## English Fun Math

Different Maths:
1. English (UK/USA) Math is playfully tricky (Math Olympiad, Math Puzzles eg. this Numberpile video)

2. French Math is abstractly theoretical (Group theory explains Symmetry, Rubik’s cube game,… )

3. Chinese Math (Abacus, “Chicken-Rabbits Problem” 鸡兔问题, Singapore Modeling Math) is applied & procedural (明朝 13CE invented “Determinant” 行列式 before the 19th CE “Matrix” by UK Sylvester，Chinese Remainder Theorem 韩信点兵).

4. Indian Math (Vedic Math , Factorization, Ramanujian-Style Math) is mysteriously spiritual.

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## AI with Advanced Math helps in discovering new drugs

Posted in Uncategorized | 1 Comment

## Why French excel in math ?

Mathematics and quantitative finance, France

Since 1990, there have been 22 winners of the Fields Medal, widely regarded as the Nobel Prize of mathematics. Thirteen came from just two countries, Russia and France. Russia has more winners (seven), but more than twice the population, so the honours go to France, with six winners.

Cédric Villani, the 2010 Fields Medallist, cited national character. “Maths is an abstract way of looking at the world, which fits well with the French mentality. We apply algebra to everything.” Elite institutions help too. France’s brightest school leavers progress to the grandes écoles, which traditionally educate top scientists, administrators and presidents. For maths, you want Monsieur Villani’s alma mater, the École Normale Supérieure (ENS). All 10 French Fields Medallists learnt there. At ENS, no teacher can stay longer than 10 years. Instead of ancient dons, students get tutors at the forefront…

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## Percentage Mental Calculation

Example:
4% of 75 = 75% of 4

Mental Steps:
75 x 4 – > 300 – > / 100 – > ＝ 3 (ANS. )
Is it easier ?

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## The Laws of Mathematics Zermelo-Fraenkel Axioms Set Theory

The Foundation of Modern Math which is based on the “Set Theory”, hit a crisis due to Bertrand Russell “Barber’s Paradox”, until the Zermelo-Fraenkel Axioms came to its rescue.

Here is a humorous example of an ISP Internet Plan violating the 9 Z-F Axioms:

How ISPs Violate the Laws of Mathematics:

Video:

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## 通俗群论

Challenge: Put ’15’ and ’14’ in the right sequence (Impossible! )

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## “Essential mathematical GIFs that will make mathematics finally make sense”

“Essential mathematical GIFs that will make mathematics finally make sense” by Ali Kayaspor https://link.medium.com/z1nWgHm9GU

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## Best Machine Learning / Deep Learning Books

After some research, I find that the best book on Machine Learning / Deep Learning currently on the market is: Deep Learning with Python.

It is written by François Chollet, who is the creator of the famous Keras library (Google Tensorflow). The most popular language for machine learning is currently Python, which is the subject of this book. (Another language is R, but many people find R to be less user-friendly as compared to Python).

The book is suitable for those who are studying deep learning from scratch, with zero prior knowledge. Currently, machine learning is at the peak of its hype, with many employers seeking to utilize machine learning in one way or another. It is very useful for students to pick up this skill for potential usage in the future.

A key competitor to Keras/Tensorflow is Pytorch, developed by Facebook. It is supposedly even more user-friendly than Keras/Tensorflow. However, the drawback is that it is too new and few books/tutorials exist.

Posted in Uncategorized | 1 Comment

## Alexa Ranking Below 1 Million

Thanks to all readers, Mathtuition88 has reached Alexa Rank of below 1 Million!

Current Global Rank: 983,883

SG Rank: 11,701

This is the first time Mathtuition88.com has broken the 1000,000 Alexa Rank barrier.

For ranking, the lower the better. For instance Google is ranked number 1, and YouTube is number 2. Facebook is ranked number 3.

## Powerpac Ceramic Cooker Review

This should be the cheapest ceramic cooker on the market. PowerPac is a reliable Singaporean brand that has been on the market for quite some time.

