Thursday, 6 June 2013
Wednesday, 5 June 2013
Polymath Project
Polymath Project initiated by Terrence Tao inviting mathematicians worldwide to improve on Yitang Zhang's 70 million bounded gap between primes.
Online Seminar by Terrence Tao on Zhang's paper:
http://terrytao.wordpress.com/2013/06/04/online-reading-seminar-for-zhangs-bounded-gaps-between-primes/
Go to this site to get regular update on progress.
http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes
Online Seminar by Terrence Tao on Zhang's paper:
http://terrytao.wordpress.com/2013/06/04/online-reading-seminar-for-zhangs-bounded-gaps-between-primes/
Go to this site to get regular update on progress.
http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes
Monday, 3 June 2013
Sabbath Number 7
Sabbath Number '7':
1. Sunday: God rested on 7th day, a Holy day.
2. Professors rest on 7th year Sabbatical leave to re-charge: overseas exchange-cum-research paid holidays.
3. All farm lands must rest on 7th year before cultivation again.
4. After 6 years (Grade 1 to 6) and the stressful Primary School Leaving Exams (PSLE), relax on Secondary 1 (Grade 7); then after 4+2 years Cambridge 'O' and 'A' levels high-school pressure, 'honey-moon' in Freshman year (1st year University), or 'switch off' from study in the Army National Service.
5. 哈佛一调查报告说，人生平均只有7次决定人生走向的机会，两次机会间相隔约7年，大概25岁后开始出现，75岁以后就不会有什么机会了。这50年里的7次机会，第一次不易抓到，因为太年轻；最后一次也不用抓，因为太老。这样只剩5次，这里面又有两次会不小心错过(*)，所以实际上只有3次机会了。
人生七年之"痒" (机会)
25: 毕业寻职: 第一痒
32: 结婚成家:第二痒
39: 创业: 第三痒 (*)
46: 名利: 第四痒
53: 中年危机: 第五痒(*)
60: 金盆洗手: 第六痒
67: 夕阳无限: 第七痒
1. Sunday: God rested on 7th day, a Holy day.
2. Professors rest on 7th year Sabbatical leave to re-charge: overseas exchange-cum-research paid holidays.
3. All farm lands must rest on 7th year before cultivation again.
4. After 6 years (Grade 1 to 6) and the stressful Primary School Leaving Exams (PSLE), relax on Secondary 1 (Grade 7); then after 4+2 years Cambridge 'O' and 'A' levels high-school pressure, 'honey-moon' in Freshman year (1st year University), or 'switch off' from study in the Army National Service.
5. 哈佛一调查报告说，人生平均只有7次决定人生走向的机会，两次机会间相隔约7年，大概25岁后开始出现，75岁以后就不会有什么机会了。这50年里的7次机会，第一次不易抓到，因为太年轻；最后一次也不用抓，因为太老。这样只剩5次，这里面又有两次会不小心错过(*)，所以实际上只有3次机会了。
人生七年之"痒" (机会)
25: 毕业寻职: 第一痒
32: 结婚成家:第二痒
39: 创业: 第三痒 (*)
46: 名利: 第四痒
53: 中年危机: 第五痒(*)
60: 金盆洗手: 第六痒
67: 夕阳无限: 第七痒
Sunday, 2 June 2013
Love Math
For those who love Math ...
