Author Archives: tomcircle

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,… )…

Originally posted on Math Online Tom Circle:
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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…

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

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/

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

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

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

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

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…

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…

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

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

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. . . .…

Originally posted on Math Online Tom Circle:
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.…

Originally posted on Math Online Tom Circle:
I am a fan of Fermat, not only because my university Alma Mater was in his hometown Toulouse (France) named after him “Lycée Pierre de Fermat (Classe Préparatoire Aux Grandes Ecoles) ” ,…

Originally posted on Math Online Tom Circle:
https://youtu.be/ZJ5b29WYWrQ To test if the infinite series converges, provided it is positive & decreasing function you can convert it to (although they converge to different values.)

Originally posted on Math Online Tom Circle:
(Traditional Method learnt at O-Level) Integration by Parts: NEW Technique taught by this UC-Berkley Chinese Mathematician: “DI” Method https://youtu.be/2I-_SV8cwsw First Stop: “D column at 0 “ 2nd Stop: 3rd Stop:

Originally posted on Math Online Tom Circle:
https://youtu.be/EWdcOID8zxU

Originally posted on Math Online Tom Circle:
Why easy analysis problems are easy by Timothy Gowers (UK, Fields Medal 1998) Timothy Gowers is teaching in Cambridge, he wrote the thick volume of “Princeton Math Encyclopedia.” He is a very good…

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

Originally posted on Math Online Tom Circle:
https://youtu.be/A54_QPXdkU0

Originally posted on Math Online Tom Circle:
Fermat Little Theorem: For any prime integer p, any integer m When m = 2, Note: 九章算数 Fermat Little Theorem (m=2) Pascal Triangle (1653 AD France ）= (杨辉三角 1238 AD – 1298 AD)…

Originally posted on Math Online Tom Circle:
[Hint] : Assume 3 cases, then by Elimination using Mr Brown’s hint (somethingS right, somethingS wrong)

Originally posted on Math Online Tom Circle:
Fibonacci Number 1 1 2 3 5 8 13 21… https://m.youtube.com/watch?v=VK7XR-wlpAk

Originally posted on Math Online Tom Circle:
［中文］历史 History: https://youtu.be/NeoDdnSlRjk Sir Atiyah Proof on 2018 September : (5 Pages PDF download here) https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY/view https://youtu.be/jXugkzFW5qY Bigger Lecture Notes video (at 34 mins, inspired in Singapore) https://youtu.be/oe4Jo4i3w_w Analytic function: preserve angle after…

Originally posted on Math Online Tom Circle:
What is your favorite theorem ? I have 2 theorems which trigger my love of Math : Chinese Remainder Theorem: 韩信点兵, named after a 200 BCE Han dynasty genius general Han Xin （韩信）…

Originally posted on Math Online Tom Circle:
China Nanjing Aviation University set the WiFi password as the answer of this integral (first 6 digits). Can you solve it? Answer : Break the integral (I) into 2 parts: I = A(x)…

Originally posted on Math Online Tom Circle:
Why did the approach to mathematics change with Common Core, rather than providing more structure to how it was previously taught? by Peter Kruger https://www.quora.com/Why-did-the-approach-to-mathematics-change-with-Common-Core-rather-than-providing-more-structure-to-how-it-was-previously-taught/answer/Peter-Kruger?share=84fb2ef6&srid=oZzP

Originally posted on Math Online Tom Circle:
Solve: Since the exponents (3+x) on both sides are equal, => 2 = 3

Originally posted on Math Online Tom Circle:
Bible Math: 153 St. Peter Fish [John 21:3-11] 3  So they went out and got into the boat, but that night they caught nothing. 6 He said, “Throw your net on the right side of…

Originally posted on Math Online Tom Circle:
Below are two French Baccalaureate Math textbooks (Volume 1 & 2) for Grade 12th (or Junior College Year 2, GCE A Level, Lycée: Terminale C) students in the late 1970s. There was a…

Originally posted on Math Online Tom Circle:
One afternoon 5 friends rented 3 bikes from 5 p.m. to 6:30 p.m. and took turns to ride on them. At any time, 3 of them cycled while the other 2 friends rested.…

