Category Archives: math

Pi hiding in prime regularities

Originally posted on Math Online Tom Circle:
Three mysterious Math Objects: Pi,? Complex Numbers,? Prime Numbers are hiding in circle. https://youtu.be/NaL_Cb42WyY

Posted in math | Leave a comment

5 Math Tips That Will Speed Up Your Calculations

5 Math Tips That Will Speed Up Your Calculations For most students, regardless of their age, studying math seems like a nightmare. Taking tuition for maths helps when you or your child struggle with calculations. Check out these 5 simple … Continue reading

Posted in math | Tagged | 2 Comments

AI “AlphaGo” beats World’s Best Go Player Ke Jie in 1st Match

Originally posted on Math Online Tom Circle:
After the defeat in 1st match, Ke Jie said “AlphaGo is approaching God!”.? This version of AlphaGo is 10x more powerful than last year’s version which has beateb the South-korean Go player Lee.…

Posted in math | 1 Comment

Google officially supports Kotlin from May 2017

Originally posted on Math Online Tom Circle:
Kotlin is the “New Java” officially supported by Google from May 2017! It is less verbose (罗唆) than Java which is clumsy with boilerplates (样板), ?interoperates with Java on JVM, with modern functional…

Posted in math | Leave a comment

Math Tricks found in Chess

Just read this very nice article on Quora, on the relationship between Math and Chess: https://www.quora.com/What-math-tricks-are-hidden-in-chess Also interesting is this YouTube documentary “My Brilliant Brain” featuring Susan Polgar. Author: Tom Boshoff, Engineering student and math enthusiast Updated May 8 There’s lots … Continue reading

Posted in math | Tagged , | Leave a comment

French youngest President Emmanuel Macron and his Education 

Originally posted on Math Online Tom Circle:
Emmanuel Macron is the youngest French President (39) since Napoleon Bonaparte (40). A brilliant student since young, he impressed his secondary school Drama teacher 24 years older, finally married her. Like any genius…

Posted in math | Leave a comment

LaTeX Thesis Template

This site (https://www.sharelatex.com/blog/2013/08/09/thesis-series-pt5.html) has a guide on how to create your own template for a thesis. Quite nice and simple, and easily customizable. The actual Tex source code is found here: https://www.sharelatex.com/project/51fa85c3db89c3c351085071. I like it as the source code is neat … Continue reading

Posted in math | Tagged , , | Leave a comment

Math Olympiad Tuition

Maths Olympiad Tuition Tutor: Mr Wu (Raffles Alumni, NUS Maths Grad) SMS/Whatsapp: 98348087 Email: mathtuition88@gmail.com Syllabus: Primary / Secondary Maths Olympiad. Includes Number Theory, Geometry, Combinatorics, Sequences, Series, and more. Flexible curriculum tailored to student’s needs. I can provide material, or … Continue reading

Posted in math | Tagged , | Leave a comment

Nanyang Girls NYGH starts school later at 8.15am

Very good idea by NYGH. Sleep is important for students. SINGAPORE: For almost a year now, Nanyang Girls High (NYGH) students have been starting school at 8.15am – a good 45 minutes later than most secondary schools. And the results have … Continue reading

Posted in math | Tagged , | Leave a comment

Jurong East Maths Tuition

Maths Tuition Tutor (Mr Wu): – Raffles Alumni – NUS 1st Class Honours in Mathematics Experience: More than 10 years experience, has taught students from RJC, NJC, ACJC and many other JCs. Also has experience teaching Additional Math (O Level, … Continue reading

Posted in math | Tagged , | Leave a comment

BM Category Theory II 8: F-Algebra, Lambek’s Lemma , Catamorphism, Coalgebra, Anamorphism

Originally posted on Math Online Tom Circle:
[Continued from previous BM Category Theory …] Intuition: [Artificial Intelligence] You teach the computer, like a Primary 6 kid, that Algebra is a?type of expression (f) which, after evaluation, ?returns a value. If…

Posted in math | Leave a comment

Bukit Batok Maths Tuition

Maths Tuition Tutor (Mr Wu): – Raffles Alumni – NUS 1st Class Honours in Mathematics Experience: More than 10 years experience, has taught students from RJC, NJC, ACJC and many other JCs. Also has experience teaching Additional Math (O Level, … Continue reading

Posted in math | Tagged , | Leave a comment

Renowned Chinese mathematician Wu Wenjun dies at 98

Source: https://news.cgtn.com/news/3d517a4e33637a4d/share_p.html Wu Wenjun, distinguished mathematician, member of the Chinese Academy of Sciences (CAS), and winner of China’s Supreme Scientific and Technological Award winner, died at the age of 98 on Sunday in Beijing, according to the CAS. Wu was … Continue reading

Posted in math | Tagged | Leave a comment

Rise in WordAds earnings March 2017

WordPress and WordAds have been doing a good job, I must say. In this year (2017), the earnings have increased gradually for my site (view count is approximately constant). Certainly a great improvement from 2016, where I got a measly … Continue reading

Posted in math | Tagged , | Leave a comment

Ye Sons and Daughters (O Filii et Filiae)

Nice traditional hymn.

