The World’s Most Beautiful Equation : Euler’s Identity

Prof Loh (CMU) is the 2019 USA IMO coach whose team (5 ABC, 1 White) co-won the IMO Championship with China.

Advertisements

Singlish Math : Toa-Cah-Soh大脚嫂

In Chinese school Sec 3 we had to memorize by hard these 3 Trigonometric formula:

正弦 sin, 馀弦cos, 正切 tan,
对边比斜边= sin,
邻边比斜边= cos,
对边比邻边= tan,

凶数学老师叫一个个学生轮流从座位上站起来背诵,不会背就罚站。

她说学高数”三角” (Trigonometry) 第一步就是死记这个公式。我最反感无趣味的学习,违背”数学精神” (Mathematical Spirit) 。尤其讨厌 “三角恒等式” (Trigonometric Identities Proof) 证明,用死记的公式纠缠地 (messy) 变来变去,"剪不断, 理还乱",考试差点不及格 (60%)。

80年代 英校数学老师发明一个记忆妙招 :Singlish TOA CAH SOH 大脚嫂👍

Who says Singlish is useless? Our Sec 3 Math students are Top PISA (#1) in the World !

Another smart Singlish Math Chant:

A Programmer’s Regret: Neglecting Math at University – Adenoid Adventures

Advanced Programming needs Advanced Math: eg.

Video Game Animation: Verlet Integration

AI: Stats, Probability, Calculus, Linear Algebra

Search Engine : PageRank: Linear Algebra

Abstraction in Program “Polymorphism” : Monoid, Category, Functor, Monad

Program “Proof” : Propositions as Types, HoTT

https://awalterschulze.github.io/blog/post/neglecting-math-at-university/

Abstraction: Monoid, Category

Category

函数概念并不难,理解“函”字是关键——函数概念如何理解】

【函数概念并不难,理解“函”字是关键——函数概念如何理解】
https://m.toutiaocdn.com/group/6714162037842248205/?app=news_article_lite&timestamp=1563301386&req_id=201907170223060101520450386849493&group_id=6714162037842248205&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share

清. 李善兰 翻译 Function 为函数。函,信也。只能有一个收信人,所以 只有一个 f(x) 值。

The unique 1 single output of a function becomes very important for subsequent development in Math & IT:
functions are composable, associative, identify function,etc (distributive,… ) => it can be treated like vector => structure of a Vector Space “Vect”

Extended to..

“Vect” is a bigger structure “Category” in which “function of functions” is a
Functor” (函子)F:F(f)

Example : F(f) = fmap (in Haskell)

fmap (+1) {2,7,6,3}

=> {3,8,7,4}

here F = fmap, f = +1

The Math branch in the study of functions is called “functional” 泛函。

IT : Functional Programming in Lisp, Haskell, Scala, ensure safety of guaranteed output by math function property. Any unexpected exception (side effects: IO, errors) is handled by a special function called “Monad” (endo-Functor).

(想看更多合你口味的内容,马上下载 今日头条)
http://app.toutiao.com/news_article/?utm_source=link

Learn Calculus With These Four Online Courses

https://lifehacker.com/learn-calculus-with-these-four-online-courses-1836377912/amp

Four Online Free Calculus Courses:
1. http://www-math.mit.edu/~djk/calculus_beginners/

2. “Calculus Made Easy” (1910 )

http://calculusmadeeasy.org/

3. “Essence of Calculus” (12 short videos, with Chinese subtitle)

4. [Best👍] “Calculus” (MIT Prof Gilbert Strang)

https://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/