Great Math Popular Books

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日本数学科普作家写的好书。深入浅出, 适合中学生读最高深数学。

結城 浩 Hiroshi Yuki (1963 -) is a Japanese Math Popular Book Writer for Secondary and High School students. In the “Galois Theory” (Chapter 10) he boldly attempted to explain to them such complicated concepts: Quotient Group, Field Extension, Group Order, Normal Sub-Group, Solvable Group …

Evariste Galois‘s genius is he built a “bridge” between Field (域/体) and Group (群) – both new concepts invented by him. The “bridge” is called Galois Group, or by Emile Artin the “Group Automorphism”. He transferred the difficult problem of solving complicated 4 -ops (+-×/) Field (coefficients) to the single-op (permutation of roots) Group.

Galois Group is the ultimate TRUTH of all Math — Fermat’s Last Theorem, and any advanced Math, will use Galois Group or Field, to solve. Prof C.N. Yang 杨振宁 Nobel-Prize Physics discovery was based on Group Theory.

Evariste Galois was a French Math genius, died at 21 in a duel during French Revolution. He is the ‘Father’ of Modern Algebra. Failed 2 years in Ecole Polytechnique CONCOURS Entrance Exams, then kicked out by Ecole Normale Supérieure, his Math was not understood by all the 19th century World’s greatest Math Masters : Gauss, Fourier, Poisson, Cauchy…

“Galois Theory” — the ultimate Math “葵花宝典” (a.k.a. “Kongfu Bible“) — is only taught in the Math Honors Undergraduate or Masters degree Course.

自己学习《Galois Theory》(Page 365):
— “高中会教这种困难的数学吗 ?”
— “…我觉得比起給高中老师教, 不如自己好好学吧。”
— ” 重要的是自己学习。”

http://m.ruten.com.tw/goods/show.php?g=21437146332387

http://www.nh.com.tw/nh_bookView.jsp?cat_c=01&stk_c=9789866097010

https://tomcircle.wordpress.com/2014/03/21/math-girls-manga/

Fun IQ Math

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7+2+5 = ?
(Test the logic pattern)

Ans: (Scroll below — only after you have tried to solve it )
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7+(2)+5= 143547
7×2=14
7×5=35
14 + 35 – (2)=47

Mental Math

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No equation, no formula, no calculator, no writing on paper, just do mental calculation.

What is the answer  in the last diagram ?

Scroll down to see the answer, but not until you have tried yourself.
(There are many methods, but one is the fastest and the best !)
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Ans:
Add the first 3 diagrams: 10+20+24 = 54 for 2x (Dog + Cat + Rabbit).

Dog + Cat + Rabbit = 54/2 = 27

Mental ‘Abacus’ Calculation Technique

Amazing calculation technique of Indian kids:

It is the advanced level of abacus calculation, whereby the physical abacus is replaced by a virtual abacus in the mind — see the kids need to move their fingers in the air, as if they touch a real abacus. The display of the workings (moving up and down of the abacus beans) in the mind is like seeing the abacus image from a computer screen. It means also the kids are still not mentally calculating per se, they just continue to calculate on the ‘virtual’ abacus.

This is different from a real mental calculation sans a physical electronic calculator, in which case no fingers playing the pressing buttons of an electronic calculator. The brain is the real calculator, with some helps of math tricks and shortcuts.

Logic or ‘Think Out of the Box’

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How nice it would be if yesterday were tomorrow, then today would be Friday.

What is ‘today’ here ?

Answer:
A. Wednesday;
B. Thursday;
C. Friday;
D. Sunday

Hints:
either use left brain (by logic) or
right brain (by EQ, after a Sunday evening).

Try before scrolling below for answers:
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Answer (1) : by logic (algebra)
Today = Wednesday

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Let today = d
If d-1 = d+1 (yesterday = tomorrow)
Then d = (d+1)+1=d+2 (today = the day after tomorrow)
and d+2 = 5 (today = Friday)
hence
d = 5 – 2 =3
Today is Wednesday.

Answer (2): by EQ
“Monday Blue”.
That is today is SUNDAY.
How nice if Tomorrow (Monday Blue) were like Yesterday (Saturday), then Today would be “T.G.I.F.” (Thank God is Friday’).