Mathtuition88

Motivational: Bear cub climbs ice mountain to reunite with mama bear

One of the most motivational nature videos of the year!

If you liked this video, you should also like this Iguana vs Snakes video:

Useful Things to Know About Science Centre Singapore Before Visiting

Singapore has a reputation for not only being one of the most toured countries in Asia, but also for being a perfect place to incorporate a business. This is strongly attributed to its excellent tourist spots and also regulations that can allow even a foreigner to set up a business in Singapore. If you are a foreigner, you just need a Visa Express entrepass to start a new business or to relocate an existing one to Singapore. If you want to take a vacation in the next few months, then Singapore is the perfect place for you to go. If you are traveling with your children, you can rest assured that the kids will have an unforgettable experience from all the fun they will have. One of the places you can visit is Science Centre Singapore, situated at Jurong East, which is a museum full of exhibitions and learning opportunities for children. If you want to visit this place, here are some useful things you need to know.

1. Free entry for Singaporeans and permanent residents on specific days
When is the right time for you to visit Science Centre Singapore? If you are a Singaporean or a permanent resident, it is recommended that you visit during the off-peak days when you are not required to pay any entry fee. The off-peak days are usually normal weekdays during school time, excluding all public holidays. School holidays, public holidays, and weekends are usually the peak days, and visiting at these times means you will have to pay an entry fee. However, if you are a Singaporean or a permanent resident, you will still get a discounted entry fee during the peak days.

2. Extra admission charges
There are special exhibitions in Science Centre Singapore located at the Annex, which require extra fees if you want to view them. Science Centre Singapore also has areas like the Butterflies Up-Close Exhibition, which likewise demands additional entry fees.

3. Closed dates
Science Centre Singapore is open almost year-round, but it is closed on certain dates each month of the year. While most of these closure dates usually fall on Mondays (but not every Monday), it is recommended that you visit Science Centre Singapore’s website in order to get a full schedule outlining the closure dates. This is to make sure that you avoid making a trip there when it is closed.

4. Science shows
For the entire day, Science Centre Singapore conducts engaging science shows for its visitors. These shows include the dramatic and electrifying Tesla Oil Demonstration, as well as the Fire Tornado Demonstration. Just like with the closure dates, you can check out their website to find out the times for the shows.

5. Where to eat
You may be planning to spend a full day at Science Centre Singapore, and it is thus convenient to know where you can have your meals. The most convenient joints are the Coffee Bee, located at the Annex, or McDonald’s, situated at the main entrance. For additional dining options, you can go to the Omni Theatre Building, where you will find the Lijiang Restaurant and a kids’ cafe.

How to Change UOB Card PIN Number

How to change UOB ATM PIN

It is recommended to change your UOB PIN number/password immediately upon receipt of the mailer. However, it is not very clear how exactly to change your UOB Debit Card PIN number.

The answer is that it is not possible to change the UOB PIN number online. (I called the UOB customer service at 1800 222 2121 to find this out.) Changing the UOB PIN Number is only possible at a UOB ATM machine.

How to change UOB Phone Banking PIN

Same as above, UOB Phone Banking PIN cannot be changed online. It can be changed at any UOB ATM machine.

The Phone Banking “Username”, or “Access Code” as it is called, is your NRIC number (numerical digits only, without “S” or the final letter).

Factorize 2^n-1 (when n is composite)

How to Factorize 2^n-1

If $n$ is composite, we may write $n=ab$ where $a,b>1$ .

Then,

$\begin{aligned} 2^n-1&=2^{ab}-1\\ &=(2^a-1)(1+2^a+2^{2a}+2^{3a}+\dots+2^{(b-1)a}). \end{aligned}$

The key point is that both factors are greater than 1.

Example

If $a=2, b=5$ , we can see that $2^{10}-1=1023=(2^2-1)(1+2^2+2^4+2^6+2^8)$ .

How to Remember this Result

The hard part is remembering this identity: $\boxed{2^{ab}-1=(2^a-1)(1+2^a+2^{2a}+2^{3a}+\dots+2^{(b-1)a})}$ . It is essentially a “telescoping sum”, and you can prove it by expanding the right hand side and cancelling all like terms.

