中国历法

Chinese calandre is both solar and lunar, unlike western (pure solar) and Muslim (pure lunar):

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13 classic mathematics books for lifelong learners

View story at Medium.com

Out of 13 must-read Popular Math books, our Singapore National Library NLB has 6 which I borrowed and read: eg. “Prime Obsession” , “What is Mathematics” , etc.

Popular math books are better than the boring textbooks (Axiom – Theorem – Proof – Exercise). They are motivational, more concrete instead of abstract, philosophical analogy with the Nature (afterall, the math ideas derived from the universe, eg. Pi, e, golden ratio, infinity, limit, …), plus the historical background in which these math ideas were first discovered, and the beauty of these inter-connected ideas such as the Euler’s Identity:

\boxed{e^{i. \pi} + 1 = 0}

Proof from the Book” – the name “Book” (God’s Theorem Proof Book) is coined by Paul Erdos the Hungarian ‘vagabond’ (homeless, single, no nationality) mathematician, who had proven 1000+ theorems (some co-operated with his students). He said he had peeped into God’s “Book” to discover these theorems.

My favorite Popular Math book which inspired me in 2005 to re-pick up the fearsome Abstract (aka Modern) Algebra is : “Unknown Quantity” by Prof John Derbyshire, avail at NLB.

Math before university is the “What and How“, whereas the University Math is the “Why” – after WW2 the French Bourbaki Reform in Math Education worldwide based on Set Theory, the post-war Philosophy Trend “The Structurism 结构主义” shaking the basic foundation of Math: Algebraic Structures. eg Group (群) , Ring (环) , Field (域) , Vector Space (向量空间) , Cateogy Theory (范畴论) .

The 70 years of WW1 & 2 taught the world Anarchism (无政府主义) was chaotic & disastrous to society, hence the more orderly “Structurism” Philosophy was born, influencing all Sciences: Chomsky Linguistics, Sociology, IT Structured Programming ‘Pascal’ , Anthropology 人类学, Abstract Algebraic Structure Math…

Mathematics (Mathematikos) = “Fond of Learning”

Μαθηματικος (Mathematikos) = Mathematics = Fond of Learning

Three simple A-level to undergraduate Mathematics a MUST for Data Science and AI:

  1. Linear Algebra (aka Matrix)
  2. Probability (Baeysian)
  3. Statistics
  4. etc

Source:

eFinancialCareers: The mathematics you must learn for a job in data science and AI.
https://news.efinancialcareers.com/us-en/329159/math-for-data-science-and-machine-learning

https://www.dataquest.io/blog/math-in-data-science/

How you pronounce German Mathematician’s Names ( and Physicists )

Germany produced many Mathematicians and Physicists who succeeded the 18 CE Newtonian England, and the 19CE Napoleonic France before WW2, after which the Americans (mostly the Jewish German immigrants) take over till now.

German names are difficult to pronounce for foreigners.

Libniz,

Euler,

Einstein,

Noether,

Gauss,

Dedekind,

Riemann,

Cantor,

etc.

For due respect, please learn to pronounce their German name correctly.

My favorite Fermat Little Theorem with Pascal Triangle

Fermat Little Theorem: For any prime integer p, any integer m

\boxed {m^{p} \equiv m \mod p}

When m = 2,

\boxed{2^{p} \equiv 2 \mod p}

Note: 九章算数 Fermat Little Theorem (m=2)

Pascal Triangle (1653 AD France )= (杨辉三角 1238 AD – 1298 AD)

1 \: 1 \implies sum = 2 = 2^1 \equiv 2 \mod 1

1\: 2 \:1\implies sum = 4 = 2^2 \equiv 2 \mod 2 \;(\equiv 0 \mod 2)

1 \:3 \:3 \:1 \implies sum = 8= 2^3 \equiv 2 \mod 3

1 4 6 4 1 => sum = 16= 2^4 (4 is non-prime)

1 \:5 \:10\: 10\: 5\: 1 \implies sum = 32= 2^5 \equiv 2 \mod 5

[PODCAST]

https://kpknudson.com/my-favorite-theorem/2017/9/13/episode-4-jordan-ellenberg

Celebrates Mathematician Gottfried Wilhelm Leibniz’s 372nd Birthday

https://www.forbes.com/sites/kionasmith/2018/06/30/sundays-google-doodle-celebrates-mathematician-gottfried-wilhelm-leibniz/

My favorite mathematician is German Leibniz, who co-invented Calculus with Newton.

Today we thank Leibniz for his elegant Calculus symbols:

\boxed {\frac{dy}{dx}}

\boxed{\int_{0}^{\infty}x^{n}e^{-x}dx}

Leibniz also invented 01 binary algebra, which he later found it was already in the 3,000-year-old Chinese “Yin-Yang” (阴阳 八卦), so impressed that he recommended to the most powerful western (French) king Louis XIV (14th) to use Chinese as the Universal Language of the world.

The rich Newton sued Leibniz for plagiarism of Calculus, until Leibniz died poor in bankruptcy, buried in a common unknown grave.

The war between Newton & Leibniz extended & lasted 100 years between UK Math Community and Continental Europe Math Community. As a result UK lost its math leadership after Newton, France (Lagrange, Fourier, Cauchy, Galois… ) followed by Germany (Felix Klein, Gauss, Hilbert, Riemann …) took over as the world center of math. After WW2 many German mathematicians (mostly Jewish eg. Noether, Gödel, Artin, …) fled to the USA which is now the Kingdom of Advanced Math.