NTU) will receive $1,600 credits each which they can use for a wide …
How can the public learn more about the history of Chinese education inSingapore?

A new book by the National Library looks back on the development of Chinese education in Singapore, through more than a century’s worth of …
How Singapore Encourages Lifelong Learning and Workforce Resilience

SkillsFuture Singapore (SSG), for example, is a statutory board under the Ministry of Education that provides an array of lifelong learning and …
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Visionary mathematician Vladimir Voevodsky

Math Online Tom Circle

A self-study Russian mathematician, kicked out 3 times in high schools, expelled from Moscow University, all because he did not attend classes, preferred to self-study in a broader scope for his curiosity, at his own faster speed than the rigid curriculum and boring test-and-exams regime in classrooms.

He did the PhD in Harvard by invitation even he did not have a Bachelor degree, and he barely passed the Harvard’s QE (Qualifying Exams) in Algebraic Geometry, a field in which he made a revolutionary discovery few years later, and for which he was awarded the highest honor : Fields Medal.

This is the typical trait of the geniuses like Evariste Galois, Albert Einstein, Ramanujian, Hua Luogeng (华罗庚), Zhang YiTang (张益唐 – proved “70m Twin Prime Gap”) [#] , Chen Jingrun (陈景润, proved Goldbach Conjecture “1+2”) [##]… with self-motivated curiosity in their field of passion, with reading from the Masters’ works…

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Univalent Foundation – Computer Proof of All Maths

Math Online Tom Circle

The scary complex field of Math worried the mathematicians who would prove a theorem relying on the previous theorems assumed proven correct by other mathematicians.

A sad example was Zhang YiTang (1955 – ) who prepared his PhD Thesis based on a previous “flawed” Theorem proved by none other than his PhD Advisor Prof Mok in Purdue University. Unfortunately his Thesis was found wrong, and the tragic happened to Zhang as he had revealed the mistake of his PhD advisor who insisted his (Mok’s) Theorem was correct. As a result Zhang failed the 7-year PhD course without any teaching job recommendation letter from his angry advisor. He ended with a Subway Sandwich Kitchen job offered by his Chinese friend, sleeping in another Chinese music conductor’s house on a sofa. It was there he spent another 7 years thinking on Math, finally an Eureka breakthrough one 2013 morning in the backyard…

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Motif (Motive 目的)

Math Online Tom Circle

Below is an excellent intuitive explanation (in Chinese) of the abstract concept Motif by Grothendieck:

Brief summaryMotif is the source of all “beautiful things” expressed in different forms.

Example : God created Natural Numbers (N), we express N in different forms: Binary (0, 1), Decimal (0, 1, 2 …9), Hexadecimal (0,1, 2…9, a, b, c, …f), etc. However, the “Motif” behind these forms is they all follow : 1) Commutative Law ; 2) Distributive Law.

Similarly, in Algebraic Geometry applying the cohomology from Algebraic Topology: étale cohomology, crystalline cohomology, de Rham cohomology are the different forms (~ Binary, Decimal, Hexadecimal), factored throught the common “Motif” of the Universal cohomology (~N).

[My Analogy in IT Language]:
Motif is like Interface or Generic, it spells out only the specification, leaving out the implementation (method) for actual classes / functions…

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Free Math Games For Everyone

Free Math Games For Everyone

Multiplication of big numbers, complex mathematical problems – there are so many issues that people can face not only at school but also in their everyday lives! People need math everywhere and always! That is why understanding the fundamental principles of math is not less important than being able to read or write! Going shopping or starting your own business – gaining the needed mathematical knowledge and being able to apply it in practice will come in handy for everyone, no matter where they go and what they do!

How to learn this subject? Just like any other science, it requires time and efforts to learn it! However, thanks to the modern technologies and the Internet, everything has become a bit easier today and now, it is enough to find a few useful resources to resolve any academic matters! Some of the most useful resources offer people not only to find the answers for their homework sheets and read the main rules but also to enjoy math games and learn while playing!

Where To Look For Free Math Games For Everyone?

It is not a secret that children of a younger age, perceive the information much better if it is presented in a fun and engaging form, for example, while playing. This explains such a high demand for online educational games. However, not only kids can enjoy free maths games, in fact, many adults will also find such activities quite useful and fun!

What are the other benefits? The platforms that offer you to study maths online by means of playing games will help you to master all the possibilities of mathematics easily – you will learn how to add, subtract, divide and multiply. For kids, such activities will be useful for admission to the school. For adults, such activities can help fill in the gaps that they have in their knowledge!