We can also view it as a Geometric Series as follows: $\dfrac{1((2^a)^b-1)}{2^a-1}$ is the sum of a Geometric Progression with first term 1, and common ratio $2^a$ , for a total of $b$ terms. That is,

$\dfrac{1((2^a)^b-1)}{2^a-1}=1+2^a+2^{2a}+\dots+2^{(b-1)a}$ . Multiplying both sides by $2^a-1$ gives the boxed result.

Applications

Primes of the form $2^n-1$ are known as Mersenne Primes. Using the result above, we can show that if $2^n-1$ is a prime, then $n$ is a prime. (We prove the contrapositive: If $n$ is composite, then we show that $2^n-1$ is also composite.)

Ohm $20 Promo Code: OHMREF25CC5A

*Ohm Promo Code: OHMREF25CC5A

After extensive research, I find that Ohm is one of the best alternative electricity suppliers. Choose either Fixed Ohm or Discount Ohm depending on your likings. I chose Discount Ohm as I have a feeling that the tariffs may drop. Fixed Ohm is also very good, and in fact better if tariffs rise.

Benefits of Ohm:

Their discount off tariff rate is currently the best at ~~22%~~ (Update: discount is now 25%)!
Very smooth transition as they are partners with SP group. For instance, there is no need for any paper work nor additional payment of deposit.
Very nicely done website. Signing up is immediate, just fill in some personal details online and you will get the Welcome Email in less than 15 minutes.
Ohm absorbs the transmission loss. (Basically electrical energy is lost as heat while travelling through the cable, Ohm absorbs this and charges consumer based on metered usage. This is worth approximately 3.4% savings.)
3-month trial period. If within 3 months you decide to change plans, there is no penalty. Hence, you are not locked in to a fixed price which may turn out to be undesirable.

Use my Ohm Referral Code to get $20 off: OHMREF25CC5A

Fixed Rate vs Discount off Tariff

Currently (1st November 2018), Ohm fixed rate is 18.14 cents/kWh (incl. GST) while the Discount off Tariff (22%) is effectively 20.14 cents/kWh (incl. GST).

However, it is not impossible for the SP Tariff to drop (see graph below). If the SP Tariff drops, say to 20.20 (excl. GST) which is the Jan 2017 price, then 22% Discount off Tariff would be effectively 16.86 cents/kWh (incl. GST) which beats the fixed rate! (Working: 20.20 x 1.07 x 0.78=16.86)

Nobody knows for sure whether the SP Tariff will drop as it depends on a lot of complex factors including oil price, etc. However, currently with 12 electricity providers in a small country like Singapore, there is a great deal of competition, and SP is likely to lower its price to remain competitive.

Historical SP Tariff (excluding GST). Source: SP Group

Conclusion: Choose Ohm

Everyone should change a supplier in the open electricity market for savings. There are no drawbacks of doing so. In particular, there is no such worry of “blackouts” or “unreliable electricity supply” as SP group is still operating the national power grid.

Scientists Use Math To Discover Why BTS Jin Is The Most Handsome

Recently, the hottest topic in Singapore is “BTS concert”. BTS is a Korean band that is extremely popular among the young students in Singapore. The BTS tickets in Singapore are completely sold out in less than 4 hours. (Possibly there are many people “scalping” tickets for resale, also known as “Yellow Cow Tickets” 黄牛票.)

Fans of BTS are known as “The Army”.

According to this website, Korean scientists have “mathematically” proven why Jin, a member of BTS, is the most handsome of all. His nickname is “worldwide handsome”.

Essentially, the idea is using the Golden Ratio, a special number that appears frequently in nature. See also our previous posts:

Source: Koreaboo

A plastic surgeon has reported that he studied 269 Asian male faces and concluded that BTS’s Jin is scientifically the most proportional and handsome Asian face.

The doctor mentioned 1:1.618 as the “golden ratio” for having a perfectly proportional face. Most often, when applied to facial symmetry, this ratio uses the measures of the width from one ear to the other (1) and for the hairline to the chin (1.618)… And Jin’s face exactly measures up.

Many of BTS videos have hundreds of millions of views. This is one of them:

The Hardest H3 Math Question (Combinatorics)

I think this may be one of the hardest H3 Math Questions in history. It is taken from RI H3 Prelim 2018. It seems that even in top schools like RI, there are less than 50 people taking H3 Maths in any given year. Part (d) is extremely hard to get the formula for general r. In fact during the exam it is probably wise to skip such questions or give partial answers (e.g. the formula for r=3) as it is not worth the time for 3 marks.