At the price of $29.90, the Ceramic Cooker even comes with a free stainless steel pot with cover (CNY Promo). Unbeatable price! It is also free delivery. It is ideal for home steamboat / hotpot cooking. By the way, ceramic cooker can cook all types of pots and pans (unlike induction cookers). [S$29.90](▼51%)[PowerPac Promo]PowerPac Ceramic Cooker (Any Pot) 2000 Watts (PPIC833) //Suitable for any use with any types of pots

WWW.QOO10.SG

## Free Philips Air Fryer (Enfagrow Promo)

Official URL: Enfagrow Homepage

## Group Theorems: Lagrange, Sylow, Cauchy

1. Lagrange Theorem:
Order of subgroup H divides order of Group G

Converse false:
having h | g does not imply there exists a subgroup H of order h.
Example: Z3 = {0,1,2} is not subgroup of Z6
although o(Z3)= 3 which divides o(Z6)= 6

However,
if h = p (prime number),
=>
2. Cauchy Theorem: if p | g
then G contains an element x (so a subgroup) of order p.
ie.
$latex x^{p} = e$ ∀x∈ G

3. Sylow Theorem :
for p prime,
if p^n | g
=> G has a subgroup H of order p^n:
$latex h= p^{n}$

Conclusion: h | g
Lagrange (h) => Sylow (h=p^n) => Cauchy (h= p, n=1)

Trick to Remember:

g = kh (god =kind holy)
=> h | g
g : order of group G
h : order of subgroup H…

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## 陈省身 SS Chern – “The 2nd Gauss”

http://www.bilibili.com/video/av5473133

Key Points:

1. SS Chern won the “Wolf Prize” in the same year with the Hungarian “Vagabond” 流浪汉 Mathematician Erdos Paul.
2. He was appointed the Scientific Advisor of President Reagan, during which Chern recommended to build the USA Center of Math in Berkeley University. After retirement, Chern built a similar center in China at his alma mater Nankai University 南开大学 where he graduated in 1930.
3. SS Chern was an assistant lecturer of Prof Yang WuZhi 杨武之, who liked to invite Chern to his house for dinners, where he saw his 8-year old son Yang ZhenNing 杨振宁 (Nobel Prize Physics 1958).
4. SS Chern has guided great PhD students eg. James Simons (Billionaire Financial Investor applying…

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## 70-million Bounded Gap Between Primes

Since Ancient Greek :

1. Euclid had proved there are infinite primes.
2. Sieve of Eratosthenes to enumerate the primes.
3. Recent time 3 Mathematicians GPY attempted another Sieve method to find the bounded gap(N) of primes in infinity, but stuck at one critical step.
4. Dr. YiTang Zhang 张益唐 (1955 -) spent 7 years in solitude after failure in academic career, in 2013 during a 10-min walk at the deer backyard of his friend’s house, he found an Eureka solution for the GPY’s critical step: $latex boxed { epsilon = frac {1} {168}}&fg=aa0000&s=2$ which gave the first historical bounded Gap (N) from an infinity large number to a limit of 70 million.

Notes:

• Chinese love the number “8” ba which sounds like the word prosperity 发 fa (in Cantonese) . He could have instead used 160, so long as $latex epsilon$ is small.
• The UltimateGoal of the Bounded…

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## Betta Fish Tricks

Betta fish are quite intelligent and curious. I trained my Betta fish to do some simple tricks.

I bought my 5 Gallon tank on Qoo10: Betta Fish Tank. The modern viewpoint is that Betta should not be kept in small bowls or vases (though they might still survive). A 2.5 gallon tank is considered the absolute minimum, with 5 gallon and above being a better choice.

## 小算盘 大乾坤 Abacus

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## 3D Rotation Matrices and Examples

The following rotation matrices rotate vectors by an angle $\theta$ in an anticlockwise direction about the $x$-, $y$-, or $z$-axis respectively (the rotated axis points towards the observer).

\begin{aligned} R_x(\theta)&=\begin{pmatrix}1 &0 &0\\ 0 &\cos\theta &-\sin\theta\\ 0 &\sin\theta &\cos\theta \end{pmatrix}\\ R_y(\theta)&=\begin{pmatrix}\cos\theta &0 &\sin\theta\\ 0 &1 &0\\ -\sin\theta &0 &\cos\theta \end{pmatrix}\\ R_z(\theta)&=\begin{pmatrix} \cos\theta &-\sin\theta &0\\ \sin\theta &\cos\theta &0\\ 0 &0 &1 \end{pmatrix} \end{aligned}

