Author Archives: tomcircle

About tomcircle

Math amateur

New Math applied in Modern Physics

Originally posted on Math Online Tom Circle:
【文小刚:物理学的新革命——凝聚态物理中的近代数学 | 众妙之门】 https://m.toutiaocdn.com/group/6712424299841454595/?app=news_article_lite&timestamp=1562923076&req_id=20190712171755010152027098774DD5D&group_id=6712424299841454595&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share Keywords: Quantum Entanglement (QE) : 量子纠缠 Topological Order (Long-range QE) : 拓扑序 Topological Insulator (Short-range QE) : 拓扑绝缘体 Rigid State : 凝聚态 Cohomology : 上同调 Tensor : 张量 Category…

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5G Polar Codes Dr. Erdal Arikan

Originally posted on Math Online Tom Circle:
Dr. Erdal Arikan (1958 -) of Bilkent University, Turkey, recieved his PhD in MIT at the age of 27. Huawei Award: The Father of Polar Codes (极化码) Industry watchers believe that the selection…

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“Poisson Distribution Intuition (and derivation)”

Originally posted on Math Online Tom Circle:
“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…

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丘成桐:数理与人文(原创完整版)

Originally posted on Math Online Tom Circle:
【丘成桐:数理与人文(原创完整版)】 https://m.toutiaocdn.com/group/6685925279874941444/?app=news_article_lite&timestamp=1561828635&req_id=20190630011715010152030216506C006&group_id=6685925279874941444&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share (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

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China Gaokao 2019 Interesting Math Question

Originally posted on Math Online Tom Circle:
Gaokao = Baccalaureate = GCE A Level …[Solution scrolled below] … … … … … … … … … … … … … … … … … … … … … … ……

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Viral Chinese 2019 Gaokao Question

Originally posted on Math Online Tom Circle:
Gaokao 高考 = Baccalaureate = Cambridge GCE A-Level Hint: f(x+1) = 2f(x) tells the height = f(x) double when x moves to x + 1 => periodicity is 1 Like Sine or Cosine…

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数学大师的数学启蒙书

Originally posted on Math Online Tom Circle:
【大师的数学启蒙书】 https://m.toutiaocdn.com/group/6712914606001488391/?app=news_article_lite&timestamp=1562988400&req_id=201907131126390100180730727967601&group_id=6712914606001488391&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share Abel / Gauss 自修数学经验: Read Directly from the Masters – 自接读大师的书 (而非读其他人注解的书) 下面这2本数学经典 "葵花宝典"(有中译版) 是WW1&2 前 世界第一流 宗师 (Noether’s ‘Abstract Algebra’ , Hardy’s ‘Number Theory’ ) 的杰作,值得阅读,收藏。 1. Modern Algebra 史上第一本抽象代数的书:…

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Simple groups, Lie groups, and the search for symmetry

Originally posted on Math Online Tom Circle:
Math History | NJ Wildberger Summary: Normal subgroup Quotient Group Finite Simple Group: Z5, D5,… Tesselation (regular) Platonic solids … Two families of Group : Symmetric Groups: Sn Linear Group: GL(n) = M,…

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Alibaba “Damo” Global Math Competition

Originally posted on Math Online Tom Circle:
https://m.damo.alibaba.com/alibaba-global-mathematics-competition/ Jack Ma is a kongfu fan, his Alibaba offices all named under the Kongfu heroes, eg. Damo Academy. “Damo” 达摩 (Bodhidharma) was an indian Buddhist monk who came to China in 5th…

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RSA Encryption – Number Theory

Originally posted on Math Online Tom Circle:
https://dev.to/renegadecoder94/understanding-the-number-theory-behind-rsa-encryption-1pdo Background knowledge: 1. Group 2. Cardinality : Euler Totient Function Note: A linguistic remark: The Latin word “totiens” (or “toties”) means “that/so many times”.

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Homotopy Type Theory: Vladimir Voevodsky

Originally posted on Math Online Tom Circle:
A self-study Math genius Vladimir Voevodsky, Fields Medalist, Russian. https://youtu.be/v5a5BYZwRx8 Voevodsky borrowed idea from Computer Science (“Interface” =hide implementation details) to Math, and vice-versa, from Math to Computer Science : Homotopy Type Theory…

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Characters, Symbols and the Unicode Miracle

Originally posted on Math Online Tom Circle:
Unicode UTF-8: 7-bit ASCII (127 characters) was invented on the back of a napkin by computer scientist in 1960s Unicode (UTF-8) was invented for WWW Web in 1990s, backward compatible with ASCII 100,000…

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Learn Calculus With These Four Online Courses

Originally posted on Math Online Tom Circle:
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) https://youtu.be/WUvTyaaNkzM 4. [Best👍] “Calculus” (MIT Prof Gilbert Strang)…

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Chinese Math Olympiad (Primary) Trick vs Singapore Modeling Math

Originally posted on Math Online Tom Circle:
Both Methods (I) & (II) below does not use Algebra, which is not taught to primary school kids until secondary school (above 12 or 13 years old). (I) Ancient Chinese Arithmetic Method: 例2:The…

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English Fun Math

Originally posted on Math Online Tom Circle:
Different Maths: 1. English (UK/USA) Math is playfully tricky (Math Olympiad, Math Puzzles eg. this Numberpile video) 2. French Math is abstractly theoretical (Group theory explains Symmetry, Rubik’s cube game,… ) 3. Chinese…

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AI with Advanced Math helps in discovering new drugs

Originally posted on Math Online Tom Circle:
https://theconversation.com/i-build-mathematical-programs-that-could-discover-the-drugs-of-the-future-110689?from=timeline Advanced Mathematical Methods with AI is a powerful tool: Algebraic Topology (Persistent Homology) Differential Geometry Graph Theory https://sinews.siam.org/Details-Page/mathematical-molecular-bioscience-and-biophysics-1

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Why French excel in math ?

Originally posted on Math Online Tom Circle:
Mathematics and quantitative finance, France Since 1990, there have been 22 winners of the Fields Medal, widely regarded as the Nobel Prize of mathematics. Thirteen came from just two countries, Russia and France.…

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Happy Birthday To Urbain Le Verrier, Who Discovered Neptune With Math Alone

Originally posted on Math Online Tom Circle:
Urbain Le Verrier, Who Discovered Neptune https://www.forbes.com/sites/startswithabang/2019/03/11/happy-birthday-to-urbain-le-verrier-who-discovered-neptune-with-math-alone/

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Percentage Mental Calculation

Originally posted on Math Online Tom Circle:
Example:4% of 75 = 75% of 4 Mental Steps: 75 x 4 – > 300 – > / 100 – > = 3 (ANS. )Is it easier ?

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The Laws of Mathematics Zermelo-Fraenkel Axioms Set Theory

Originally posted on Math Online Tom Circle:
The Foundation of Modern Math which is based on the “Set Theory”, hit a crisis due to Bertrand Russell “Barber’s Paradox”, until the Zermelo-Fraenkel Axioms came to its rescue. Here is a humorous…

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Quora: Is Abstract Math a fluke (偶然) ?

Originally posted on Math Online Tom Circle:
Answer to Why can humans understand abstract mathematics if such things were never needed in our ancestral environment? Is it a fluke?

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通俗群论

Originally posted on Math Online Tom Circle:
https://youtu.be/RLuqMxZiTQM Challenge: Put ’15’ and ’14’ in the right sequence (Impossible! ) 以下无解:群论

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“Essential mathematical GIFs that will make mathematics finally make sense”

Originally posted on Math Online Tom Circle:
“Essential mathematical GIFs that will make mathematics finally make sense” by Ali Kayaspor https://link.medium.com/z1nWgHm9GU

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RMM Olympiad 2019

Originally posted on Math Online Tom Circle:
https://m.toutiaocdn.com/i6662602678880698894/?iid=63376357991&app=news_article_lite&timestamp=1551357660&group_id=6662602678880698894&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share

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Group Theorems: Lagrange, Sylow, Cauchy

Originally posted on Math Online Tom Circle:
1. Lagrange Theorem: Order of subgroup H divides order of Group G Converse false: having h | g does not imply there exists a subgroup H of order h. Example: Z3 = {0,1,2}…

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陈省身 SS Chern – “The 2nd Gauss”

Originally posted on Math Online Tom Circle:
陈省身香港科技大学 演讲经典 (Highly Recommended – spoken in English & Chinese) http://www.bilibili.com/video/av5473133 他的女婿是香港科大校长。现任校长是 Prof 陈繁星 Tony F. Chan , the ‘Search Algorithm Thesis’ supervising Prof of the 2 Google founders in Stanford University, Applied…

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70-million Bounded Gap Between Primes

Originally posted on Math Online Tom Circle:
Since Ancient Greek : Euclid had proved there are infinite primes. Sieve of Eratosthenes to enumerate the primes. Recent time 3 Mathematicians GPY attempted another Sieve method to find the bounded gap (N)…

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小算盘 大乾坤 Abacus

Originally posted on Math Online Tom Circle:
浙江临海市 算盘博物管主人 雷国华 收藏算盘20年,散尽储蓄,感慨涕下不已。 https://youtu.be/d3ua6tz4Gos 中国的算盘上面2珠 (2×5),下面5珠(5), 共15,加1 = 16 进位。古代是16位 (Hexadecimal) 制, 半斤 八两 (= 1/2 斤 x 16 两 = 8 两)。 日本改良成10位制: 上面1珠 (1×5),下面4珠(4), 共9,加1 = 10 进位。 https://youtu.be/DiHfHJAjAlk

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十二平均律 12-tone Equal Temperament

Originally posted on Math Online Tom Circle:
《十二平均律》 是明朝 "布衣王子" 朱载堉 (1536年-1610年) 发明的,由当时在中国传教的意大利人 利马窦 (Matteo Ricci, 1552 – 1610), 传给欧洲的法国数学家 Marin Mersenne (Mersenne Prime ) 。现代音乐之父 巴哈 Bach 第一个采用,制作世界第一架钢琴有12黑白键,并作曲 《Bach 12-tone Equal Temperament》。 朱载堉把 “1” 到 “i” 的八度 (Octave) 分为等比…

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Richard Dedekind

Originally posted on Math Online Tom Circle:
Julius Wilhelmina Richard Dedekind (6 Oct 1831 – 12 Feb 1916) – Last student of Gauss at Göttingen – Student and closed friend of Dirichlet who influenced his Mathematical education – Introduced the…

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Dedekind Cut : “Prove 0.9999… = 1”

Originally posted on Math Online Tom Circle:
Key Notes: Rational Numbers Q eg. 1/2, … Complete but non Continuous. Irrational numbers eg. Real number is Complete and Continuous Dedekind Cut The Proof of “0.999… = 1” by using Set Theory…

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Bit Coin and Block Chain

Originally posted on Math Online Tom Circle:
Bit Coin is only one application of Block Chain. https://youtu.be/g_fSistU3MQ

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Machine Learning is Just Mathematics! Free Machine Learning Resources

Originally posted on Math Online Tom Circle:
https://youtu.be/tGyfmzuR4d4

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Learn NUMPY in 5 minutes – BEST Python Library!

Originally posted on Math Online Tom Circle:
https://youtu.be/xECXZ3tyONo

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Imaginary Numbers

Originally posted on Math Online Tom Circle:
FINAL EPISODE – Riemann Complex Plane : 4 dimension but viewed in 3 dimensions Episode 1 – 9 : History Episode 10: Complex function Function : 1 input mapped to 1 output Multi-function…

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Math for AI : Gradient Descent

Originally posted on Math Online Tom Circle:
Simplest explanation by Cheh Wu: (4 Parts Video : auto-play after each part) Revision: Dot Product of Vectors https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/dot-cross-products/v/vector-dot-product-and-vector-length Gradient Descent (opposite = Ascent) https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/gradient-and-directional-derivatives/v/why-the-gradient-is-the-direction-of-steepest-ascent

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Mathematician Couple’s Wedding Math Questions

Originally posted on Math Online Tom Circle:
https://m.facebook.com/nikita.nikolaev.752/posts/2208321356091587 It is fun for the guests who are also mathematicians like the wedding couple… Why don’t the IT couples do the same with computer questions (eg. private cloud, serverless, containers, DevOps,… )…

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Cute Graph Cheatsheet

Originally posted on Math Online Tom Circle:
Math Online Tom Circle View original post

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Sir Michael Atiyah obituary

Originally posted on Math Online Tom Circle:
Atiyah is so-called the “2nd Newton” in being both a Mathematics & a Physics Grandmaster, his life achievement extends the ancient Greek Geometry to Topology and Algebra since Euclid till now, providing useful…

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中国历法

Originally posted on Math Online Tom Circle:
Chinese calandre is both solar and lunar, unlike western (pure solar) and Muslim (pure lunar): https://youtu.be/qXFeQmb2gU8

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Byrne’s Euclid

Originally posted on Math Online Tom Circle:
https://www.c82.net/euclid/ My Modern Met: Geometry Lovers Will Enjoy This Interactive Version of Byrne’s Euclid. https://mymodernmet.com/byrnes-euclid-nicholas-rougeux/

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Modern Mathematics and the Langlands Program | Institute for Advanced Study

Originally posted on Math Online Tom Circle:
https://www.ias.edu/ideas/modern-mathematics-and-langlands-program

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The Error Function & The Integral of e^(-x^2)

Originally posted on Math Online Tom Circle:
https://youtu.be/jkytxdedxhU The Bell Curve: https://youtu.be/aSjWXMkDazY

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The most beautiful and important mathematical equations

Originally posted on Math Online Tom Circle:
https://www.zmescience.com/other/feature-post/mathematical-equations-beautiful-30112018/amp/

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From Polynomial to Modern Algebra

Originally posted on Math Online Tom Circle:
Examples Polynomial with degree > 5 https://youtu.be/3B0TqabK2a8

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13 classic mathematics books for lifelong learners

Originally posted on Math Online Tom Circle:
https://medium.com/however-mathematics/13-classic-mathematics-books-for-lifelong-learners-7ec2759142da?from=timeline 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…

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Logic & Math (Set Theory)

Originally posted on Math Online Tom Circle:
Cambridge Prof Peter Smith: You can download the book at the bottom link from the below web site. https://boingboing.net/2018/12/26/beyond-a-equals-a.html/amp?from=singlemessage Philosophy using Math – that is cool! Set Theory is Philosophy, see this “Set…

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How Singapore Data Scientists caught the subway MRT “Circle line” rogue train

Originally posted on Math Online Tom Circle:
https://blog.data.gov.sg/how-we-caught-the-circle-line-rogue-train-with-data-79405c86ab6a

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Quara: Strategy to teach yourself math from basic algebra to high level mathematics

Originally posted on Math Online Tom Circle:
If you had to teach yourself math from basic algebra to high level mathematics, what would be your strategy? https://www.quora.com/If-you-had-to-teach-yourself-math-from-basic-algebra-to-high-level-mathematics-what-would-be-your-strategy/answer/Cornelius-Goh?ch=3&share=be44143e&srid=oZzP

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Chinese Primary School Math

Originally posted on Math Online Tom Circle:
As shown in the picture below, find the height of the table? (No Algebraic equation please for Primary School Math). Answer: [hint = 130 cm] Try yourself before scrolling down. . . .…

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