# The Math Power of Number 4

Despite Chinese & Japanese don’t like ‘4’ for the same sound as \si (death), ‘4’ is the magic number for all ideal compositions:

1) All TCM 药方 has 4 compositions : 君臣佐使

(佐药 Assistant ) 甘草,..
(使药 Smoothening, sweetening ) 蜂蜜

2）烹饪 Cuisine :
eg. 炒饭

3) Music
eg. Quartet

4）Maths
Eg. “4-Color” Problem : the only one Math impossible by mathematicians but proven only by computer.

5) Exemplary Nation Racial Harmony
Eg. Switzerland / Singapore : 4 races & official languages.

6) War against Evils:
Eg. WW2 Allied :
USA, UK, France, China, against evils Japan & German (+Italy).

7) Four seasons :

8) Healthy Meal:
Eg.
Fill 1/4 plate with wholegrains.
• Fill 1/4 plate with good sources of protein.
• Fill 1/4 plate with fruit and 1/4 plate of vegetables.

That’s why the 19-year-old Math genius Galois (1832 AD) proved by his invention Abstract Algebra the “Group Theory” that Polynomial equations with radical solution (+ – */,nth root) ONLY possible up to maximum degree 4.
That explains why the “A5-Group” Icosahydron (二十面体) structured SARs-like viruses (eg. COVID-19) WILL NEVER have “radical” drug SOLUTION, only possble killed by our own Antibody pre-trained by Vaccines (eg. mRNA or Sinovac… ).

Also humans impossible to have more than 四代同堂。

The 5th Generation Computer “Prolog Machine” by Japan in 1980s failed miserably.

Anything more than 4G has only “particular case” solution with physical limit beyond which we have to shift paradigm / technology to restart on another track.
Eg 5G by Huawei facing so much difficulty by Western sabotage, only by jumping to new “Quantum Communication Technology” to overcome these physical & artificial human resistance, whether they like it or not by Western countries.

https://v.ixigua.com/eH7ktyu/

Linear Algebra (Quadratic Form 二次型 椭圆 / 双曲线 )

# Physics proves Maths

He applied Physics (flux ) Gauss Divergence Theorem ‘DIV’ operator to get the derivative of Volume = Surface Area “

👍 That’s beautifully an example of using Physics to prove Math.

https://en.m.wikipedia.org/wiki/Divergence_theorem

# IMO 2020 (6th Question)

2020 IMO (6th problem) only one Chinese 李 student scored full 7 marks.

This question is similar to Analysis finding epsilon-delta value of N:

(Epsilon-Delta Analysis, aka Advanced Calculus ) definition for “Limit of Series” :
It exists N such that, for all n > N…

[Solution] :

# 3 Math Foundation Skillsets for Engineering / Finance Students

【普通人学数学系列-下集：学到什么程度】

1) Calculus
2) Linear Algebra
3) Probability / Statistics

Prerequisites for the 3 above in
1) O/A level : Trigonometry, Algebra, Geometry
2) Vector Space (with some basic Algebraic Structures : Group, Ring, Field )
3) O/A level : Permutation/Combinatorics

https://m.ixigua.com/video/6967105499342832166/?app=video_article&timestamp=1622200486&utm_source=native_share&utm_medium=android&utm_campaign=client_share

# 金庸武林江湖与数学江湖

1）华山正邪二派 ： 气宗 (正) vs 剑宗 (邪)

2）虚竹 ：忘掉以前的少林功夫才能学 消遥派

3) 少林寺僧好高鹜远：还没学精本派“一阳指”，就想去换 印度鸠摩罗的功夫。

https://v.ixigua.com/e5Y62ye/

# Math Education Video : The Age of Big Data

Good education video for students on Maths applied in Big Data.

https://v.ixigua.com/ePWfEV6/

# Integrate x^x

The integration is meaningless if

$\displaystyle {\int x^{x} dx}$

unless specifying the domain of defintion, eg. interval [0,1] :

$\displaystyle {\int_{0}^{1} x^{x} dx = \frac {\pi^{2}}{12} }$

Note: Gamma function proof by Feynman trick : differentiate under integral.