## Example 1

Rotating $\begin{pmatrix}1\\ 0\\ 0\end{pmatrix}$ $45^\circ$ anticlockwise about $z$-axis:

\begin{aligned} R_z(45^\circ)\begin{pmatrix}1\\ 0\\ 0\end{pmatrix}&=\begin{pmatrix} \cos 45^\circ &-\sin 45^\circ &0\\ \sin 45^\circ &\cos 45^\circ &0\\ 0 &0 &1 \end{pmatrix} \begin{pmatrix}1\\ 0\\ 0\end{pmatrix}\\ &=\begin{pmatrix}\sqrt{2}/2\\\sqrt{2}/2\\0\end{pmatrix}. \end{aligned}

## Example 2

Rotating $\begin{pmatrix}0\\ 1\\ 0\end{pmatrix}$ $45^\circ$ anticlockwise about $z$-axis:

\begin{aligned} R_z(45^\circ)\begin{pmatrix}0\\ 1\\ 0\end{pmatrix}&=\begin{pmatrix} \cos 45^\circ &-\sin 45^\circ &0\\ \sin 45^\circ &\cos 45^\circ &0\\ 0 &0 &1 \end{pmatrix} \begin{pmatrix}0\\ 1\\ 0\end{pmatrix}\\ &=\begin{pmatrix}-\sqrt{2}/2\\\sqrt{2}/2\\0\end{pmatrix}. \end{aligned}

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## 十二平均律 12-tone Equal Temperament

《十二平均律》 是明朝 ＂布衣王子＂ 朱载堉 (1536年－1610年) 发明的，由当时在中国传教的意大利人 利马窦 (Matteo Ricci, 传给欧洲的法国数学家 Marin Mersenne (Mersenne Prime ) 。现代音乐之父 巴哈 Bach 第一个采用，制作世界第一架钢琴有12黑白键，并作曲 《Bach 12-tone Equal Temperament》。

Side Note:

1977年法国大学数学教授在课堂好奇地问我，你们祖先如何解代数？是用算盘吗？当时计算机还不流行，复杂的算法只能用Log Table 或 计算尺 (Slide Rule) 。

Bach 12-tone Equal Temperament

https://zh.m.wikipedia.org/wiki/%E5%8D%81%E4%BA%8C%E5%B9%B3%E5%9D%87%E5%BE%8B

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## Richard Dedekind

Julius Wilhelmina Richard Dedekind (6 Oct 1831 – 12 Feb 1916)

– Last student of Gauss at Göttingen
– Student and closed friend of Dirichlet who influenced his Mathematical education
– Introduced the word Field (Körper)
– Gave the first university course on Galois Theory
– Developed Real Number ‘Dedekind Cut‘ in 1872
– Accomplished musician
– Never married, lived with his unmarried sister until death
“Whatever provable should be proved.”
– By 1858: still yet established ?
$latex sqrt{2}.sqrt{3} = sqrt{2.3}$
– Gave strong support to Cantor on Infinite Set.

http://www-history.mcs.st-and.ac.uk/Biographies/Dedekind.html

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## HDB Low Water Pressure: Phone Hotline

For those living near the top floor of HDB blocks, you may experience low water pressure since the water tanks are typically built at the rooftop of HDB flats.

The pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation $\displaystyle\boxed{p=\rho gh},$ where g is the gravitational acceleration.

By this equation, you can understand why those at the top floors experience low water pressure, due to the low height h (from the water tank). There is probably a need for a pump to increase the pressure. For low floors, it is typically ok, the natural pressure should be enough to make the water flow fast.

## Water Pressure Low Hotline: 1800-CALL-PUB

The number you should call when experiencing low water pressure for HDB flats is:

1800-CALL-PUB
(1800-2255-782)

## My Experience with Low Water Supply

I experienced unbelievably quick action by PUB on Chinese New Year, around 9pm. I called the PUB hotline due to very low water pressure (insufficient for even bathing). Mentally, I was prepared that probably they could only fix it the next working day (which is 2 days later).

To my amazement, a repairman arrived 15-20 minutes later, and proceeded to fix the water tank. The water pressure was back to normal in just half an hour from the time I dialed the hotline. I was quite impressed by the high efficiency.

I am not sure what caused the problem in the first place though. This problem of low water pressure has been reported by Channel News Asia.

## HDB Low Water Pressure What To Do

Firstly, you should check with neighbors on the same floor whether they experience the problem of low water pressure. This is to confirm whether the problem is with the water tank pump/pipes, or an isolated problem only pertaining to your unit.