Test your Circuit Breaker today; Circuit breaker can save you from electrocution

Do forward this to your family and friends. Especially for older homes, the circuit breaker could have broken down silently without anyone noticing.

Source: https://www.straitstimes.com/singapore/circuit-breaker-could-be-a-lifesaver

Pressing a button at home regularly could save your life.

This is the “test” button, typically denoted by a “T” on the circuit breaker, a safety device found in all households and buildings.

If you press that button and all electricity cuts off, that means it is functioning. A working circuit breaker will cut off electricity in the event of a current leakage, like when someone touches a live wire, minimising the chances of fatal electrocution.

New York Professor: Blockchain is a lie, and the least useful technology

The most famous application of Blockchain is “Bitcoin”. Whoever bought just $1000 worth of Bitcoin around year 2010 would be a millionaire now. However, other than “Bitcoin” and cryptocurrencies, blockchain technology do have other uses. So is blockchain useful or not? Only time will tell.

Integration by parts, DI method

This DI method is American way, better than the UK Cambridge O level technique.

Math Online Tom Circle

(Traditional Method learnt at O-Level) Integration by Parts:

NEW Technique taught by this UC-Berkley Chinese Mathematician: “DI” Method

First Stop: “D column at…“

2nd Stop:

3rd Stop:

$latex displaystyle int {e^{x}}sin {x} dx$

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The Best Movies For Mathematicians

Math Online Tom Circle

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Analysis by Timothy Gowers

Math Online Tom Circle

Why easy analysis problems are easy
by Timothy Gowers (UK, Fields Medal 1998)

Timothy Gowers is teaching in Cambridge, he wrote the thick volume of “Princeton Math Encyclopedia.”

He is a very good mathematician, who likes to explain simple fundamental Math questions (like why 2+2=4, multiplication is commutative,…), in the process making abstract math simple to understand.

“If you have recently met epsilons and deltas for the first time, then you may find the problems you are asked to solve on examples sheets very hard. On the other hand, you will notice that your lecturers, supervisors etc. do not find them hard at all. Why is this? ” Read on …

https://www.dpmms.cam.ac.uk/~wtg10/autoanalysis.html

Below is my attempt to rewrite the Example 1 with Latex epsilon-delta notation for easy reading.

Example 1.

I wish to prove that the sequence (1,0,1,0,1,0,…) does not converge.

$latex text{Let me set the sequence }

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Book of Wisdom

1 Wis 7:7-11 (Book of Wisdom or “Wisdom of Solomon”)

I prayed, and prudence was given me; I pleaded, and the spirit of wisdom came to me.

I preferred her to scepter and throne, and deemed riches nothing in comparison with her, nor did I liken any priceless gem to her; because all gold, in view of her, is a little sand, and before her, silver is to be accounted mire.

mire – deep mud

No Exams Singapore

The latest policy update is that there will be reduced or no exams for certain levels such as lower primary and lower secondary.

Do check out our Poll writeup for more details: Poll: Opinion on Fewer exams for Primary and Lower Secondary Students?

It seems that it is quite a dilemma; parents find exams stressful, yet exams are viewed as necessary by most parents to measure how their child is learning. According to Today Online, tuition centres have great success offering their own “in-house exams” to fill in the gap. At the end of the day, the “big exams” like PSLE, O-Levels, A-Levels are still present, and that is the major feature in the education landscape.

It is quite like “lump sum payment” (single exam at end of the year) versus “payment by installments” (multiple exams throughout the year). In the end, the full sum still has to be paid (students still have to study the material to pass the final exam).

Inequalities : RMS, AM, GM, HM

Math Online Tom Circle

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Integral of x^x from 0 to 1

Math Online Tom Circle

$latex boxed {displaystyleint_{0}^{1}{x^{x}dx }= frac {1}{1^1} – frac {1}{2^2} +frac {1}{3^3} – frac {1}{4^4} + frac {1}{5^5} +…}$

$latex boxed {displaystyleint_{0}^{1}{x^{-x}dx }= frac {1}{1^1} +frac {1}{2^2} +frac {1}{3^3} + frac {1}{4^4} + frac {1}{5^5} + …}$

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10 cents Mr Bean Soya Milk (with Masterpass @ Qoo10)

A small reward for yourself/ your children this October? Coupled with the ongoing Masterpass promotion ($1 off) at Qoo10, and this Mr Bean promotion, the soya milk ends up costing only 10 cents!

