Author Archives: tomcircle

Originally posted on Math Online Tom Circle:
The USA IMO coach Prof Loh is the son of 2 Singaporean Math Prof (dad) & JC Math teacher (mom). He uses the Chinese “drill” style + American “think” style to beat China…

Originally posted on Math Online Tom Circle:
https://m.toutiaocdn.com/group/6786617693777691144/?app=news_article_lite&timestamp=1580561339&req_id=202002012048590100120651491D5E0A50&group_id=6786617693777691144

Originally posted on Math Online Tom Circle:
These 2 smart Singaporean students invented “Silver Ratio” , “Bronze Ratio” … equally good as the Golden Ratio. Recap: Golden Ratio https://plus.maths.org/content/silver-ratio

Originally posted on Math Online Tom Circle:
https://youtu.be/hyerB4Ek8sU https://www.businessinsider.sg/leap-year-animation-how-february-29-maintains-seasons-2020-2/?r=US&IR=T

Originally posted on Math Online Tom Circle:
To really appreciate music, you must understand this Math & history : 5 notes to 7 notes to 12 notes. & fractions: 3/2, 3/4, 2/1 (octave) Music = Math + History 1. Ancient…

Originally posted on Math Online Tom Circle:
Historical Background: Ideal (理想) was a by-product by mathematicians in the 350-year proof of the 17CE Fermat’s Last Theorem, wherein they found a violation of the existing “Fundemental Law of Arithmetic” (Unique Prime…

Originally posted on Math Online Tom Circle:
This “Simple Car Parking” is the Decision Making Strategy demonstrated in our daily life, even in the micro-cell biological level in nature. In the current USA-China Trade War, China Xi is taking the…

Originally posted on Math Online Tom Circle:
https://interestingengineering.com/11-of-the-best-youtube-channels-for-understanding-mathematics Below are some of the best and Free Math channels from Secondary School to University to Public Math Enthusiasts. 1. Khan Academy (School Math, Sponsored by Bill Gates) 2. Numberphile (Math Curiosity)…

Originally posted on Math Online Tom Circle:
She is a Cambridge PhD in Quantum Computing. https://youtu.be/nEhhQtq9gp4 How to learn Quantum Mechanics on your own : https://youtu.be/Rs572Cf4zkk

Originally posted on Math Online Tom Circle:
【掌握这五大统计学知识，让你笑傲数据科学界】 https://m.toutiaocdn.com/group/6723020943871967751/?app=news_article_lite&timestamp=1565375984&req_id=20190810023944010152028205708822C&group_id=6723020943871967751&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share 1. MEAN / MEDIUM 2. PERCENTILE 3. SKEWNESS 4. STANDARD DEVIATION 5. PCA = Pricinpal Component Analysis 【学习大数据，我不会数学怎么办？还要不要学啦？】 https://m.toutiaocdn.com/group/6706386149763449356/?app=news_article_lite&timestamp=1565378178&req_id=20190810031618010152042134003992B&group_id=6706386149763449356&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share 1. Probability & Statistics 2. Linear Algebra (Matrix, Eigenvectors, Eigenvalues) 3. Optimisation…

Originally posted on Math Online Tom Circle:
【中国科学院林群院士告诉你，怎样才能学好数学？】复制这条信息€80cKc€ZjlaWx€后打开👉今日头条极速版👈 林群院士很谦虚，自称很笨, 看到200页的数学教科书头也会晕： 他用学习Calculus例子，批评＂教科书不教真理，只教证明 (Proof)＂ : …把简单道理讲得很复杂: …其实一个日常生活的案例(火车 Case), 就可以解释清楚。 Note: 林群院士是第一个把复杂吓人的Cauchy Epsilon-Delta Analysis (aka Advanced Calculus) 用中学数学简单化。 Video: 大自然的悟性发现数学: … 文学 《The War & The Peace》： 托尔斯泰用Calculus 证明Napoleon 必败。 ＂不是你听不懂数学，是数学老师教得不好。＂ https://baike.baidu.com/wikisecond/videoflow?secondId=332699&lemmaId=11364&from=lemma&feedInlemma=1

Originally posted on Math Online Tom Circle:
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)…

Originally posted on Math Online Tom Circle:
Given: 3 circles of radius 2 Find: Shaded Area? Hint: Sum of 3 angles in the triangle = π = 1/2 (2π) ＝1/2 circle => its Area = 1/2(π. 2^2) = 2π =…

Originally posted on Math Online Tom Circle:
Prof Loh (CMU) is the 2019 USA IMO coach whose team (5 ABC, 1 White) co-won the IMO Championship with China. … https://youtu.be/IUTGFQpKaPU

Originally posted on Math Online Tom Circle:
https://towardsdatascience.com/data-science-jobs-with-their-salaries-171acd3bf9be Gone are the days where Math graduates were destined to low-pay teachers in the 60s to 90s. Now Math career is the hottest high pay job in the 2 key engines of…

Originally posted on Math Online Tom Circle:
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…

Originally posted on Math Online Tom Circle:
【打破美国35年纪录的天才，与中国奥数、信息学双料冠军的巅峰对决】 https://m.toutiaocdn.com/group/6714952524924715531/?app=news_article_lite&timestamp=1563521442&req_id=20190719153042010152029169696E814&group_id=6714952524924715531&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share USA Team (2016 & 2018 World Champion) : China IMO Team : … … 【2019国际数学奥赛结果公布 中美两国并列团体冠军】 https://m.toutiaocdn.com/group/6715594110440309261/?app=news_article_lite&timestamp=1563682066&req_id=20190721120745010025067136905FD11&group_id=6715594110440309261&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share Two observations: 1. Why almost all Chinese in top China, USA, Canada, NZ, Singapore…

Originally posted on Math Online Tom Circle:
【10部关于数学的顶级纪录片，带你进入奇幻之门】 https://m.toutiaocdn.com/group/6719737122653209101/?app=news_article_lite&timestamp=1564575985&req_id=201907312026250101520222026997CB8&group_id=6719737122653209101&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share 10 Math Videos: The Joy of Math The Joy of Stats The Joy of Logic The Code A Brilliant Madness The Great Math Mystery How Long is a piece of string…

Originally posted on Math Online Tom Circle:
Find the last 2 in Singapore NLB libraries: “The Joy of X” , “How to bake Pi”

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…