Author Archives: tomcircle

About tomcircle

Math amateur

Hans Rosling’s Best TED Talk & Book “Factfulness”

Originally posted on Math Online Tom Circle:
http://time.com/5224618/bill-gates-hans-rosling-factfulness/ https://www.ted.com/talks/hans_rosling_shows_the_best_stats_you_ve_ever_seen/up-next?referrer=playlist-the_best_hans_rosling_talks_yo

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Why Prime Numbers Still A Mistery

Originally posted on Math Online Tom Circle:
Prime Numbers since Euclid 2300 years ago remains a mystery today… Riemann’s Hypothesis is the Top Conjecture Unsolved in 21st Century. https://theconversation.com/why-prime-numbers-still-fascinate-mathematicians-2-300-years-later-92484

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Joseph Fourier is Still Transforming Science

Originally posted on Math Online Tom Circle:
Key Words: 250 years anniversary Yesterdays: Fourier discovered Heat is a wave , Fourier Series, Fourier Transformation, Signal processing… Today: IT imaging JPEG compression, Wavelets, 3G/4G Telecommunications, Gravitational waves … Friends / bosses:…

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Louis-Le-Grand, un lycée d’élite 法国(巴黎)精英学校: 路易大帝中学

Originally posted on Math Online Tom Circle:
Lycée Louis-Le-Grand is the best high school (lycée) for Math in France – if not in the world – it produced many world-class mathematicians, among them “the Father of Modern Math” in 19th…

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Senior Wrangler: Singapore Prime Minister

Originally posted on Math Online Tom Circle:
Senior Wrangler is the First position in the Math Tripos in Cambridge. Singapore Prime Minister Lee Hsien Loong was the Senior Wrangler in 1973, the first Singaporean student with such great honors, among…

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Topological Data Analysis

Originally posted on Math Online Tom Circle:
Three Key Ideas: Cloud of Points Filter function: f (x,y,z) –> x Cluster: Overlapping bins Draw network: Vertices: clusters Edges: connecting lines between clusters. https://youtu.be/6Hll-SzcrS0

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Crash course in Category Theory

Originally posted on Math Online Tom Circle:
Key Point: Haskell & any FP compiler don’t check the Category Theory proof if your codes (eg. fmap) follow Functor’s Laws (eg. Preserve structure, identity) or Monad’s Laws ! https://youtu.be/iJ7V1KXJpsE

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God’s Book of Perfect Proof

Originally posted on Math Online Tom Circle:
https://www.quantamagazine.org/gunter-ziegler-and-martin-aigner-seek-gods-perfect-math-proofs-20180319/

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Canadian mathematician Langlands wins Abel Prize

Originally posted on Math Online Tom Circle:
http://www.thehindu.com/sci-tech/science/canadian-mathematician-langlands-wins-abel-prize/article23304119.ece/amp/ See also: Langland’s Program

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Michael Bishop’s Science

Originally posted on Math Online Tom Circle:
Michael Bishop (Nobel Medicine 1989) School Science subjects should be taught in this sequence (unless in single ‘Combined Science’): 1st Physics 2nd Chemistry 3rd Biology

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Mind over Matter : Bruce Lipton

Originally posted on Math Online Tom Circle:
Key Points: 1. The Foundation of Science has changed since Newtonian Era, except Biology / Medicine and Psychology which don’t keep up: Math => Fractal Math Newton Physics (Matter)=> Quantum Physics (Energy) (Organic)…

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“Deep Learning” Online Book

Originally posted on Math Online Tom Circle:
Most popular AI Deeplearning Book by MIT : [English] http://www.deeplearningbook.org/ [中文版] https://exacity.github.io/deeplearningbook-chinese/

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Choosing a Programming Language

Originally posted on Math Online Tom Circle:
https://dev.to/drminnaar/choosing-a-programming-language-493h

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Programmers need Advanced Math ?