1x8+1=9
12x8+2=98
123x8+3=987
1234x8+4=9876
12345x8+5=98765
123456x8+6=987654
1234567x8+7=9876543
12345678x8+8=98765432
123456789x8+9=987654321
1x9+2=11
12x9+3=111
123x9+4=1111
1234x9+5=11111
12345x9+6=111111
123456x9+7=1111111
1234567x9+8=11111111
12345678x9+9=111111111
123456789x9+10=1111111111
9x9+7=88
98x9+6=888
987x9+5=8888
9876x9+4=88888
98765x9+3=888888
987654x9+2=8888888
9876543x9+1=88888888
98765432x9+0=888888888
1x1=1
11x11=121
111x111=12321
1111x1111=1234321
11111x11111=123454321
111111x111111=12345654321
1111111x1111111=1234567654321
11111111x11111111=
123456787654321
111111111x111111111=
12345678987654321
1x8+1=9
12x8+2=98
123x8+3=987
1234x8+4=9876
12345x8+5=98765
123456x8+6=987654
1234567x8+7=9876543
12345678x8+8=98765432
123456789x8+9=987654321
1x9+2=11
12x9+3=111
123x9+4=1111
1234x9+5=11111
12345x9+6=111111
123456x9+7=1111111
1234567x9+8=11111111
12345678x9+9=111111111
123456789x9+10=1111111111
9x9+7=88
98x9+6=888
987x9+5=8888
9876x9+4=88888
98765x9+3=888888
987654x9+2=8888888
9876543x9+1=88888888
98765432x9+0=888888888
1x1=1
11x11=121
111x111=12321
1111x1111=1234321
11111x11111=123454321
111111x111111=12345654321
1111111x1111111=1234567654321
11111111x11111111=
123456787654321
111111111x111111111=
12345678987654321
Saturday, 1 June 2013
100-digit Pi
One fine day when we reach above 80 years old, if the doctor accuses us of having dementia, then prove the doctor wrong by shocking him with 100-digit Pi memory :)
With Chinese single-syllable sound for numbers, better still if can sing it as a song, memorizing 100-digit pi is easy!
With Chinese single-syllable sound for numbers, better still if can sing it as a song, memorizing 100-digit pi is easy!
Friday, 31 May 2013
Derivative Meaning
The derivative of a function can be thought of as:
(1) Infinitesimal: the ratio of the infinitesimal change in the value of a function to the infinitesimal change in a function.
(2) Symbolic: The derivative of
$Latex x^{n} = nx^{n-1} $
the derivative of sin(x) is cos(x),
the derivative of f°g is f'°g*g',
etc.
(3) Logical:
$Latex \boxed{\text{f'(x) = d}} $
$Latex \Updownarrow $
$latex \forall \varepsilon, \exists \delta, \text{ such that }$
$latex \boxed{
0 < |\Delta x| < \delta,
\implies
\Bigr|\frac{f(x+\Delta x)-f(x)}{\Delta x} - d \Bigr| < \varepsilon
}$
(4) Geometric: the derivative is the slope of a line tangent to the graph of the function, if the graph has a tangent.
(5) Rate: the instantaneous speed of f(t), when t is time.
(6) Approximation: The derivative of a function is the best linear approximation to the function near a point.
(7) Microscopic: The derivative of a function is the limit of what you get by looking at it under a microscope of higher and higher power.
(8) The derivative of a real-valued function f in a domain D is the Lagrangian section of the cotangent bundle T*(D) that gives the connection form for the unique flat connection on the trivial R-bundle ßxR for which the graph of f is parallel.
[Source]: Extract from "On Proof and Progess in Mathematics" by William Thurston.
(1) Infinitesimal: the ratio of the infinitesimal change in the value of a function to the infinitesimal change in a function.
(2) Symbolic: The derivative of
$Latex x^{n} = nx^{n-1} $
the derivative of sin(x) is cos(x),
the derivative of f°g is f'°g*g',
etc.
(3) Logical:
$Latex \boxed{\text{f'(x) = d}} $
$Latex \Updownarrow $
$latex \forall \varepsilon, \exists \delta, \text{ such that }$
$latex \boxed{
0 < |\Delta x| < \delta,
\implies
\Bigr|\frac{f(x+\Delta x)-f(x)}{\Delta x} - d \Bigr| < \varepsilon
}$
(4) Geometric: the derivative is the slope of a line tangent to the graph of the function, if the graph has a tangent.
(5) Rate: the instantaneous speed of f(t), when t is time.
(6) Approximation: The derivative of a function is the best linear approximation to the function near a point.
(7) Microscopic: The derivative of a function is the limit of what you get by looking at it under a microscope of higher and higher power.
(8) The derivative of a real-valued function f in a domain D is the Lagrangian section of the cotangent bundle T*(D) that gives the connection form for the unique flat connection on the trivial R-bundle ßxR for which the graph of f is parallel.
[Source]: Extract from "On Proof and Progess in Mathematics" by William Thurston.
Math Chants
Math Chants make learning Math formulas or Math properties fun and easy for memory . Some of them we learned in secondary school stay in the brain for whole life, even after leaving schools for decades.
