Author Archives: mathtuition88

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What Is The Shape of the Universe (Video)

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(Important Changes) PSLE Math: Arrow -> vs Equal=

Source: Facebook For those taking PSLE, please take note of this important update regarding the difference between arrow and equal sign. Forward this to your friends taking PSLE! Basically, I think MOE is trying to instill students to be mathematically … Continue reading

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PhD Comic: 大智若愚

The new PhD Comic is related to the Chinese proverb: 大智若愚, which is roughly translated as “a wise man looks stupid.; great wisdom takes the looks of folly [appearance of stupidity]”.

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SG Education News: More places for Medicine Students

Good news for those aspiring to be medical doctors. Med school places to rise to 500 by next year The Straits Times The National University of Singapore (NUS) has had more than 2,000 top students fight for the 300 spaces … Continue reading

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Unique Cars and Parts

There are hundreds if not thousands of Automotive websites to be found on the net, so often it can be a little hit and miss as to finding the best of the best that is out there. Unique Cars and … Continue reading

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Free tutoring app for peer-tutoring

Do try out the new app AsknTeach. Quite a good idea, the app creator reportedly invested more than $100,000 to $200,000 into it. Only problem I can foresee is that overall quality of answers may not be that good, since it … Continue reading

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Summary: Shapes, radius functions and persistent homology

This is a summary of a talk by Professor Herbert Edelsbrunner, IST Austria. The PDF slides can be found here: persistent homology slides. Biogeometry (2:51 in video) We can think of proteins as a geometric object by replacing every atom by a … Continue reading

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Brain has 11 dimensions

One of the possible applications of algebraic topology is in studying the brain, which is known to be very complicated. Site: https://www.wired.com/story/the-mind-boggling-math-that-maybe-mapped-the-brain-in-11-dimensions/ If you can call understanding the dynamics of a virtual rat brain a real-world problem. In a multimillion-dollar supercomputer … Continue reading

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How to explain this math magic trick?

Quite impressive math magic trick, that even impressed the very strict judge Simon Cowell. I am not sure how he did it, other than possible prearranged volunteers. Another possibility is that the calculator is modified. Site: http://www.usmagazine.com/entertainment/news/americas-got-talent-contestant-performs-crazy-magic-trick-w488672 London had the volunteers … Continue reading

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Yitang Zhang’s Santa Barbara Beach Walk

Professor Yitang Zhang is a famous Math professor who made important progress in number theory (Twin Prime Conjecture). Most strikingly, he made this progress in his fifties, which is kind of rare in the mathematical world. Source: Quanta Magazine Yitang … Continue reading

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Finally received WordAds payout by WordPress

Thanks to all readers of mathtuition88.com, I have received WordAds payout by WordPress. Mathtuition88.com first joined WordAds in 01-2014, where the payout was quite miserable (less than $1 for 5000 views). The payout has since increased considerably, thanks to higher quality … Continue reading

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Guide to Starting Javaplex (With Matlab)

Guide to Starting Javaplex (With Matlab) Step 1) Visit https://appliedtopology.github.io/javaplex/ and download the Persistent Homology and Topological Data Analysis Library 2) Download the tutorial at http://www.math.colostate.edu/~adams/research/javaplex_tutorial.pdf and jump to section 1.3. Installation for Matlab. 3) In Matlab, change Matlab’s “Current … Continue reading

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Subtle Error in Wikipedia: Dedekind’s number

On Wikipedia (https://en.wikipedia.org/wiki/Dedekind_number), it is stated that the Dedekind’s number M(n) is the the number of abstract simplicial complexes with n elements. This is incorrect, at least based on the Wikipedia definition of abstract simplicial complex, which does not allow the … Continue reading

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Habitica Mage Highest Intelligence Gear Guide

Habitica is a productivity app, something like a to-do list in a gamified form. Users gain experience and gold from completing tasks, and can join in quests with a party to defeat monsters. The mage class has one of the highest … Continue reading

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Donald Trump Math: 17×6=?

What is 17×6? (without using calculator) Practicing basic mental math without calculator is good. Even for PSLE, where calculator is allowed, it is a good idea not to rely on it too much.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Ye Sons and Daughters (O Filii et Filiae)

Nice traditional hymn.

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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

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Five Loaves and Two Fishes – Corrinne May (Illustrated)

Corrinne May is a Singaporean singer.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Resucitó (Spanish Easter Song)

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

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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

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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

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Real World Applications of Algebra, Geometry and Topology

Quite a nice video here:

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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

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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

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SO(3) diffeomorphic to RP^3

} Proof: We consider as the group of all rotations about the origin of under the operation of composition. Every non-trivial rotation is determined by its axis of rotation (a line through the origin) and its angle of rotation. We … Continue reading

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SU(2) diffeomorphic to S^3 (3-sphere)

(diffeomorphic) Proof: We have that Since , we may view as Consider the map It is clear that is well-defined since if , then . If , it is clear that . So is injective. It is also clear that … Continue reading

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Echelon Form Lemma (Column Echelon vs Smith Normal Form)

The pivots in column-echelon form are the same as the diagonal elements in (Smith) normal form. Moreover, the degree of the basis elements on pivot rows is the same in both forms. Proof: Due to the initial sort, the degree … Continue reading

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Persistent Homology Algorithm

Algorithm for Fields In this section we describe an algorithm for computing persistent homology over a field. We use the small filtration as an example and compute over , although the algorithm works for any field. A filtered simplicial complex … Continue reading

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Everyone’s Unique Timezone (Motivational)

Relax. Take a deep breath. Don’t compare yourself with others. The world is full of all kinds of people – those who get successful early in life and those who do later. There are those who get married at 25 … Continue reading

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De Rham Cohomology

De Rham Cohomology is a very cool sounding term in advanced math. This blog post is a short introduction on how it is defined. Definition: A differential form on a manifold is said to be closed if , and exact … Continue reading

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Singular Homology

A singular -simplex in a space is a map . Let be the free abelian group with basis the set of singular -simplices in . Elements of , called singular -chains, are finite formal sums for and . A boundary … Continue reading

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Mapping Cone Theorem

Mapping cone Let be a map in . We construct the mapping cone , where is identified with for all . Proposition: For any map we have if and only if has an extension to . Proof: By an earlier … Continue reading

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