DEMO:

https://v.ixigua.com/efX9Lqk/

# French Baccalaureate Math Paper 2 (Analysis)

【「给我进来做题啦!」法国高考数学题难度如何？居然只有四道题？】

Baccalaureate Scientifique Math 2019 (Analyse).

Yet to see the Baccalaureate (S) Paper 1 “Algèbre” which is tougher on Abstract Algebra (Group, Ring, Field, Vector Space / Linear Algebra,…)

https://m.ixigua.com/video/6867459333400035851/?app=video_article&timestamp=1621316174&utm_source=native_share&utm_medium=android&utm_campaign=client_share

# 吴文俊 Wu WenJun

https://v.ixigua.com/efrQhx8/

# Princeton 《Calculus Lifesaver》

This is a free video lecture series of the Princeton Math Textbook 《Calculus Lifesaver》(link Amazon.com) for university non-math majors.

He explains the “funny” but smart Calculus basics : First & 2nd Fundamental Theorems of Calculus (by Newton’s co-inventor Leibniz), some how never taught in the 1970s GCE A level (now also ? ) bcos not Newton’s Anglo-saxxon invention. Neither the French textbooks teach so (bcos Leibniz was German ?). They only appear in pure American/German Calculus books.

“Funny” bcos by “1st Theorem” you could ‘d/dx’ any intergral to get the anti-derivative . Richard Feymann self-learnt this trick in High school to solve complex integrations.

Also why the “Coset” (+ C) is explained by the 2nd Theorem in this video.

# Coset & Index 陪集，指数

https://v.ixigua.com/eU7pf3V/

｜Z : nZ｜Index is easy ?

0Z，1Z, 2Z,… (n-1)Z 个陪集,
Total = n个

｜Z : nZ｜＝ n

Note: Coset in Calculus ( Indefinite Integration) :

Integral Solution “+ C” 就是 Right Coset ＝ solution的右陪集：意思所有 “+C” 都是solution Set 的 右陪伴。

# 2021人口普查的契机：大学普及改革先废高考

2021人口普查数据 ：14.1亿，新生婴儿减少，男多于女，老人（＞60岁）佔20％…

（1）缩短基本 小学-中学教育 ：废除高考，省下2年准备高考的时间，12年减2年。

（2）高中到 大学本科 ：直通车（看高中学校成绩）。

（3）名牌大学（清/北/211/918 等）：不设本科undergrads，直接 研究生 Masters/PhD ， 像法国Grandes Ecoles 制度 (2nd Cycle Tertiary education, 本科设在普通 universities / 工程科预备班 Classes Préparatoires).

（4）所有 普通大学universities 只 教 本科undergrad 学生为主。

10年 (强迫 中/小学) ＋2 or 4年 (专校 or 大学)， 即20岁 / 22 岁 专科/大学本科毕业, 解决“人才荒”的问题。

– 大学改革不可操之过急，要按步就班， 先试点 一些top高中附属大学的 “直通车”（例如：人民大学附属中学）， 这样就省下2年高考准备时间。慢慢推行到全国各省内大学和结盟高中。十年完成直通车，百年树人才。

– 名牌大学集中精力/资金在培养 硕士/博士科研人才，把本科教育的资源分散给各省普通大学，直接提升后者的教育水平。这样也可留住中国人才，防止外流去美国读博深造而不回国。

https://m.toutiaocdn.com/i6960914813585392158/?app=news_article&timestamp=1620752197&use_new_style=1&req_id=20210512005637010212205224381BC609&group_id=6960914813585392158&wxshare_count=1&tt_from=weixin_moments&utm_source=weixin_moments&utm_medium=toutiao_android&utm_campaign=client_share&share_type=original

# a^a^a^… a

$\boxed{a^{a^{a^ {{...}^{a}}}} =? }$ $\text {.... [A] }$

$\text {Let } a = \sqrt {2}$

Method 0: Wrong !!!

