# Maximum Equalangular lines in N-dim Space

MIT助理教授赵宇飞团队登数学四大顶刊，华人作者中两位是本科生

2 Dimensional plane, max 3 lines to cross to have opposite angles equal (cross at 90° or 60°).

3 Dim space, max 6 (eg COVID virus icosahydron, all diagonal lines)

N dim ?

Application: code the photo imaging data points sent from Mars in N dim Matrix, verify the codes accuracy with this “Max” Theorem.

# 代数学发展简史

【代数学发展简史 – 今日头条】
Algebra 代数 =》
Number Theory 数论 =》 Abstract Algebra 抽象代数

https://m.toutiao.com/is/RRTENFh/

# Applied Math in Machine Learning

【鄂维南：机器学习是应用数学几十年未有之机遇 – 今日头条】

https://m.toutiao.com/is/RJetHU4/

Supervised Machine Learning (ML), Unsupervised ML, Reinforced ML, use Function Approximation, Probability Distribution, Bellman Equation, resp.

https://zhuanlan.zhihu.com/p/139559442

# 陈景润 百鸡问题

【智慧之光：陈景润解“百鸡问题” – 今日头条】

https://m.toutiao.com/is/dEt18Kv/

# 苏联《数学：它的内容、方法和意义》

https://m.toutiaocdn.com/i6921674844417425931/?app=news_article&timestamp=1634666245&use_new_style=1&req_id=202110200157240102121401540D64F378&group_id=6921674844417425931&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share&share_token=981558c1-2d55-45c5-9f3e-ef27a4615ea4

http://search.dangdang.com/?key=%B6%ED%20%CA%FD%D1%A7%20%CB%FC%B5%C4%C4%DA%C8%DD&act=input

# Math in movie “X+Y”

Math in movie “X+Y”

# Vedic Factorisation of Polynomial E(x,y,z)

Any Algebra Theory to explain this Vedic Polynomial Factorization ?

Why it works by setting y=0, z=0 ?

E'(x,y,0)= 0 when {x= -2y} or {x=y}

E'(x,0,z)= 0 when {x= -3z} or {x=z}

Why ? Combine them:

E(x,y,z) = 0 when {x=-2y-3z} or {y+z}

which implies:

E(x,y,z) = (x+2y+3z)(x-y-z)

Note: The 2 Ideals of Polynomial Ring E are therefore :

E/(x+2y+3z),

E/(x-y-z)

# Steve Jobs Anniversary

Steve Jobs (1955) should be honored as the most influential technopreneur cum inventor in the 21st century.

Bill Gates (also 1955) did not invent anything new, his MSDOS, MSWindows, MS Word/Excel Office are all copycats, respectively, from QuickDos, Xerox GUI/ Mouse, WordPerfect/SuperCal.

https://www.cnbeta.com/articles/tech/1186757.htm

# 马尔可夫链 Markov Chain

【【数之道 18】”马尔可夫链”是什么？了解它只需5分钟! – 今日头条】https://m.toutiao.com/is/db9ehhk/

# Singapore Modeling Math (PSLE 2021) sans Algebra

Please try it yourself. PSLE Exams is for all 12 year-old Singapore pupils.

This question is tough for adults, yet easy if the pupils with logical mind trained in the “Singapore Modeling Math”.

A Tutor’s advices on coping with tough PSLE Math:

https://www.tutorcity.sg/blog/how-to-prepare-for-the-difficult-psle-maths-questions

. [Solution: scrolled far far below… ]

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

https://mothership.sg/2021/10/psle-coin-question/

# Hilbert Problem : “Polynomial equation of degree 7”

Galois had proved Polynomial equations of degree 5 & above have no ‘radical ‘ ((+*/, nth root) roots