Originally posted on Math Online Tom Circle:
As software becomes more complicated for high-speed trains, driverless cars, missile weapons. .. and AI deeplearning algorithm, we can’t depend our life safety on the programmers who don’t understand the advanced maths behind…

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Which Countries Produce Best Programmers

Originally posted on Math Online Tom Circle:
https://blog.hackerrank.com/which-country-would-win-in-the-programming-olympics/ The result is surprising … China, Russia, Poland are the top 3 countries based on the tests, not the usual expected countries such as USA, India, UK. Reason: Mathematics ! China, Russia…

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Prime Number Theorems Conjectures Explained

Originally posted on Math Online Tom Circle:
1. Twin Primes Conjecture : there are infinitely many pairs of Twin Primes among the infinitely many prime numbers. Note: 2013 Zhang YiTang proved the gap between the twin primes is no more…

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The Best Job: Mathematician

Originally posted on Math Online Tom Circle:
The above survey was 2009 USA Job Market. By 2018, Number 1 Job is AI / Data Scientist in USA / China / Europe high-tech market, which still needs Mathematics. eg. Linear Algebra…

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French Math “Coniques” : ellipses, paraboles, hyperboles.

Originally posted on Math Online Tom Circle:
French Math is unique in treating these 3 conic curves: (ellipse, parabola, hyperbola), always starts from the first principle – a la the Cartesian Spirit “I think therefore I am” (我思故我在). “Catersian” Analytical…

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数学范畴化 Categorification

Originally posted on Math Online Tom Circle:
https://www.zhihu.com/question/31823394/answer/53592663?from=timeline Key Points: Category and Functor are above the underlying algebraic structures (Set, Group, Ring, Vector Spaces, etc), study the relations between these structures. Early 19 CE mathematicians before “Category Theory” already knew…

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Why Math is so Sexy?

Originally posted on Math Online Tom Circle:
Cédric Villani (Field Medal 2010) mathematician becomes a deputé (Member of Parliament) in President Emmanuel Macron’s new party “En Marche” consisting of 90% non politicians. His new revolution in French Primary School Math…

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Comment montrer qu’une fonction n’est pas surjective

Originally posted on Math Online Tom Circle:
This is French “Abstract Algebra” in Math Superieure (Baccalauréat + 1 year) : rigorous and unique French way! Others: Injective, Injective

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Six books that have shaped my mathematical worldview

Originally posted on Math Online Tom Circle:
https://medium.com/@fjmubeen/six-books-that-have-shaped-my-mathematical-worldview-7adb5cdd147 First book: The 17th CE French Mathematician-cum-Judge Fermat is the name of my alma-mater French Engineering (undergraduate) University. https://tomcircle.wordpress.com/2015/08/05/new-book-《birth-of-a-theorem-a-mathematical-adventure》/

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AI – DeepLearning – Machine Learning

Originally posted on Math Online Tom Circle:
3 Waves of AI Evolution: 1st Wave (1950s) : Alan Turing “The Father of AI” and his Princeton Prof Alonzo Church (Lambda Calculus). MIT Prof Malvin Minksy’s “Lisp” Functional Programming (a.k.a. Symbolic or…

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《The Master Algorithm》

Originally posted on Math Online Tom Circle:
Main Point: One single “Master Algorithm” for all kinds of knowledge from chess to Go to Medicine to Stocks to …, only differ in ‘Data’ context, but the same One thinking “Mind”. 《The…

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The Pros & Cons of the French Elitist Grandes Ecoles

Originally posted on Math Online Tom Circle:
The French Grandes Écoles System is characterized by one unique Ultra-Selective Exams – “Concours” (pronounced as Kongu) or 科举 (pronounced in Chinese dialect Fujian as “Kogu”) a la the 1,300- year Chinese Imperial…

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Reform in French Baccalaureat