Method 1 : Rigorous!

1) Prove [A] Convergent ?

2) If converge, find Limit ?

https://v.ixigua.com/eUHCEkb/

Method 2: by RMI Homomorphism

# Cédric Villani

Mathematician Cédric Villani (Fields Medal) is a MP in President Macron’s young party “En Marche”.

He introduced “Singapore Modeling Math” to French primary schools Arithmetic in 2017.

https://v.ixigua.com/eUNaWHf/

# FTA Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic | by Maths and Musings | Cantor’s Paradise

Note:

The Fundamental Theorem of Arithmetic (FTA):

2300 years ago Euclid 《Elements》proved prime factorisation :
If p | x. y then p | x or p |y

19CE Gauss proved FTA. Uniqueness of prime factorisation.

French 《Bezout Theorem》 is the useful tool: if p, q co-prime, then there exist n, m integers such that
np + mq = 1
eg. Prove 5, 7 co-prime,
(3) *5+ (-2) *7 = 15-14=1

Strange, why Bezout Theorem not taught in A level ?

# 一个数学家的叹息

This American Math educator proposes teaching Primary/Sec math in new ways :

1. HISTORY : how human discovered the math ideas
2. Do not separately teach Geometry & arithmetics: eg.
1+3+5+7 =16=4^2
3. Have fun of Math thru discovery by students, not by remember formula.
4. Intuition 直觉 : use more

https://v.ixigua.com/er2cStN/

# 新数启蒙 (1-5) – 给16岁以上的中学生

This “Modern Math” Introductory Course is based on the French Baccalaureate “Modern Math” for 16+ years old, simplified & customized for local students in Chinese.

https://v.ixigua.com/e6mRFnP/

（1）集合： 等价关系 Equivalence Relation

https://v.ixigua.com/e6mDFhw/

（2）集合与集合的关系：映射 Mapping

https://v.ixigua.com/e6mfC4C/

(3) 新数 历史： Bourbaki 学派

https://v.ixigua.com/e6mjedR/

（4）由外向内看代数结构 : 域Field，环 Ring，群 Group，向量空间 Vector Space

https://v.ixigua.com/e6mj5sd/

(5) 域 Field : 足球场

https://v.ixigua.com/e6mkau7/

# 中国的中学数学教育出错 在一刀切 ？

https://v.ixigua.com/e6aTkww/

# 唐. 王孝通的一元三次方程特例解

Probability * (or＋) between P(A) and P(B) whether A, B are (in-) dependent event.

https://v.ixigua.com/ej7X49B/

# Modern Math Education : Time for Reform

Modern Math Foundation : Set + Logic (Equivalence Relation).

A level (H2 level) / International Baccalauréat Math should study the big red square box (Number System, Set Theory, Logic).

All STEM university Year 1 & 2 study these 3 Math foundations : Algebra, Analysis & Vector Space.

The Math major university Year 3&4 study more : real /complex analysis, Topology, Galois Theory, graph theory, etc…

# mRNA剪接Splicing 原理 – 施一公

3 Step Splicing : first & last steps are linear, 2nd step 3D syructure (non-linear) .

The Hungarian lady scientist Katalin Karikó jumped on his newly published DNA code to invent the mRNA PfizerBioNTech vaccines.

https://m.toutiaoimg.cn/a6936774993665589790/?app=news_article&is_hit_share_recommend=0&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share

# 数学与物理的关系

（小学生与诺奖得主杨振宁的对话）

Math was a tool for Physics (Newtonian Physics)

Math & Physics were independently developed ( Physics Gauge Field = Math Fibre Bundle )

Physics is a tool for discovering Math (Quantum Physics : String Theory)

https://m.toutiaoimg.cn/a6936190545714741798/?app=news_article&is_hit_share_recommend=0&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share