This is probably the cheapest drink in Singapore currently! (other than NEWater 🙂 )

URL: https://qoo.tn/BSSwbR/Q100000595

[$1.10](▼48%)[Mr Bean][ 10.10 Special ] Grass Jelly Soya Milk or Classic Soya Milk – $1.10 only!

WWW.QOO10.SG

H3 Mathematics Resource Page

H3 Mathematics is the pinnacle of the Junior College Mathematics syllabus in Singapore. It contains a glimpse of actual Math that Mathematicians do, and it requires true mathematical understanding and technique to do well. (H1/H2 math requires a lot of practice, but not true understanding. It is quite common for students to “apply the method” and get the correct answer without having any idea of what they are actually doing.)

Topics in H3 Mathematics include Functions, Sequence and Series, Combinatorics, and even Number Theory. Certain schools also include topics like Linear Algebra and Differential Equations. Certainly, the H3 Math questions have a Math Olympiad style to them.

Here are some practice questions for H3 Math (more will be added in the future), with some hints. Questions are adapted from actual H3 prelim papers.

Functions

Q1) The function $f$ is such that $f(x+2)=af(x+1)-f(x)$ , for all real $x$ and some constant $a$ .

(i) In the case that $f$ is a linear function, find all possibilities for $f$ and $a$ .

(ii) In the case that $f(0)=0$ and $|f(1)|=1$ , use mathematical induction to prove that $f(n-1)f(n+1)+1=[f(n)]^2$ for all positive integers $n$ .

(iii) In the case that $a=2$ , sketch one possibility for $f$ which is not linear.

Hint:

(i) Write $f(x)=mx+c$ and substitute it into the question. You should reach two cases, $a=2$ or $m=0$ . For the case $a=2$ , there is no other restriction. For the case $m=0$ , either $a=2$ or $c=0$ .

(iii) Try a step function.

Sequence and Series

Combinatorics

Q1) Mr H uses a software to generate distinct codes of the form $\overline{x_1x_2x_3x_4x_5}$ , where $x_i\in\{0,1,2,3,4,5\}$ . What is the least number of codes Mr H should generate such that there are at least two distinct codes that satisfy: $\boxed{x_1+x_3=x_2+x_4}$ . [3 marks]

Hint: No, the answer is not 12. Draw a possibility diagram for $x_1+x_3$ , essentially a table with 6×6=36 entries detailing what combinations are there for $x_1+x_3$ . Then list cases (a popular technique for combinatorics), based on each value of $x_1+x_3$ . For example, the case $x_1+x_3=0$ only has 1 option namely $x_1=x_3=0$ . Then $x_2+x_4$ can have 35 other options such that $x_2+x_4$ is different from $x_1+x_3$ . The last digit $x_5$ has no restrictions so there are 6 options. Hence the total number of ways for this case is 1x35x6=210. Finally, after adding up all the cases, use pigeonhole principle (add one) to conclude the answer, which is 6901.

Q2) See The Hardest H3 Math Question (Combinatorics)

Number Theory

Q1) Let m, n, M and N be positive integers. Given that gcd(M,N)=1 and $mN^2=nM^2$ , use Mathematical Induction to show that $M^2\mid m$ and $N^2\mid n$ . [5 marks]

Hint: First prove for the trivial case M=1 or N=1. Then write $M=p_1p_2\dots p_k$ and $N=q_1q_2\dots q_l$ , where $p_i$ , $q_j$ are primes. Use Euclid’s Lemma twice to prove that $p_1^2\mid m$ . By induction, show that $M^2\mid m$ . I think the key point is that Generalized Euclid’s Lemma is probably not allowed otherwise it is very easy.