If your neighbors also experience low water pressure, then most likely it is a problem pertaining to the water tank pump/pipes. You should dial the PUB hotline (1800-2255-782) and inform them of the low water pressure. They will liaise with the Town Council and send a technician to investigate. (The service is free of charge.)

If the situation still does not improve, you may wish to purchase this “Wind Storm” High Pressure Shower Head. Basically, it turns a low pressure stream of water into a high pressure spray of water, to the extent that you can feel a “wind” blowing. It also saves water so it will pay for itself in the long run (by reducing your water bills).

[S$11.90](▼77%)[Restock] Wind Storm Shower Head ★Powerful High Pressure Shower heads ★ For Bath WWW.QOO10.SG Also see: Free Water Saving Kit (Singapore) Posted in Uncategorized | Tagged , | Leave a comment ## Dedekind Cut : “Prove 0.9999… = 1” Key Notes: 1. Rational Numbers Q eg. 1/2, … Complete but non Continuous. 2. Irrational numbers eg.$latex sqrt {2}$3. Real number is Complete and Continuous 4. Dedekind Cut The Proof of “0.999… = 1” by using Set Theory :$latex A subset B$and$latex B subset Clatex implies A = B $View original post Posted in Uncategorized | Leave a comment ## Bit Coin and Block Chain Bit Coin is only one application of Block Chain. View original post Posted in Uncategorized | Leave a comment ## Happy Chinese New Year Happy Chinese New Year to all readers of Mathtuition88.com! Do check out and follow my Facebook page, where I post interesting news on Math/Education. Posted in Uncategorized | Tagged , | Leave a comment ## Machine Learning is Just Mathematics! Free Machine Learning Resources Posted in Uncategorized | Leave a comment ## Learn NUMPY in 5 minutes – BEST Python Library! Posted in Uncategorized | Leave a comment ## Formula for 3×3 Matrix Inverse Let $\displaystyle A=\begin{pmatrix}a &b &c\\ d& e& f\\ g& h& i \end{pmatrix}.$ Then, $\displaystyle A^{-1}=\frac{1}{\det(A)}\begin{pmatrix} ei-fh &ch-bi &bf-ce\\ fg-di &ai-cg &cd-af\\ dh-eg &bg-ah &ae-bd \end{pmatrix}.$ This method is about the same speed as the Gaussian-Elimination method. However, if you have already calculated det(A), using the formula may be slightly faster. The formula provides an insight on why A is singular (not invertible) if det(A)=0. (Because, if det(A)=0, in the formula we would be dividing by 0 which is not allowed.) Posted in Uncategorized | Tagged , | 1 Comment ## Men’s wallet with coin compartment Singapore Despite many cashless initiatives like PayLah, Singapore is not yet a truly cashless country. Coins are still needed to buy coffee or tea at the “Kopitiam”, or to put a$1 coin for pushing a trolley at supermarkets. Even if you carry paper notes, when you receive coins as change you will need a place to put them.

Many wallets do not have coin compartments. On Qoo10, this brand “Arete First” is a Singaporean brand that sells Leather Wallets at a reasonable price, with coin compartment. The quality is good, and it is genuine leather. It can also put a decent number of cards (nine card slots).

Do check it out if you are interested in a wallet with coin compartment.