Originally posted on Math Online Tom Circle:
Current Baccalaureat Drawback: Study too many subjects, High Drop out New Reform: Specialised on 4 major subjects – include compulsory French Literature (penultimate year before Bac) & Philosophy. ala British A-level on 4…

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英国留学生带你回忆被数学支配的恐惧

Originally posted on Math Online Tom Circle:
这位中国留英数学专业的小伙子有很好的口才: 数学之美, 他的数学遗憾。 华威大学(The University of Warwick),famous for mathematics in UK. Key Points: Einstein用 Riemann Geometry 数学救了Newton 物理。 中国数学的没落: 自从明朝科举废除数学考试 3位大师救近代中国数学: 华罗庚, 陈省身, 苏步青 数学光明的未来: AI, Big Data, Cloud Computing https://youtu.be/XtGZe229gc0 天才的崎岖道路: “扫地僧”张益唐…

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Top 20 Math Books on Machine Learning / AI

Originally posted on Math Online Tom Circle:
https://www.quora.com/If-you-could-buy-20-math-books-for-machine-learning-what-books-would-you-buy/answer/Sridhar-Mahadevan-6?share=75acc7bc&srid=oZzP The first 4 books (by Strang, Lang, etc) are the Masterpieces. Linear Algebra by Strang. He writes math like few folks do, no endless paragraphs of definitions and theorems. He tells you…

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Singapour : Les Maths Singapour- Une Methode Miracle

Originally posted on Math Online Tom Circle:
La remise du rapport Villani au Ministre de l’Education nationale Mr. Blanquer préconisant 21 mesures pour l’enseignement des mathématiques en France, a mis à l’honneur, par ricochet et par voix de presse, la…

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Visionary mathematician Vladimir Voevodsky

Originally posted on Math Online Tom Circle:
A self-study Russian mathematician, kicked out 3 times in high schools, expelled from Moscow University, all because he did not attend classes, preferred to self-study in a broader scope for his curiosity, at…

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Univalent Foundation – Computer Proof of All Maths

Originally posted on Math Online Tom Circle:
The scary complex field of Math worried the mathematicians who would prove a theorem relying on the previous theorems assumed proven correct by other mathematicians. A sad example was Zhang YiTang (1955 –…

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Motif (Motive 目的)

Originally posted on Math Online Tom Circle:
Below is an excellent intuitive explanation (in Chinese) of the abstract concept Motif by Grothendieck: Brief summary – Motif is the source of all “beautiful things” expressed in different forms. Example : God…

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Song of Simple Group

Originally posted on Math Online Tom Circle:
The lyrics to the song can be found in “Contemporary Abstract Algebra” (Seventh Edition) by Joseph A. Gallian (ISBN 978-0-547-16509-7) pages 422 & 423.

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10招教你用Google搜技巧

Originally posted on Math Online Tom Circle:
https://youtu.be/9PNf_u9adZs

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One of the world’s most influential math texts is getting a beautiful, minimalist edition – The Verge

Originally posted on Math Online Tom Circle:
https://www.theverge.com/2017/9/2/16247282/euclids-elements-kroncker-wallis-math-text-beautiful-minimalist-kickstarter Little print-edition of Math Classics: Euclidean 《The Elements》(几何原理) – the second printing by volume after 《The Bible》. The Euclidean Geometry was less emphasised in Secondary school from 1970s in the world (80s…

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The Evolution of Software

Originally posted on Math Online Tom Circle:
https://medium.com/@cscalfani/so-you-want-to-be-a-functional-programmer-part-1-1f15e387e536

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Zhihu 知乎: 环Ring, 域Field, (半Semi-)群Group, 幺半群 MonoId

Originally posted on Math Online Tom Circle:
数学中代数的有两个名词:环,半群,请问环为什么叫做环,它和汉字里的环(字典中的意思)有什么相同之处;同样,半群为什么叫做半群,这个”半“字是怎么解释呢? [葛利流,数学科技] (I) 环和域 环 (Ring) 是德文, 这名词是David Hilbert发明的。 “环”最好的例子: 整数(Integer) 记作 Z (德文Zahl) 是个环。 他研究 Clock Arithmetic 时钟 是个 Modular Arithmetic (Mod 12)运算, 比如 15 = 3 mod 12 … 钟表上的整数 Z…