My favorite Fermat Little Theorem with Pascal Triangle

Math Online Tom Circle

Fermat Little Theorem: For any prime integer p, any integer m

$latex boxed {m^{p} equiv m mod p} &s=3$

When m = 2,

$latex boxed{2^{p} equiv 2 mod p}&fg=aa0000$

Note: 九章算数 Fermat Little Theorem (m=2)

Pascal Triangle (1653 AD France ）= (杨辉三角 1238 AD – 1298 AD)

$latex 1 : 1 implies sum = 2 = 2^1 equiv 2 mod 1$

$latex 1: 2 :1implies sum = 4 = 2^2 equiv 2 mod 2 ;(equiv 0 mod 2)$

$latex 1 :3 :3 :1 implies sum = 8= 2^3 equiv 2 mod 3$

1 4 6 4 1 => sum = 16= 2^4 (4 is non-prime)

$latex 1 :5 :10: 10: 5: 1 implies sum = 32= 2^5 equiv 2 mod 5$

[PODCAST]

https://kpknudson.com/my-favorite-theorem/2017/9/13/episode-4-jordan-ellenberg

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Math Challenge: Teaching Subject

Math Online Tom Circle

[Hint] : Assume 3 cases, then by Elimination using Mr Brown’s hint (somethingS right, somethingS wrong)

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Math Paradox : Toroflux

Math Online Tom Circle

Fibonacci Number 1 1 2 3 5 8 13 21…

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Backpack/School Bag Review: Targus Pandora

This bag (Targus brand) is very affordable at $19.90 (limited time only). It is suitable for students and even working adults, who would like a backpack that can store securely a laptop. It even has a raincoat (!!!) to protect your bag against the heavy rain that is so common in Singapore.

Students in Junior College, Polytechnic, and University will likely find it very good and useful since they have to bring their computer laptop to school. It can store a lot of books/laptop equipment such as wires, chargers, etc.

Do grab it fast if you like it, it is available on Qoo10 for a limited time only. From my experience, there is no where else online/or in retail where you can get such a good deal in terms of laptop bags.

URL: https://qoo.tn/BawdbR/Q100000595

[$19.90](▼67%)[Samsonite]Authentic Samsonite n Targus Backpack / Laptop Backpack / Laptop Bag / Unisex / School backpack

WWW.QOO10.SG

How do students in Singapore from the Express, Normal Academic and Normal Technical streams perceive each other?

Recently, this CNA (Channel News Asia) video is very popular on YouTube. Do check it out. Basically, due to the segregated nature of the education system, GEP, IP (Integrated Programme), Express, Normal Academic and Technical students rarely mix with each other, if at all. Hence, there may be some prejudices and biased views from each side towards the other.

A more in depth official commentary can be found here: https://www.channelnewsasia.com/news/cnainsider/regardless-class-race-religion-survey-singapore-income-divide-10774682

In light of this, the story of From PSLE 124 to PhD A*Star Researcher is very remarkable, on how a student overcame prejudices from society to reach his full potential. Do read it if you haven’t.

No More Recontract Voucher from Singtel? Best Phone to Recontract and Sell

It is an “open secret” last time that if you call the Singtel customer service hotline at 1688, they may give you a recontract voucher for you to get a new phone. In previous times it used to be as high as $100, then over the years it slowly reduced to $50. It seems that the voucher is gone now, for low usage customers (e.g. Combo 2 plan). That is, no more recontract voucher. That was my experience in September 2018. That being said, experiences may differ from user to user, you may still want to phone in to try your luck. The only reason I am still using Singtel is that the rest of my family is on the “Singtel Circle” plan.

Important Update: There is a new form of voucher, called the Singtel Referral Voucher, worth $100! Basically you switch to a new Combo Plan and get $100 off the phone.

Best Phone to Recontract and Sell Off

Traditionally, the best phone to recontract and sell has always been the latest iPhone. This is based on the strong demand for iPhone. For instance, as of now, the most popular seems to be iPhone XS, Gold color, 256 GB. Do take note of the color/storage size as unpopular combinations may fetch a lower price. At the time of writing, recontracting and selling an iPhone may earn as much as $300 or more (buy at $1338 and sell off at $1640).

How to get Singtel Voucher (2019 onwards Method)

Are you still looking for the elusive Singtel Discount Voucher to offset your phone purchase? Do not bother to call 1688 anymore, that is the old-school method that does not work nowadays (you can still try if you want, you will find it hard to even speak to a human Singtel operator).

The new method is to use the Singtel Referral Voucher which is worth $100. Click here to go directly to the official Singtel website where your $100 voucher will be applied automatically.

Poll: Opinion on Fewer exams for Primary and Lower Secondary Students?

I have added a poll to see what readers think of this new proposal?