[S$19.90](▼88%)[Arete First] Genuine Leather Wallet for Men | RFID blocking | Bifold | Coin compartment WWW.QOO10.SG Posted in Uncategorized | Tagged | Leave a comment ## Horned Nerite Snails Some video footage of my new Horned Nerite Snails in the Betta Tank. Really amazing and bright colors. Taken using Canon PowerShot: Canon Camera and Camera Case Singapore The fish tank is 5 Gallon: Betta Fish Tank Posted in Uncategorized | Tagged , , , | Leave a comment ## Imaginary Numbers FINAL EPISODE – Riemann Complex Plane : 4 dimension but viewed in 3 dimensions Episode 1 – 9 : History Episode 10: Complex function Function : 1 input mapped to 1 output Multi-function : 1 input mapped to (n > 1 ) output View original post Posted in Uncategorized | Leave a comment ## Math for AI : Gradient Descent Posted in Uncategorized | Leave a comment ## My most exciting Bishop’s Opening ever Game URL: https://lichess.org/pKHiu5ey/white#1 I did make a few serious blunders, hence it is not my best game. But it is certainly quite exciting. My heart pounded furiously as I played 22. f6! sacrificing my queen… If my opponent takes the queen, it will be checkmate in 3. (He didn’t.) White has just played 22. f6! My opponent, being 2000 rated, played quite well. He missed punishing my blunder at around move 14. Currently, my white opening repertoire involves the Bishop’s opening (1. e4 e5 2. Bc4), with a view towards playing f4 whenever possible to transpose into Vienna/King’s Gambit. Posted in maths tuition | Tagged , | Leave a comment ## Forest Man of India Previously, I blogged about the Mountain Man of India: Mountain Man Motivational Story Today, I learnt that there is also a Forest Man of India. By planting one tree a day (for many years), Jadav Payeng (a.k.a Forest Man of India) has planted a forest bigger than Central Park in New York! This principle of doing small things everyday also applies to students and learning. By doing one Math question per day, at the end of one year, a student would have completed 365 Math questions! This would be a considerable amount that would certainly help to boost the student’s Math grade and also Math understanding. Posted in maths tuition | Tagged , , | Leave a comment ## Goby and Shrimp Video (GEP Science) Amazing “teamwork” between a goby fish and a shrimp! Basically, the shrimp is in charge of digging the burrow, but it is almost blind. The goby fish acts as the sentry to alert the shrimp in case of danger. This video may be useful for GEP science, it may be tested as an example of “symbiotic relationships” in animals. GEP Science syllabus includes a brief introduction to different types of symbiosis (Mutualism, Commensalism and parasitism). It is also very entertaining and can promote interest in science for children. Also check out: Posted in maths tuition | Tagged , | Leave a comment ## Python Online Courses for Teenagers/Adults If your child is interested in a Computer Science/Data Science career in the future, do consider learning Python beforehand. Computer Science is getting very popular in Singapore again. To see how popular it is, just check out the latest cut-off point for NUS computer science, it is close to perfect score (AAA/B) for A-levels. According to many sources, the Singapore job market (including government sector) is very interested in skills like Machine Learning/ Deep Learning/Data Science. It seems that Machine Learning can be used to do almost anything and everything, from playing chess to data analytics. Majors such as accountancy and even law are in danger of being replaced by Machine Learning. Python is the key language for such applications. I just completed a short course on Python: Python A-Z™: Python For Data Science With Real Exercises! The course fee is payable via Skillsfuture for Singaporeans, i.e. you don’t have to pay a single cent. (You have to purchase it first, then get a reimbursement from Skillsfuture.) At the end, you will get a Udemy certificate which you can put in your LinkedIn profile. The course includes many things from the basic syntax to advanced visualization of data. It teaches at quite a basic level, I am sure most JC students (or even talented secondary students) with some very basic programming background can understand it. The best programming language for data science is currently Python. Try not to learn “old” languages like C++ as it can become obsolete soon. Anyway the focus is on the programming structure, it is more or less universal across different languages. Related posts on Python: Posted in maths tuition | | 1 Comment ## Superposition Principle of Linear Algebra ## Superposition Principle If $\mathbf{u}$ is a solution to $\bf{A}\mathbf{x}=\mathbf{b}$, and $\mathbf{v}$ is a solution to $\bf{A}\mathbf{x}=\mathbf{c}$, then $\mathbf{u}+\mathbf{v}$ is a solution to $\bf{A}\mathbf{x}=\mathbf{b}+\mathbf{c}$. Proof: $\mathbf{A}(\mathbf{u}+\mathbf{v})=\mathbf{A}\mathbf{u}+\bf{A}\mathbf{v}=\mathbf{b}+\mathbf{c}$ ## Properties of Matrix Transpose 1) $(A^T)^T=A$ 2) $(A+B)^T=A^T+B^T$ 3) $(kA)^T=kA^T$ 4) $(AB)^T=B^T A^T$ Posted in maths tuition | Tagged , | Leave a comment ## Hangout @ Chinatown Includes a review on “The Coconut Club”, which serves one of the best Nasi Lemak in Singapore. Well, today I have one day off and my husband also has time. We planned to go to Chinatown and have lunch there. He wanted to try a nasi lemak restaurant there. It’s the first time for us to go to Chinatown and hunt for non-Chinese food. Chinatown of Singapore is really close to to the CBD. You can actually walk from Chinatown to CBD and also see blocks of tall buildings from Chinatown. There are many places to have nice food in Chinatown, such as Amoy Street and Chinatown Food Street. Chinatown has many traditional buildings of Nanyang style. The restaurant we went is at Ann Siang Rd. There are many bars, restaurants and cafes