Posted in math | Tagged , , | Leave a comment

What is a Module (模)? 

Originally posted on Math Online Tom Circle:
Replace Field scalar as in a Vector Space to Ring scalar in a Module. https://youtu.be/IvukAijXgLE Module is more powerful than Vector Space – because Ring has an “Ideal” (理想) which can partition it…

Posted in math | Leave a comment

American Genius Series 1 1of8 Jobs vs Gates (2015)

Originally posted on Math Online Tom Circle:
https://youtu.be/prstbP2cG6M

Posted in math | Leave a comment

Structure Preserving

Originally posted on Math Online Tom Circle:
Abstract Algebra studies all kinds of?mathematical structures?(Group, Ring, Vector Space, Category, …) , and relationship between them if the structures are preserved after mapping.

Posted in math | Leave a comment

The Cry of the Poor by John Michael Talbot

Recently I discovered a classical guitar Christian composer on YouTube – John Michael Talbot. His music is quite amazing, and one of a kind. The Cry of the Poor 2. Be not afraid

Posted in math | Tagged , , | Leave a comment

Five Loaves and Two Fishes – Corrinne May (Illustrated)

Corrinne May is a Singaporean singer.

Posted in math | Tagged , , | Leave a comment

Mathematics: Beauty vs Utility – Numberphile

Originally posted on Math Online Tom Circle:
https://youtu.be/xopM9BFjcNo

Posted in math | Leave a comment

2 minutes pour le théorème de Bézout

Originally posted on Math Online Tom Circle:
https://youtu.be/0_ZzZzvxnP0

Posted in math | Leave a comment

Maths -Topologie

Originally posted on Math Online Tom Circle:
https://youtu.be/L3HXZfLsuXU

Posted in math | Leave a comment

How the Staircase Diagram changes when we pass to derived couple (Spectral Sequence)

Set and . The diagram then has the following form: When we pass to the derived couple, each group is replaced by a subgroup . The differentials go two units to the right, and we replace the term by the … Continue reading

Posted in math | Tagged , | Leave a comment

How do you overcome the fear of the future? Pope Francis provides the keys

Source: http://aleteia.org/2017/04/26/how-do-you-overcome-the-fear-of-the-future-pope-francis-provides-the-keys/ Have you ever been gripped by a fear of the future that left you walking in circles or paralyzed from moving forward? Today, Pope Francis provided a deeper answer to this common human fear, urging Christians to remember that faith is the anchor … Continue reading

Posted in math | Tagged , , , | Leave a comment

Relative Homology Groups

Given a space and a subspace , define . Since the boundary map takes to , it induces a quotient boundary map . We have a chain complex where holds. The relative homology groups  are the homology groups of this … Continue reading

Posted in math | Tagged , | Leave a comment

Prayer of St Thomas Aquinas for Students (English and Latin)

Source: http://www.aquinascollege.edu/prayer-before-study-exams-spring-2013/ A Prayer Before Study Ineffable Creator, Who, from the treasures of Your wisdom, have established three hierarchies of angels, have arrayed them in marvelous order above the fiery heavens, and have marshaled the regions of the universe with such artful skill, You are proclaimed the true font … Continue reading

Posted in math | Tagged , , | Leave a comment

Exact sequence (Quotient space)

Exact sequence (Quotient space) If is a space and is a nonempty closed subspace that is a deformation retract of some neighborhood in , then there is an exact sequence where is the inclusion and is the quotient map . … Continue reading

Posted in math | Tagged , , | Leave a comment

Reduced Homology

Define the reduced homology groups to be the homology groups of the augmented chain complex where . We require to be nonempty, to avoid having a nontrivial homology group in dimension -1. Relation between and Since , vanishes on and … Continue reading

Posted in math | Tagged , , | 2 Comments

8 JCs to merge (i.e. 4 JCs to close down)

The latest education news in Singapore is that 4 pairs of JCs to merge as student numbers shrink; 14 primary and 6 secondary schools also affected. The effect on the primary and secondary schools is not that significant, due to the … Continue reading

Posted in math | Tagged , , | Leave a comment

中国初中生集体挑战美国高考数学SAT题

Originally posted on Math Online Tom Circle:
[Hint]:? https://youtu.be/mllw55JQy7Y

Posted in math | Leave a comment

The World’s Best Mathematician (*)

Originally posted on Math Online Tom Circle:
Terence Tao:? Weakness in Math: Algebraic Topology Collaborative & “Lone Wolf” Not attempting the Riemann Hypothese: tools not there yet. https://youtu.be/MXJ-zpJeY3E 3 Phases of Math Training: Pre-rigourous: intuition Rigorous: formal prove Post-rigourous: 1…

Posted in math | Leave a comment

The Legend of Question Six (IMO 1988)