Below you can find a list of top five free sources where you can learn mathematics fast and easily while enjoying an exciting game right from your browser in the online mode!

Math Playground

The website is convenient. There are many different categories, which make it simple to find suitable activities for everyone, while good graphics make the whole process really fun and enjoyable!

Math Game Time

This is one of the best platforms! All the games are organized by grade, but what really makes this site stand out is a wide range of additional opportunities like problem-solving, shapes and geometry, algebra or time and money games!

Cool Math Games

There are many strategy and logic activities. Also, on this platform, you can find some exciting and useful “skill games” that are aimed at developing the basic mathematical skills, and they can come in handy not only for the children but also for the whole family!

Knowledge Adventure

Unlike the previous platforms, this website offers a wide variety of fun educational activities on numerous subjects, including spelling, reading, science, etc. All the games are bright and colorful. This creates a pleasant atmosphere and will be especially interesting for younger kids. The highest age for games specified on the site is 12. However, some of them will also be useful for grown-ups!

Learning Games For Kids

Although from the first glance it seems like this site is created exclusively for children, I am sure that adult users will also find something interesting and useful for them! There is a wide range of choices. All activities are divided by their goals and grades, and there are also addition and random math activities; such divisions help to navigate through the website with ease and find exactly what you were looking for! There are also many other possibilities. The site also features many vocabularies, art, science, health, brain, literature, and some other activities!

There are just a few sources of many! You can look for more opportunities on the Internet. Find out what options you have – test a few games from different platforms to compare their efficiency, and, without a doubt, you should find something suitable for yourself! Also, if you are enjoying playing on the go – there are numerous applications for tablets and smartphones that you can use at any time and from any place, which will be convenient for busy people!

Final Words

Why is math so important in our lives? It is one of the basic sciences that every person should understand. It does not mean that each of you needs to become well-versed on this subject because if you lack certain skills that are needed to cope with your homework, you can always hire a tutor or turn to www.customwriting.com for academic help. However, having the necessary knowledge base is a must! Without it, you will find it difficult to do the most usual things like count the change in the grocery store, and thus, you will feel less confident!

 

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How to prepare for ASEAN Scholarships Pre-U Entrance Test

Recently I received an email from a reader (name removed for anonymity). Just posting here in case it is useful to other readers. Good luck for those interested in applying for the scholarship!

I am a 16-year old Malaysian student and I am interested in applying for the ASEAN scholarships for Malaysian Pre-University One Scholarships, yet I am lost as to how to prepare for the entrance tests(especially the mathematics test) and thought that i could ask you since I’ve frequently browsed your website for a while and have read that you’re experienced in the O’level and A’level fields of mathematics.

If you wouldn’t mind, I have a few questions to ask:
1. How should i prepare for the entrance tests?(as in what should i study/focus on for the Math entrance test)
2. Is it necessary for me to learn the SEAB A-levels/ JC syllabus? If yes, what textbooks would you recommend me buying in order to prepare for the exam?
3. What is the difference between IGCSE Additional Math syllabus(I’m in the IGCSE class in my school) and the Singapore O’level syllabus?(I’d like to know what I’d possibly be lacking in)

It would be most helpful if you could answer my questions. I hope to hear from you. Thank you!


Here are my answers:

Thanks for visiting my website.

I will try to answer your questions:

1. I think you should focus on the Additional math / Elementary math for O Levels.

2. I don’t think JC syllabus should be necessary as that is usually taught for 17-18 year old students, which should be beyond the scope of the pre-university exams.

3. Overall it should be the same, but there may be some small differences. You may check out this new syllabus: http://www.seab.gov.sg/content/syllabus/olevel/2017Syllabus/4047_2017.pdf

For example, for the Singapore syllabus, there is this sum of cubes/differences of cubes formula that is tested: https://mathtuition88.com/2014/10/27/sum-of-cubes-a-maths-tuition/

For practice questions, you may want to check out this set of papers (with solutions): https://sellfy.com/p/l4w2/

They are representative of what is tested in the Singapore A Maths syllabus.

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Song of Simple Group

Group Theory is abstract, but the song…

Math Online Tom Circle

http://www.youtube.com/watch?v=lJhmJJ_q6Go&NR=1

The lyrics to the song can be found in “Contemporary Abstract Algebra” (Seventh Edition) by Joseph A. Gallian

(ISBN 978-0-547-16509-7) pages 422 & 423.

Simple Group 1

Simple Group 2

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10招教你用Google搜技巧

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