there. The blue restaurant is the one we were going. The Coconut Club. It is not a very big restaurant. Their signature dish is nasi lemak, which can be told from the menu. Actually… View original post 487 more words Posted in maths tuition | Leave a comment ## To those starting JC life in today’s Singapore Excellent post by top GP tutor Mr Steven Ooi. This post sums up the current competitiveness of the Singaporean education system. Similarly for Math, there is a knowledge “arms-race” to the extent that a typical Primary 3 student should know how to calculate 1+2+3+…+100 in case this question pops up in the exam. The textbook syllabus remains just as easy as in the past, but what is tested has become 10 times more difficult. [Writer’s note: While this article is addressed specifically to Singapore-based students, it may hold some truth for students in many other places as well.] Dear young friend, I’m writing this to share some thoughts that I used to convey to every one of my students when I was still a full-time tutor in Singapore (I retired in 2016). It is just my personal opinion, formed through years of experience as a student in the 1980s and 1990s, then as a tutor in the 2000s and 2010s. Observing student life in the 90s and then in the 2010s, I can only conclude that the school system in Singapore has become 10 times more competitive than during my time. At least 10 times. During the 90s, most of my junior college classmates didn’t even attend private tuition. We could hang out at the bowling alley, the arcade or the hawker centre most… View original post 1,324 more words Posted in maths tuition | Leave a comment ## Malayan Aqua Fern This “Malayan Aqua Fern” is a very mysterious plant, there is very little information on Google about it. There are two views on it, based on online writings. ## First viewpoint on Malayan Aqua Fern: The “Malayan Aqua Fern” is none other than Peacock Fern, or Selaginella willdenowii. It is NOT an aquatic plant, and will die if fully submerged under water. This is quite reasonable, based on the pictures of Peacock Fern online, it does look like the pictures of the “Malayan Aqua Fern”. Nonetheless, it can be planted in a crab/terrapin tank where it is not fully submerged under water. The “Malayan Aqua Fern” may give the illusion of surviving under water when it may be slowly dying (takes around a month to die). Websites that support this view: ## Second view: The “Malayan Aqua Fern” is an amphibious plant, able to live both submerged or in moist conditions. If this is true, then “Malayan Aqua Fern” would be an incredible aquarium plant as it looks very good in a fish tank. Websites that support this view: ## Is Malayan Aqua Fern Aquatic or Not? The main question is whether the Malayan Aqua Fern is aquatic or not? Can it grow fully submerged under water? If you have experience with the Malayan Aqua Fern, please leave your comments below! Malayan Aqua Fern and Betta Posted in maths tuition | Tagged , , | Leave a comment ## Chromatic Fingering for Moonlight Sonata 3rd Movement In Beethoven’s Moonlight Sonata 3rd movement, there is a very fast stretch of chromatic notes in bar 187. I was wondering if the most basic fingering is good, or a more advanced fingering involving the 4th or even 5th finger would be better. (Read more on advanced chromatic fingering here: http://www.pianisttopianist.com/?p=486) Some people on Reddit suggest some very fanciful fingerings, including “using LH (Left Hand!!) (faster playing up)4321,4312,4321,4321. So, groups of 4321 with the exception starting on the C. That part goes 4312. Just play all the way up with the LH and smack that top A (was it?) with yer Right Hand”! This fingering is apparently attributed to Alfred Brendel. It turns out that at least 2 professional pianists seem to use the basic chromatic fingering: 2 13 123 13 123 … etc. They do not use the fourth finger at all. The starting fingering of the first note (G#) may vary. The first pianist is Valentina Lisitsa. Watch at 0.25 speed to see the fingering at around 6:07 time. Lisitsa seems to use a “special trick” by using her left hand to play the lowest G# in the chromatic range. The second pianist is Rousseau. You can see his fingering clearly, it is the basic chromatic fingering at around 6:34 time. Hence, it seems that for Moonlight sonata it is not needed to use the advanced chromatic fingering. Using the pedal during the chromatic (both pianists use it to some extent) gives the illusion of a fast chromatic. For other pieces like Fantasie Impromptu, the advanced chromatic fingering works well for greater speed. Posted in maths tuition | Tagged , | 4 Comments ## BTS Fan Products BTS is one of the most popular Korean bands. Previously, we wrote on how Scientists Use Math To Discover Why BTS Jin Is The Most Handsome. Their dance steps are also amazing, hence it is no question why they are so popular worldwide. Basically, nowadays top artistes need to be good at dance + singing in order to be popular. BTS seems very popular locally in Singapore, their concert tickets are often sold out within an hour. By the way, if a youth says that they are in “the Army”, it may not mean that they are soldiers/National Cadet Corps. BTS fans are also known as “the Army”. I once conversed with a taxi driver who told me that his daughter is in RGS, and most of her classmates are fans of K-pop including BTS. Korea is also now a top tourist destination for Singaporeans. Both Qoo10 and Amazon have BTS fan paraphernalia, with Amazon having a more extensive collection. Most of the items ship to Singapore, with the delivery charge being quite affordable considering the huge distance from America to Singapore. An example of a BTS cosmetic set from Qoo10. [S$64.90](▼36%)[VT Cosmetic]【VT X BTS】★THE SWEET SPECIAL EDITION SET(Cushion(Choice 21 or 23 Tint 2 pcs included) /TTBEAUTY