Hilbert Problem : “Polynomial equation of degree 7” : Algebraic Geometry + Topology + Number Theory

https://m.toutiaocdn.com/i6929731728265380355/?app=news_article&timestamp=1633099505&use_new_style=1&req_id=2021100122450401021207221357213E6B&group_id=6929731728265380355&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share&share_token=59a40173-8e12-4f7d-87fa-ff383cb1aee6

# Clojurescript

Clojurescript is a front end of Clojure functional programming language :

ClojureScript Tutorial

# Magic : Topology Game

CD 穿过方洞 ？魔术 数学Topology (拓扑)

https://v.ixigua.com/dMM6WhS/

# 唱背Periodic Table

Periodic Table 唱背

# Phyton GUI

Fastest way to make GUI’s with Python | by Manpreet Singh | Aug, 2021 | Medium

# AI SRCNN Photo

https://v.ixigua.com/ddNdKJ3/

# Butterfly Theorem

https://v.ixigua.com/eoReF6N/

# 孙子算经开平方

https://v.ixigua.com/ewewDnA/ $\sqrt {234567} =484 \frac{311} {968}$ $(a+b+c) ^{2} = a^{2}+b(2a + b)+ c(2a + 2b + c)$

Estimate : 400 < a < 500, take a = 4 $(4+b+c) ^{2} = 4^{2}+b(2*4 + b)+ c(2*4+ 2b + c)$

# Why need to study Group , Ring , Field？

Why need to study Group(群 or Groupe) , Ring (环 or Anneau) , Field (域 or Corps)… 还有 模(Module, a “Vector-Space” over Ring in place of Field).

https://v.ixigua.com/ev54kku/

# IMO 2021 Gold Medalists

Singapore 1 Gold.

The only Perfect Score Gold from China Wang 王一川.

# How to Study University Math 如何学好高等数学

Different from Secondary (O-level) or High school (A-level) Math, University Math (aka Higher Math 高等数学) is proof-oriented (证明) based on student’s understanding of the abstract concepts (概念) 。

https://v.ixigua.com/e7Rvcje/

Interesting to note the last 2 examples 2.4 & , 2.6 how tricky (astucieux) by ‘高级规则’ to find N in terms of expression (ε) +1. Doesn’t matter any expression (ε) bcos N is not UNIQUE, as long as you could magnify (放大) to get a simple expression (ε) eg ε/2, ε/3…

# Intuitive Group

Intuitive Group & Action.

Group Action is an alternative, more powerful than Combinatorics (排列组合) when calculating complex combinations.

If the Math profs had used this intuitive teaching of Group Theory, then Abstract Algebra would be not so scary to all students – even 40 years  after University Math !

# Naïve Bayes Model

https://v.ixigua.com/ebbtHmc/

# Galois Theory explains Quintic Equation sans radical root

Get to appreciate the reasoning outline is enough, “the devil is in the details” for the Math grads in the 4th year Hons degree.

https://v.ixigua.com/ebAQRjJ/

https://v.ixigua.com/eqMxeoh/

https://v.ixigua.com/eqM4mya/

https://v.ixigua.com/eqMa3rw/

https://v.ixigua.com/eqMQXFT/

https://v.ixigua.com/eqMsXoq/

# Math Rigor

Rigorous proof (O-level Math but Modern Math technique) by reductio ad absurdum (反证法).

【一道题检验你是否具有数学思维(视频版) – 今日头条】

https://m.toutiao.com/is/e4QeQFQ/

# Principle of Deep Learning Network

Principle of DNN (MIT)

# Symmetry & Vibrations

👍 Some Symmetry in GROUP Theory.

# 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

# Leibniz’s original proof : Integration by Parts

Leibniz’s original proof : Integration by Parts (分部积分公式”)

https://m.toutiaocdn.com/i6965860180663976452/?app=news_article&timestamp=1621922350&use_new_style=1&req_id=202105251359090102120610721E3A8184&group_id=6965860180663976452&tt_from=android_share&utm_medium=toutiao_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/

# Microsoft Math Solver

https://v.ixigua.com/efTqdVm/