Actually mid-year exams and assessments may have a role as a “buffer” to reduce the weightage of the final exam. Removing mid-year exams actually has the effect of transferring more weightage to the final exam, making it more stressful? It boils down to whether people prefer a grading based on 100% weightage for final year exam, or something like 30% mid-year, 20% assessments and 50% final exams. Based on personal experience, many students (including myself) do prefer having a mid-year exam so that their results of the year is not entirely based on the final exams.

Also, for people who are natural procrastinators, who tend to do things at the last minute (possibly around 90% of the human population?), cancelling exams at the Primary 1 and Primary 2 level may end up causing a false sense of security, leading to a frantic panic attack at Primary 3? As a tutor, I receive numerous tutoring requests as late as September/October (for the final year exam), hence I know that numerous students/parents tend to panic at the last minute due to procrastination.

Possibly a worst case scenario that can end up is that the child does not learn well the fundamentals during P1 and P2, and this is undetected by his/her parents due to the absence of exams. Suddenly at P3, the reality is unveiled and it comes as a sudden shock. The P3 student has to catch up with the two years of fundamentals (P1 & P2) quickly before it is too late, as many subjects are cumulative in the sense that P3 topics relies on previous knowledge of P1 and P2 material.

Nonetheless, it is a new policy and it is good to see some changes coming that is intended to reduce the stress of young students. The time “saved” from doing exams can potentially be channeled into learning something new that is not found in the traditional syllabus. Scrapping the class/level position is good, there is no need to be obsessed with being “first” in class at such a young age. Possibly a percentile grade is still necessary for parents to gauge how their child is doing. Keeping PSLE is also good, despite PSLE being stressful it is actually a meritocratic system that theoretically allows a talented student from a poor family to rise to the top.

Source: Channel News Asia

The changes will be implemented in stages, beginning with the removal of all weighted assessments and exams for Primary 1 and 2 students from next year. Weighted assessments, said MOE, can take various modes such as class tests, presentations or group projects.

Currently, Primary 1 students do not have exams, but weighted assessments are conducted throughout the year. Primary 2 students now have weighted assessments throughout the year, as well as a year-end exam.

Secondary 1 students will also no longer have a mid-year examination from next year. From 2020 and 2021, this will also be removed for Primary 3, Primary 5 and Secondary 3 students.

Read more at https://www.channelnewsasia.com/news/singapore/exams-assessments-scrap-mid-year-primary-secondary-schools-10767370

Chope.co Review

Chope.co is a restaurant reserving website that provides diners with benefits and rewards for reserving their seats at restaurants! “Chope” is a Singlish slang for “reserving a seat”. Reserving a seat is often important since the majority of Singaporeans eat out on weekends/weekday dinner/and special occasions. This means that the restaurant is crowded during those popular times, and failing to reserve a seat may mean long waiting times or even worse, not finding a seat.

Join me on Chope and earn a SGD$10 restaurant voucher!

Fulfill your first Chope reservation and earn a SGD$10 restaurant voucher after dining. Simply book through Chope using this link https://cho.pe/hna9y and you’re all set.

Cool Fact: Cockroaches are becoming Endangered/Extinct in Russia (and other post-Soviet states)

Quite amazing that the cockroach, which is one of the most hardy animals, is actually becoming endangered/extinct in Russia? Possibly the cold weather has something to do with it, in addition to modern technology. Any Russian readers would like to confirm that this is true?

A side note that in tropical Singapore, cockroaches are far from endangered despite frequent fuming and spraying of insecticides, usually at the rubbish chutes. In fact, in most HDB apartments, spraying insecticides at the rubbish chutes actually may increase the number of cockroaches in the house due to those escaping/flying from the rubbish chute where they ordinarily live.

Source: https://en.wikipedia.org/wiki/Depopulation_of_cockroaches_in_post-Soviet_states

Quote: A mass depopulation of cockroaches has been observed since the beginning of the 21st century in Russia and other countries of the former USSR. Observers have noted a quick disappearance of various types of cockroaches from cities and towns in Russia, Azerbaijan, Kazakhstan, Ukraine, Moldova, and Belarus.

Another source: http://www.pravdareport.com/society/stories/09-09-2009/109175-cockroach-0/

Quote: House cockroaches began to disappear in Moscow during the beginning of the 2000s. Many Russians were even making jokes about it saying that it was one of advantages of Putin’s regime.