Originally posted on Math Online Tom Circle:
This question was submitted ?by West Germany to the IMO Committee, the examiners could not solve it in 6 hours.? In the IMO (1988) only 11 contestants solved it, ?one of them proved…

Posted in math | Leave a comment

The Shortest Ever Papers 

Originally posted on Math Online Tom Circle:
https://youtu.be/QvvkJT8myeI

Posted in math | Leave a comment

Klein Bottle as Gluing of Two Mobius Bands

This is a nice picture on how the Klein bottle can be formed by gluing two Mobius bands together. Very neat and self-explanatory! Source: https://math.stackexchange.com/questions/907176/klein-bottle-as-two-m%C3%B6bius-strips

Posted in math | Tagged , | Leave a comment

Mayer-Vietoris Sequence applied to Spheres

Mayer-Vietoris Sequence For a pair of subspaces such that , the exact MV sequence has the form Example: Let with and the northern and southern hemispheres, so that . Then in the reduced Mayer-Vietoris sequence the terms are zero. So … Continue reading

Posted in math | Tagged , | Leave a comment

Resucitó (Spanish Easter Song)

Wishing all readers a happy Easter! This is a famous Spanish Easter Song: Resucitó, with translation.

Posted in math | Tagged , , , | Leave a comment

Spectral Sequence

Spectral Sequence is one of the advanced tools in Algebraic Topology. The following definition is from Hatcher’s 5th chapter on Spectral Sequences. The staircase diagram looks particularly impressive and intimidating at the same time. Unfortunately, my LaTeX to WordPress Converter … Continue reading

Posted in math | Tagged , | Leave a comment

Holy, Holy, Holy Lord: Lyrics and Music

Amazing organ music. Lyrics: Holy, holy, holy Lord, God of power and (God of) might Heaven and earth are full of Your glory Hosanna in the highest Blessed is He who comes in the name of the Lord Hosanna in … Continue reading

Posted in math | Tagged , , | 1 Comment

Real World Applications of Algebra, Geometry and Topology

Quite a nice video here:

Posted in math | Tagged | 2 Comments

Love Jesus in all who suffer, pope says on Palm Sunday

Source: https://cnstopstories.com/2017/04/09/love-jesus-in-all-who-suffer-pope-says-on-palm-sunday/ By Carol Glatz Catholic News Service VATICAN CITY (CNS) — Jesus does not ask that people only contemplate his image, but that they also recognize and love him concretely in all people who suffer like he did, Pope Francis … Continue reading

Posted in math | Tagged , | Leave a comment

OneKey Token Out of Battery — What to do?

It seems like the OneKey Token (used for 2 factor authentication) runs out of battery quite fast. I have barely used mine (usually use SMS), yet its battery has died surprisingly soon, compared to my other bank tokens. What should … Continue reading

Posted in math | Tagged , , , | Leave a comment

Unknown German Retiree Proved The “Gaussian Correlation Inequality” Conjecture

Originally posted on Math Online Tom Circle:
https://www.wired.com/2017/04/elusive-math-proof-found-almost-lost Case “=” : if (a, b) independent? Case “>” : if (a, b) dependent Thomas Royen used only high-school math (function, derivative) in his proof in 2014. He then published it in…

Posted in math | Leave a comment

Tough Math : Diophantine Equation

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

Posted in math | Leave a comment

Fun Math

Originally posted on Math Online Tom Circle:
Answer : (scroll below) . . . . . . . . . . . . . . . . . . . . Answer = 3 mins See clearer if change person…

Posted in math | Leave a comment

Category Adjunctions 伴随函子

Originally posted on Math Online Tom Circle:
Adjunction is the “weakening?of Equality” in Category Theory. Equivalence of 2 Categories if: 5.2 ?Adjunction definition: such that the 2 triangle identities below ( red and blue) exist. 6.1?Prove: Let C any category,…

Posted in math | Leave a comment

Category Theory (Stanford Encyclopedia of Philosophy)

Originally posted on Math Online Tom Circle:
https://plato.stanford.edu/entries/category-theory/

Posted in math | Leave a comment

Beautiful Math Olympiad Problem

Originally posted on Math Online Tom Circle:
[INMO 1993]

Posted in math | Leave a comment

The genius who rejected Fields Medal & Clay Prize: Grigori Perelman 

Originally posted on Math Online Tom Circle:
Russian mathematician Grigori Perelman proved the Poincaré Conjecture in 7 years of solitude research in his Russian apartment ?- same 7 years of solitude for?Andrew Wiles (The Fermat’s Last Theorem)?in the Cambridge attic…

Posted in math | Leave a comment

The Yoneda Lemma

Originally posted on Math Online Tom Circle:
Representable Functor F of C ( a, -): 4.2?Yoneda Lemma Prove 😕 Yoneda Lemma?: Proof: By “Diagram chasing” below, shows that Left-side: is indeed a (co-variant) Functor. Right-side: Functor “F a“. Note: When…

Posted in math | Leave a comment