WWW.QOO10.SG

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

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

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

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

Most of BTS videos have 100 million views or more:

## Free American Tourister 25” Luggage (Dumex)

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

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

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

WWW.QOO10.SG

## Mathematician Couple’s Wedding Math Questions

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

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

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

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

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

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

View original post

## The Best Way to Take Online Exams

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

• Can be taken as per the convenience

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

• Helps to save money as well as time

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

• The convenient way to take a test

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

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

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

• Safe, secure and accurate way that is

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

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

• It is free way of exam

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

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

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

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

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

Easy to share

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

The easy and simple it works

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

## How to stay Cool in Singapore

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

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

[S$1,898.00](▼58%)[MITSUBISHI ELECTRIC]Mitsubishi Inverter Multi Split AirCon FN Series – SYS. 2 – 4 [5 Ticks] WWW.QOO10.SG However, for short term purposes (e.g. rental, or do not want the hassle of installing a permanent air-con), a portable aircon is the solution. A portable aircon will be enough to cool a small room (i.e. most HDB rooms and small Condo rooms). Whatever you do, DO NOT buy those mist fans, they are close to useless since Singapore’s humidity is already close to 90%. Those mist fans work well in hot and dry desert-like environments, possible like Saudi Arabia or Australia. They work by making the mist evaporate, which does not work well in Singapore due to the high humidity. Not to mention, the constant mist may lead to some mold problems. You might as well buy a powerful fan with vortex action: [S$58.80](▼41%)[PULLMAN][XMAS SALE] PULLMAN AIR CIRCULATOR FAN TURBO FORCE With Remote Control

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## Cheap Portable Aircon Singapore

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

[S$399.00](▼51%)[Europace][LAST 5 SETS] EuropAce Portable AirCon (10KBTU / 12KBTU) (EPAC 12T8/10Q/10P/12P) – 5 YEARS WARRANTY* WWW.QOO10.SG This is another newer model of Europace: [S$399.00](▼64%)[Europace]EuropAce Portable Air Conditioner with HepaCarbon filter 10K/12K/14K BTU- (EPAC 10T6/12T6/14T6)

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

[S$288.00](▼68%)[TRENTIOS]Trentios/Avolta Portable Aircon 10000/12000/14000 BTU / (Include Air Freshener/Dehumidifying) WWW.QOO10.SG ## Bonus Cooling Tip Another good way of staying cool at home is to wear Uniqlo DRY-EX T-Shirts. They are much more cooling than cotton shirts. Wearing one of these can be equivalent to a drop of 1-2 degrees Celcius. Sometimes the online Uniqlo stores do have 50% discount, do grab them during the discount if possible. Posted in maths tuition | Tagged , , | 1 Comment ## Cute Graph Cheatsheet Posted in maths tuition | Leave a comment ## Sir Michael Atiyah obituary Atiyah is so-called the “2nd Newton” in being both a Mathematics & a Physics Grandmaster, his life achievement extends the ancient Greek Geometry to Topology and Algebra since Euclid till now, providing useful application to Quantum Physics. Vector Bundle 向量丛 K-Theory : Vector Bundle invariant In Sept 2018, Atiyah claimed in a seminar of his astonishingly simplest proof of the Riemann Hypothesis (one of the 6 outstanding millenian problems with US$1 million Clay Prize) – but sadly nobody believes him even after his death 3 months later !

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

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