What is Riemann’s Hypothesis ?

Math Online Tom Circle

［中文］历史 History:

Sir Atiyah Proof on 2018 September : (5 Pages PDF download here)

https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY/view

Bigger Lecture Notes video (at 34 mins, inspired in Singapore)

Analytic function: preserve angle after transformation

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From PSLE 124 to PhD A*Star Researcher

Source: A-star Official Website

For those familiar with the Singapore education system, you would know that PSLE 124 is not a good score by any standard. Yet Dr Vincent Lim, through his hard work and perseverance, managed to push on and graduate from university with first class honours, eventually earn a PhD and land a job at the prestigious A*STAR’s Institute of Medical Biology.

I believe the chances of this happening is truly rare in Singapore, possibly even rarer than striking 1st prize in TOTO. Singapore’s education system is known to be not too forgiving, once you make a “slip”, it is hard to get back onto the fast track. It must have taken tremendous courage, perseverance and hard work to overcome the odds to achieve this.

Truly amazing! Do share this to encourage those with children not doing too well in primary school. Certainly, late developers do exist and if given the right environment and nurturing support, they can blossom to reach their fullest potential.

Inspirational quote:

My advice for people who didn’t do well in school is this: it’s never the end. Society may sometimes seem to say: ‘This is your one job, you need to do well in school!’ But that’s not true. There’s never just one job; that’s not the reason you were born for.

Grades are not the most important thing. It is merely a stepping stone; if you’ve got no stone to step on, then run, jump, and climb. What is important is to never give up on yourself and to always keep your options open.”

-Dr Vincent Lim

Get Official Ivy League (U Penn) degree online

Source: The Inquirer

Note that this is the first time an Ivy League university is offering a full degree online. Previously, some universities do offer some module credit or unofficial courses online, but this time University of Pennsylvania is offering its new bachelor of applied arts and sciences degree online.

Do check out their official course page here: Penn LPS Online.

So far I don’t see any restriction on nationality, that means possibly Singaporeans can apply too.

Some pointers that you may want to take note:

If post-secondary credentials are from an institution outside the US, transcripts must be evaluated on a course-by-course basis by World Education Services, Inc. (WES).
BAAS students are only required to come to campus for two extended weekends as they complete the program.

Varignon’s Theorem (Surprising Geometry Theorem)

I first learnt it from Quora:

“Take any quadrilateral. It doesn’t have to be any special kind of a quadrilateral. Then connect the midpoints of its sides.

Surprisingly, you will always get a parallelogram!”

Quite a nice result. Some googling revealed that the name of this theorem is called Varignon’s Theorem.

An illustration is found here:

RI vs HCI vs NUSH

Many excellent P6 students will be spoilt for choice at this stage, as they have been accepted by multiple schools under the DSA. Here are some views on RI versus HCI versus NUS High, which are the top 3 choices for boys strong in math/science:

RI emphasize “all-rounder” and “leadership” in their culture. My personal experience is that it can get a bit competitive since many people there are literally good in all forms of studies (all subjects in humanities/sciences/languages maybe except Chinese), sports, and music, etc. The culture is similar in RGS. I find that there are some cultural and personality differences between the typical RI/RGS student and the typical HCI/NYGH student.

The good points are that RI does have a lot of activities and opportunities like overseas school trips, top coaches for most CCAs, etc, that many schools don’t have. Also, many RI students are successful in securing government scholarships for top universities since their portfolio will be built up in a balanced way during their studies; there are many Community Involvement Programmes and other activities to boost the student’s portfolio.

Certainly NUSH and HCI are very good schools too. Possibly advantages of NUSH is greater focus on science/math and advantage of HCI is greater emphasis on Chinese culture and tradition, which is useful as China is becoming a world power.

Maybe you can check out this thread on RI vs HCI: https://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=48&t=25209&start=370.

Sir Michael Atiyah to reveal his awesome proof of the Riemann Hypothesis

Source: https://twitter.com/HLForum/status/1042670700652318720

According to the official twitter account of the Heidelberg Laureate Forum, Sir Michael Atiyah will prove the Riemann Hypothesis during the talk on Monday Sept. 25.