Math chant is particularly easy in Chinese language because of its single syllable sound with 4 musical tones (like do-rei-mi-fa) - which may explain why Chinese students are good in Math, as shown in the International Math Olympiad championships frequently won by China and Singapore school students.
1. A crude example is the quadratic formula which people may remember as a little chant:
"ex equals minus bee plus or minus the square root of bee squared minus four ay see all over two ay."
$latex \boxed{
x = \frac{-b \pm \sqrt{b^{2}-4ac}}
{2a}
}$
2. $latex \mathbb{NZQRC}$
Nine Zulu Queens Rule China
3. $latex \boxed {\cos 3A = 4\cos^{3} A - 3\cos A }$
cos = $ 1 (kö, Singapore Chinese Fujian福建話 / Taiwan 台湾闽南语dialect) [一元]
cos 3= $1.3
4cos^3 = $4.3
3cos = $3
$1.3 = $4.3 - $3
4. $latex \boxed{\pi = 3.14159\dots}$
Chant in Chinese Mandarin (Beijing):
山顶一寺一壶酒
Chinese sound means: On the mountain (3) top (.) there is one (1) temple (4) with a (1) bottle (5) of wine (9)
Note : Below is the 22 decimal memory chant:
山顶一寺一壶酒，尔乐, 我三壶把酒吃，酒杀尔，杀不死，乐而乐。
$latex \boxed{
\pi = 3.14159 \:26 \:535897 \:932 \:384 \:626 \dots
}$
5. Group Properties:
$latex \boxed{\text{CAN I ?} }$
C: Closure
A: Associative
N: Neutral (e)
I: Inverse
If only 50%, it is Semi-Group(C, A) 半群
If No Inverse, it is MoNoId (C,A,N) 幺群
(MoNoId : No I)
6. The eccentric choice of letters (a,h,g,b,f,c, skipping iand e) for the coefficients in Conic equation: $latex \boxed
{ ax^{2} + 2hxy + 2gx + by^{2}+ 2fy + c = 0
}$
Math Chant for the coefficients:
{a h g b f}
"all hairy guys big feet"
c: constant term (understood)
Math chant is particularly easy in Chinese language because of its single syllable sound with 4 musical tones (like do-rei-mi-fa) - which may explain why Chinese students are good in Math, as shown in the International Math Olympiad championships frequently won by China and Singapore school students.
1. A crude example is the quadratic formula which people may remember as a little chant:
"ex equals minus bee plus or minus the square root of bee squared minus four ay see all over two ay."
$latex \boxed{
x = \frac{-b \pm \sqrt{b^{2}-4ac}}
{2a}
}$
2. $latex \mathbb{NZQRC}$
Nine Zulu Queens Rule China
3. $latex \boxed {\cos 3A = 4\cos^{3} A - 3\cos A }$
cos = $ 1 (kö, Singapore Chinese Fujian福建話 / Taiwan 台湾闽南语dialect) [一元]
cos 3= $1.3
4cos^3 = $4.3
3cos = $3
$1.3 = $4.3 - $3
4. $latex \boxed{\pi = 3.14159\dots}$
Chant in Chinese Mandarin (Beijing):
山顶一寺一壶酒
Chinese sound means: On the mountain (3) top (.) there is one (1) temple (4) with a (1) bottle (5) of wine (9)
Note : Below is the 22 decimal memory chant:
山顶一寺一壶酒，尔乐, 我三壶把酒吃，酒杀尔，杀不死，乐而乐。
$latex \boxed{
\pi = 3.14159 \:26 \:535897 \:932 \:384 \:626 \dots
}$
5. Group Properties:
$latex \boxed{\text{CAN I ?} }$
C: Closure
A: Associative
N: Neutral (e)
I: Inverse
If only 50%, it is Semi-Group(C, A) 半群
If No Inverse, it is MoNoId (C,A,N) 幺群
(MoNoId : No I)
6. The eccentric choice of letters (a,h,g,b,f,c, skipping iand e) for the coefficients in Conic equation: $latex \boxed
{ ax^{2} + 2hxy + 2gx + by^{2}+ 2fy + c = 0
}$
Math Chant for the coefficients:
{a h g b f}
"all hairy guys big feet"
c: constant term (understood)
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