Source: http://www.takepart.com/photos/ten-surprising-facts-finlands-education-system-americans-should-not-ignore/finland-knows-whats-best

Just to summarize the 10 Surprising Facts:

1. School Starts Later
2. More Recess
3. No Testing (and little homework)
4. Extra Teachers for Struggling Students
5. More Languages
6. Instruction Guidelines, Not Prescriptions
7. Less Teaching
8. Professional Teacher
9. Teachers Stick with Students
10. 43 Percent Attend Vocational School

Read more at: http://www.takepart.com/photos/ten-surprising-facts-finlands-education-system-americans-should-not-ignore/more-languages

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Featured book:
The Temperament God Gave Your Kids: Motivate, Discipline, and Love Your Children

This book is highly recommended for those who are interested in the 4 Temperaments and related research (Introvert, Extrovert, Sanguine, Choleric, Melancholic, Phlegmatic, etc.)

Prove : For any positive integers p, k,
$latex (p^k)! text { is divisible by p }$
Proof:
Apply Factorial Formula:
$latex boxed {n!=n.(n-1)! } $

$latex (p^k)! = (p^k). (p^k -1)!
= p.(p^{k-1}).(p^k -1)!
$
hence divisible by p. [QED]

Sounds bizarre, but it is true! Something “uniquely Singapore” as 92 marks is usually the top echelon for most other countries.

Students need not be disappointed, as 88 to 92 marks is already a very respectable score. Most important is to understand the subject well, and try to improve.

Source: http://news.asiaone.com/news/education/tuition-no-enough

Despite scoring between 88 and 92 marks for his subjects, he was placed in the third quartile of his cohort.

“Which means he was not among the top 50 per cent,” says his mum, Mrs Jaclyn Chew, 41.

Her son, who attends an all-boys school in north-eastern Singapore, was crestfallen after he asked his parents how he fared.

“I had to tell him the truth about where he stood compared to his peers,” Mrs Chew says.

“It’s just bizarre that with his grades and the tuition, he’s still in the lower half of the grade spectrum.”

– See more…

“It is more blessed to give than to receive.” – Acts 20:35

Source: http://www.bbshare.sg/

Join the Boys’ Brigade in spreading the Christmas cheer to needy families in Singapore.

To most of us, items like rice and biscuits are ordinary and common, but to the needy and elderly in Singapore, they are necessities and much needed items.

There are 3 ways to help:

1. Volunteer to Deliver Food Hampers
2. Donate Essential Items
3. Online Donation

Wishing all our readers a Merry Christmas!

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Featured Book:
Bright Minds, Poor Grades: Understanding and Motivating your Underachieving Child

For any parent who has ever been told, “your child isn’t performing up to his or her potential,” this book has the answer. Renowned clinical psychologist Michael Whitley, Ph.D. offers a proven ten-step program to motivate underachieving children. This easy-to follow book identifies the six types of underachievers from the procrastinator to the hidden perfectionist to the con artist, and it…

https://mathtuition88.com/2014/11/20/what-is-vixra/

“arXiv” opposite is “viXra”.

The former “arXiv” is administered by Cornell University for Math paper publishing online. The traditional math journals would take 2 years to review and publish. 

The Russian Mathematician G. Perelman was fed up of the long and bureaucratic review process, sent his proof of the 100-year-old unsolved “Poincaré Conjecture” to arXiv site. Later it was recognized to be correct but Perelman refused to accept the Fields Medal and $1 million Clay Prize. 

See http://tomcircle.wordpress.com/2013/03/31/grigory-perelman-arxiv/

The new site “viXra” is open to  anybody in the world while “arXiv” is still restricted to academics. 

This young Singapore mathematician William Wu proved his new found Math Theorem on “viXra” site:

Prove that: if p is prime, for any number k,
$latex boxed {(p – 1)^{p^k} equiv -1 mod {p^k}}$

[By using the Binomial Theorem and Legendre’s Theorem.]

Example: p = 3, k=2, 3^2=9

2^9 = 512…

This “Butterfly Lovers Violin Concerto” (梁山伯与祝英台) composed 50 years ago by 2 Chinese music students, now played so lovely by a Japanese lady violinist. 

Only in the kingdom of Music (the other one is Mathematics) where human political hatred does not exist between countries due to past wars: Japan and China, Germany and the Allied Nations, … Just only yesterday China President Xi and Japan PM Abe both showed awkward “poker face” hand-shake at the APEC Beijing meeting; contrast to the 20th century’s greatest mathematician David Hilbert from Nazi Germany was welcome  in America to chair  the inauguration of the International Conference of Math.

If more students love Math and Music, the world of tomorrow will be more peaceful.

Watch 諏訪內晶子 -《梁祝小提琴協奏曲》   Butterfly Lovers Violin Concerto:

Notes:
1. The legendary love story is the Chinese version of “Romeo & Juliette”:

http://en.m.wikipedia.org/wiki/Butterfly_Lovers’_Violin_Concerto

2. On [13:27mins] the only single…

我现正在上2010全国华乐比赛-大师班。
大师音乐评分标准：
1. 大法（基本功）
2. 小法（特色）
3. 无法（风格）

数学大师Math Masters 也是如此，
1. 大法（基本功 Classical Math）
2. 小法（特色 Math Olympiad techniques）
3. 无法（风格 Abstract Math -> French “Math Composition“）

Answer: (don’t scroll down until you have tried)

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Answer : 2889 = 5

Draw ONE line to divide the following diagram into 2 triangles:

Recently I was giving a talk at a school in London and had cause to think about sums of kth powers, because I wanted to show people the difference between unenlightening proofs and enlightening ones. (My brief was to try to give them some idea of what proofs are and why they are worth bothering about.) On the train down, I realized that there is a very simple general argument that can be used to work out formulae for sums of kth powers. After a brief look online, I haven’t found precisely this method, though I’ve found plenty of methods in the vicinity of it. It’s bound to be in the literature somewhere, so perhaps somebody can point me towards a reference. But even so, it’s worth a short post.

I’ll start with the case $latex k=1$. I want to phrase a familiar argument in a way that will make…

Anything inside x outside still comes back inside

=> Zero x Anything = Zero

=> Even x Anything = Even

Mathematically,

1. nZ is an Ideal, represented by (n)

Eg. Even subring (2Z) x anything big Ring Z = 2Z = Even

2. (football) Field F is ‘sooo BIG’ that

(inside = outside)

=> Field has NO Ideal (except trivial 0 and F)

Why was Ideal invented ? because of ‘failure” of UNIQUE Primes Factorization” for this case (example):

6 = 2 x 3
but also
$latex 6=(1+sqrt{-5})(1-sqrt{-5})$
=> two factorizations !
=> violates the Fundamental Law of Arithmetic which says UNIQUE Prime Factorization

Unique Prime factors exist called Ideal Primes: $latex mbox{gcd = 2} , mbox{ 3}$, $latex (1+sqrt{-5})$, $latex (1-sqrt{-5}) $

Greatest Common Divisor (gcd or H.C.F.):
For n,m in Z
gcd (a,b)= ma+nb
Example: gcd(6,8) = (-1).6+(1).8=2
(m=-1, n=-1)

Dedekind’s Ideals (Ij):
6 =2×3= u.v =I1.I2.I3.I4…

【一分鐘學物理】在雨中應該走還是跑比較好？【木瓜貓翻譯】:

I remembered it was a Pre-U One (JC-1) Physics Quiz:

It is common sense to run as fast as possible – but here is the Physics explanation.

Test p is prime:

$latex (x-1)^p – (x^p -1) =
$
all coefficients are divisible by p

孤岛天才 超强记忆: