Author Archives: tomcircle

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…

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…

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…

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

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

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…

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:…

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,…

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…

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”.

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…

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…

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)…

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…

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…

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

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.…

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/

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 ?

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…

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?

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

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

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

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}…

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…

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)…

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

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…

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…

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…

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

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

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

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…

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