https://www.popularmechanics.com/science/math/gmp29008356/hard-math-problems/

# Tag Archives: Group

# “Poisson Distribution Intuition (and derivation)”

“Poisson Distribution Intuition (and derivation)” by Aerin Kim 🙏

https://link.medium.com/bho611jxSX

Poisson was a 19CE French mathematician, or Statistician, who invented the Poisson Distribution.

**Note**: “**Applied” Math vs “Pure” (aka Modern / Abstract**) **Math**

Poisson, being an Applied Math expert in the French Science Academy, did not understand the “abstract” Math paper submitted to him by the 19-year-old Evariste Galois in “Group Theory” for the “**Insolvability*** of Quintic Polynomial Equations*“. Poisson rejected the paper commenting it was too vague, destroying the final hope of Galois to make his invention the “Modern Math” known to the world. The dejected poor Galois died at 21 after a duel during the chaotic era of the French Revolution.

# From Polynomial to Modern Algebra

Examples Polynomial with degree > 5

# The “Prime Number” of Group: “Simple Group”

**Group** :

**Simple Group** :

**Monster Group**: its “discoverer” Simon Norton is an eccentric Cambridge Trinity College Math genius (same class year as Singapore PM Lee Hsien Loong).

# 直观 数学 Intuition in Abstract Math

Can Abstract Math be intuitive, ie understood with concrete examples from daily life objects and phenomena ?

**Yes**! and Abstract Math should be taught by intuitive way!

1. **直观 线性空间 : Intuition in Linear Space**

**(Part I & II) 矩阵 (Matrix), 线性变换 (Linear Transformation)**

http://m.blog.csdn.net/myan/article/details/647511

(Part III)

http://m.blog.csdn.net/myan/article/details/1865397

**Animation**: English (Chinese subtitles)

http://m.bilibili.com/video/av6731067.html

2. **直观 群论** (Intuition in Group Theory)

# Symmetry, Algebra and the “Monster”

Very good introduction of Modern Math concept “Group” to secondary school math students by an American high school teacher.

https://www.quantamagazine.org/symmetry-algebra-and-the-monster-20170817/

** Summary**:

- Symmetry of a Square
- Isometry (*) or Rigid Motion (刚体运动) = no change in shape and size after a transformation
- What is a Group (群 “CAN I” ) ? =
**C**losure**A**ssociative**N**eutral**I**nverse - Monster Group = God ?
- String Theory: Higgs boson (玻色子) aka “God Particles”

Note (*): “保距映射” (**Isometry**），是指在度量空间 (metric space) 之中保持距离不变的”**同构**“关系 (**Isomorphism**) 。几何学中的对应概念是 “**全等变换”**。

# 苏联老师Arnold 如何 教中小学 抽象”群”

How this Russian math prof taught secondary school kids the advanced math in Group & Field Theory without the boring axiomatic approach which tortures most math students.

**Table of Contents**: