Author Archives: mathtuition88

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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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记叙文开头的几种方式 How to Write The Start of Narrative Composition

Originally posted on Chinese Tuition Singapore:
记叙文是以记人,叙事,写景,状物(描绘事物)为主,主要内容是人物的经历和事物的发展变化。 记叙文有五种主要表达方式:叙述,描写,议论,抒情,说明。而记叙文的开头主要有以下几种形式: 一,叙述 把人物的经历和事物的发展变化过程表现出来。用简单的话说,就是,这件事怎么发生的,过程是什么,结果怎么样。当然,如果用这种方式开头,就不需要把整个事情的过程交代清楚,一般只要把事情的起因表述清楚即可。过程和结果可以在正文中体现。 比如: 1. 描写母爱——上幼儿园的时候,妈妈给我买了一把可爱的小花伞。伞的大小对我来说刚刚好,因为正好能遮住我小小的身体。妈妈说,自从我有了小花伞,就特别喜欢下雨天。只要一下雨,我就会把小花伞找出来,拉着妈妈往外跑。妈妈就撑起一把大伞来遮住我的小伞,陪着我在雨里玩。 2. 描写一次难忘的经历——清晨,大街上异常忙碌,人来人往,像一条畅流的小溪。忽然,两辆自行车撞在一起,像一块石头横挡在小溪中间,小溪变得流动缓慢,渐渐停止了。 3. 描写一次闯祸——在故事发生时,他还是个七八岁的孩子,他常常做些让大人们意想不到的恶作剧。但是,因为他还只是个孩子,所以大人们除了偶尔斥责几句之外,都不把他做的那些调皮捣蛋的事放在心上。就这样,他的胆子越来越大,闯的祸也越来越大。 作文开头交代了事情的起因,下面就可以直接写事情的经过。 二, 描写 主要是对人物的外貌,动作,心理,事物的形态,样貌等具体的刻画。通常对人物的这种描写会从侧面反映出人物的性格特点。 例如: 1. 描写邻居——我有一位小邻居,她的名字叫小红,今年九岁。她远远的小脑袋上扎着两条小辫子,有着一双水灵灵的大眼睛。她的耳朵粉红小巧,像贝壳一样。红嘟嘟的小嘴整天叽叽喳喳不知疲倦。 2. 描写亲人——我弟弟很可爱,他那圆圆的小脸蛋上嵌着一双水灵灵的大眼睛。嘴唇薄薄的,一笑小嘴一咧,眼睛一眯,还生出一堆小酒窝,非常可爱。要是谁惹他生气了,他就会瞪大眼睛,撅起小嘴。 如果作文中需要写关于某个人的事情,那在作文的一开始就告诉读者这个人的性格特点,将会为作文的正文做好铺垫。 三, 抒情 通过文中要描写的人或事来表达自己内心的情感。 例如: 描写母爱——如果说我有向全世界的人宣布一件事情的权力的的话,我一定会说,我要感谢那个赋予我生命,教会我勇敢,关爱我成长的,我心中最漂亮的女人-妈妈。 如果作文题目是关于“后悔”,“感激”,“难过”等对一个人或一件事的心情,在作文开头就表现出这种情感是一个很好的选择。 四, 回忆 通常用于写时间比较久的事情,比如,童年,几年前,几个月前,等发生的事情。 例如: 1. 描写童年——在偌大的世界上,人人都有一个栖息之地—家庭。有的家庭富丽堂皇,有的家庭美满甜蜜。对无忧无虑的小孩子来说,这是一块充满慈爱和乐趣的生命之地。然而,我是个不幸的孤儿,从小失去了父母,跟姐姐住在外婆家。回忆起自己在外婆家度过的那几年,我的泪水就像断了线的珠子。 2.…

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CP1 and S^2 are smooth manifolds and diffeomorphic (proof)

Proposition: is a smooth manifold. Proof: Define and . Also define by and . Let be the homeomorphism from to defined by and define by . Note that is an open cover of , and are well-defined homeomorphisms (from onto … Continue reading

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Tangent space (Derivation definition)

Let be a smooth manifold, and let . A linear map is called a derivation at if it satisfies The tangent space to at , denoted by , is defined as the set of all derivations of at .

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Looking for Home Tutors?

If you are looking for home tutors (any subject, e.g. Mathematics, Chinese, English, Science, etc.) contact us at: SMS/Whatsapp: 98348087 Email: mathtuition88@gmail.com We are able to recommend you highly qualified tutors, free of charge, no obligations. Note that usually tutors’ … Continue reading

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Secondary Chinese Tuition (IP / O Level)

Ms Gao specializes in tutoring Secondary Level Chinese. Can teach composition, comprehension, etc, according to student’s weaknesses. Has taught students from RI (IP Programme), MGS, and more. Familiar with IP and O Level (HCL/CL) Chinese syllabus. Website: https://chinesetuition88.com/ Contact: 98348087 … Continue reading

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Homology Group of some Common Spaces

Homology of Circle Homology of Torus Homology of Real Projective Plane Homology of Klein Bottle Also see How to calculate Homology Groups (Klein Bottle).

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Summary of Persistent Homology

We summarize the work so far and relate it to previous results. Our input is a filtered complex and we wish to find its th homology . In each dimension the homology of complex becomes a vector space over a … Continue reading

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Cast Iron Pan Singapore Review

Recently bought a cast iron pan/skillet for home cooking. Cast iron is an ancient technology that has several benefits over the more modern non-stick technology. It is supposed to be cheap (just US$15 in America Lodge L8SK3 Cast Iron Skillet, … Continue reading

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Inspirational Scientist: Dan Shechtman

Source: https://www.theguardian.com/science/2013/jan/06/dan-shechtman-nobel-prize-chemistry-interview To stand your ground in the face of relentless criticism from a double Nobel prize-winning scientist takes a lot of guts. For engineer and materials scientist Dan Shechtman, however, years of self-belief in the face of the eminent Linus … Continue reading

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Structure Theorem for finitely generated (graded) modules over a PID

If is a PID, then every finitely generated module over is isomorphic to a direct sum of cyclic -modules. That is, there is a unique decreasing sequence of proper ideals such that where , and . Similarly, every graded module … Continue reading

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Secondary Level Chinese Tuition

Looking for O Level / IP / JC Chinese Tuition? Ms Gao specializes in teaching secondary level chinese (CL/HCL) tuition in Singapore. Ms Gao has taught students from various schools, including RI (Raffles Institution IP Programme). Teaches West / Central … Continue reading

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Persistence Interval

Next, we want to parametrize the isomorphism classes of the -modules by suitable objects. A -interval is an ordered pair with . We may associate a graded -module to a set of -intervals via a bijection . We define for … Continue reading

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The Map of Mathematics (YouTube)

A nicely done video on how the various branches of mathematics fit together. It is amazing that he has managed to list all the major branches on one page. Also see: Beautiful Map of Mathematics.

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Homogenous / Graded Ideal

Let be a graded ring. An ideal is homogenous (also called graded) if for every element , its homogenous components also belong to . An ideal in a graded ring is homogenous if and only if it is a graded … Continue reading

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Donate to help Stray Dogs in Singapore

URL: https://give.asia/movement/run_for_exclusively_mongrels 3 Singaporeans – Dr Gan, A Dentist, Dr Herman, A Doctor, and Mr Ariffin, a Law Undergraduate will be taking on the Borneo Ultra Trail Marathon on Feb 18th 2017 to raise 30k for Exclusively Mongrels Ltd; a welfare … Continue reading

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