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2017 PSLE Math Question

Originally posted on Math Online Tom Circle:
Answer: 10 (Yes!) but why ? …(see explanation here )

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ZAPZAP : Math + Game

Originally posted on Math Online Tom Circle:
https://vulcanpost.com/613827/zapzap-math-malaysia-education-app/

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Mathematical Functions vs Programming Functions

Originally posted on Math Online Tom Circle:
Key Points: Pure Function Partial Function Total Function https://medium.com/the-accepted-forest/mathematical-functions-vs-programming-functions-cf4c7e6f9f4b

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Symmetry, Algebra and the “Monster”

Originally posted on Math Online Tom Circle:
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…

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Math Problem Solver – SymboLab

Originally posted on Math Online Tom Circle:
A new alternative to the UK Mathematica’s “Wolfram Alpha” online tool: http://www.makeuseof.com/tag/not-wolfram-alpha-solve-math-equation-symbolab/ https://m.youtube.com/watch?v=Dinl6I77AoU

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UK Textbooks à la Chinese / Singapore Math Style

Originally posted on Math Online Tom Circle:
[Original Financial Times Article] Google: UK maths books fail DfE test UK, USA, France are copying Chinese Math (from which the “Singapore Modeling Math” derived) in Primary schools, this proves my above-mentioned “Ideal…

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How (not) to memorise mathematics

Originally posted on Math Online Tom Circle:
Many excellent Math students after leaving universities more than 10 years forget 90% of math they learned, save some primary school arithmetics – few could do Singapore PSLE Modelling Math or solve quadratic…

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Math drives Biology

Originally posted on Math Online Tom Circle:
https://youtu.be/X-8MP7g8XOE https://futurism.com/math-help-treat-diseases-develop-better-vaccines/

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The Ring Z/nZ, Fermat Little Theorem, Chinese Theorem (French)

Originally posted on Math Online Tom Circle:
Revision: Modulus Arithmetics (1/2) Fermat Little Theorem https://youtu.be/UaF-piufq84 (1/2) Chinese Theorem (Note: This is the “RING” foundation of “The Chinese Remainder Theorem” which deals with remainders ) https://youtu.be/_xTSQu8Ft5I

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Ideal Math Education

Originally posted on Math Online Tom Circle:
C = Chinese 中文 = Primary school Arithematics sans “Algebra” (= Singapore Modeling Math). Abacus-Algorithmic thinking. E = English = Secondary School Math=> Applied, Tricky, Math Olympiad-style=> Engineering, Business, Applied Science. F =…

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Math Olympiad (Primary Schools) 一筐鸡蛋

Originally posted on Math Online Tom Circle:
One basket of eggs.1粒1粒拿,正好拿完。Remove 1 by 1, nothing left in basket. 2粒2粒拿,还剩1粒。Remove 2 by 2, one left in basket. 3粒3粒拿,正好拿完。Remove 3 by 3, nothing left in basket. 4粒4粒拿,还剩1粒。Remove 4 by 4, one left…

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Les Categories Pour Les Nuls

Originally posted on Math Online Tom Circle:
“Categories for Dummies” (French) https://youtu.be/LVHoROSF3KA Example 1: Paris (P) -> Rome (R) -> Amsterdam (A) Objects: cities {P, R , A} Morphism (Arrow): railway? Identity: railway within the city Associative: (P -> R)…

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Debate (French): Set Theory vs Category Theory

Originally posted on Math Online Tom Circle:
https://sites.google.com/site/logiquecategorique/dcm 4. Category, Logic and IT https://youtu.be/Shk3TNagC-4

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