According to him, it is a “simple” proof, based on previous work by von Neumann, Hirzebruch and Dirac. It is likely to have some relation to theoretical physics, since Dirac is a theoretical physicist. It has been rumored for quite some time that the Riemann Hypothesis is related to theoretical physics.

The Riemann Hypothesis is the most famous and most difficult problem in mathematics. Sir Michael Atiyah is a 89 year old gentleman currently. It will be really groundbreaking if the Riemann Hypothesis is found to be successfully proved.

Do check out our previous posts on the Riemann Hypothesis:

Amazon Founder Jeff Bezos Originally Wanted to be a Theoretical Physicist

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

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

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

Also check out our previous posts on Partial Differential Equations:

NTUC Income Insurance Review

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

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

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

Key Product Highlights:

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

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

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

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

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

URL: Official NTUC Insurance Website

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

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

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

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

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

Source: Today

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

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

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

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

Life Beyond Grades (http://lifebeyondgrades.sg/)

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

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

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

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

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

The most addictive theorem in Applied mathematics

Math Online Tom Circle

What is your favorite theorem ?

I have 2 theorems which trigger my love of Math :

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

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

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

https://blogs.scientificamerican.com/roots-of-unity/the-most-addictive-theorem-in-applied-mathematics/

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Win Mercedes-Benz CLA 180 Coupé by donating to charity

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

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

To take part, go to their official website at: https://www.given.company/.

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

WiFi Password = Integral Answer

Math Online Tom Circle

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

Can you solve it?

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

I = A(x) + B(x)

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

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

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

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

Let x = 2 sin t => dx = 2 cos t. dt
x = 2 = 2 sin t => sin t = 1 => t = π/2
x = 0 = 2 sin t => sin t = 0 => t =…

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

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Alibaba launches scholarship programme in S’pore with generous funding

Source: Today Online

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

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

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

The official application page and other details can be found on the NTU webpage: http://www.ntu.edu.sg/alibaba-NTU/PhD-application/Pages/index.aspx.

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

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

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

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

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

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

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

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

% !TEX encoding = UTF-8 Unicode

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

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

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

“Critical ctex error:”fontset-unavailable

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

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

Hyperref Problems with Chinese TeX

A known problem is that hyperref does not work well with xetex or xeLaTeX. This may be a problem if you are using xeLaTeX in conjunction with Hyperref. The proposed solution is to use the option

\usepackage[xetex]{hyperref}

Note that if you have multiple options for hyperref, xetex should be the first of all the options.

TeXShop opens Chinese documents showing Gibberish

This is quite common, especially if your Mac or Windows system is not set with Chinese as primary language. A proposed solution (there may be a better solution) is to:

Set the primary language of your Mac / Windows as Chinese. The entire system, including all your taskbars, icons should be in Chinese.
Open the TeX file containing Chinese characters with Notepad/TextEdit, not TeXShop. Ideally, the Chinese characters should display ok there.
Copy and paste the entire file from NotePad to TeXShop.
Add the line % !TEX encoding = UTF-8 Unicode at the start of your TeX document to ensure that the Chinese characters will continue to stay there after closing of the document.

Chinese Lessons in Singapore (Video)

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

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

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

Notable Quotes:

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

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

Read more at https://www.channelnewsasia.com/news/singapore/singapore-chinese-syllabus-changed-back-to-school-10664986

[Quora] Common Core Math

Math Online Tom Circle

Why did the approach to mathematics change with Common Core, rather than providing more structure to how it was previously taught? by Peter Kruger

https://www.quora.com/Why-did-the-approach-to-mathematics-change-with-Common-Core-rather-than-providing-more-structure-to-how-it-was-previously-taught/answer/Peter-Kruger?share=84fb2ef6&srid=oZzP

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Spot The Mistake?

Math is rigor. Where went wrong?

Math Online Tom Circle

Solve:

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

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

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

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

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

=> 2 = 3

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GEP PSLE Discussion

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

Does GEP help PSLE?

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

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

Viewpoint 1: GEP helps PSLE but not directly

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

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

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

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

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

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

(by entei17) Does GEP help PSLE

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

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

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

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

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

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

– Does GEP help DSA

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

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

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

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

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

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

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

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

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

Solution

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

Where to buy dumplings (饺子) in Singapore

新加坡哪里有卖饺子

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

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

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

Do check out their 10 different flavors!

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

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

WWW.QOO10.SG

Morse Inequalities

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