Originally posted on Math Online Tom Circle:
Key Points: Bus Waiting Time Pattern Biology Chicken eyes Physics: Random matrix / Eigenvalues / Riemann Zeta-function for Prime Numbers Universal Pattern: Normal Distribution Curve https://www.quantamagazine.org/the-universal-pattern-popping-up-in-math-physics-and-biology-20180823/

Originally posted on Math Online Tom Circle:
Key Points: Normed Distance: Euclidean Expander Graph https://www.quantamagazine.org/universal-method-to-sort-complex-information-found-20180813/

Originally posted on Math Online Tom Circle:
The most interesting “Category Theory” （范畴论) for Programmers course III by Dr. Bartosz Milewski , a follow-up of last year’s course II. Prerequisites: Fundamental of Category Theory: Functor, Natural Transformation, etc. (Course II…

Originally posted on Math Online Tom Circle:
Keywords: Dijkstra, Edge Wyber (born 1930 Rotterdam) Goto is harmful Structures: sequence, selection, iteration Three Programming Paradigms: 1. Structured Programming (1968 Dijkstra) Impose discipline on direct transfer of control aka “Goto“. “If/ then…

Originally posted on Math Online Tom Circle:
https://youtu.be/BzyOoo4AOxs

Originally posted on Math Online Tom Circle:
Functional Programming (FP) Languages : Lisp, Haskell, Scala, Kotlin, etc. Other non-FP influenced by Lambda Calculus: Python, Ruby, Javascript, Java 8, C++ Inventor of Lambda Calculus : Alonzo Church (1903 – 1995), whose…

Originally posted on Math Online Tom Circle:
The Big Internet Math-Off, Round 1 – James Tanton v Nira Chamberlain | The Aperiodical http://aperiodical.com/2018/07/the-big-internet-math-off-round-1-james-tanton-v-nira-chamberlain/ https://youtu.be/M7e-LByl_68

Originally posted on Math Online Tom Circle:
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: Leibniz also invented 01 binary algebra, which he later found it was…

Originally posted on Math Online Tom Circle:
https://youtu.be/AoecIZ64sIk Keywords: Fermat’s Last Theorem (FLT): Pierre de Fermat (France 17CE): FLT Conjecture or Prank ? Euler (n= 3) Taniyama-Shimura-Weil Conjecture: Modular Form = Elliptic Curve Galois Group Symmetry Andrew Wiles (UK Cambridge…

Originally posted on Math Online Tom Circle:
Science Friday: How Abstract Math Can Analyze Social Injustice. Dr. Eugenia Cheng https://www.sciencefriday.com/segments/how-abstract-math-can-analyze-social-injustice/ [Sound]: https://m.soundcloud.com/scifri/how-abstract-math-can-analyze-social-injustice Interview: Yoneda Lemma

Originally posted on Math Online Tom Circle:
Worldcup 2018 Surprising Result: World No.1 (Germany) Lost to World No.59 (Korea) – why ? Reason: Math ! For weak Korea to win, the best strategy is to keep the goals number as…

Originally posted on Math Online Tom Circle:
The “war” of OOP vs FP is akin to Applied Math vs Pure Math. The formers (OOP & Applied Math) are not “rigourous” but practical, compared to the laters (FP & Pure Math)…

Originally posted on Math Online Tom Circle:
Landau’s book “Symmetry” explains it as follow: Automorphism = Congruence= 叠合 has 1). Proper 真叠合 (symmetry: left= left, right = right) 2). Improper 非真叠合 (non-symmetry: reflection: left changed to right, vice-versa). Congruence => preserve…

Originally posted on Math Online Tom Circle:
Symmetry (hence Group) explains : 1. Conservation of Energy; 2. Conservation of Angular Momentum; 3. Periodic Table; 4. Laws of Thermodynamic. Emmy Noether Theorem (1918): Conservation Laws owes to Symmetry : 1. In…

Originally posted on Math Online Tom Circle:
https://www.sciencenews.org/article/emmy-noether-theorem-legacy-physics-math

Originally posted on Math Online Tom Circle:
It is not only owed to the Ecole Normale Superieure where the 11 Fields medalists were educated, but the prominent “Math Culture” in French society. This is similar to the International Math Olympiad…