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11 of the Best YouTube Channels for Understanding Mathematics

Math Online Tom Circle

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)

3. WooTube (School Math)

4. Linear Algebra (Undergrad Math)

5. Rigourous French Math (Classe Prepa, Undergrad Math)

Set Theory Basics (Baccalaureate Math Revision)

Espace Vectorielle (French Abstract Version of Linear Algebra)

Rigorous French Math (Classe Prepa)

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$54 Promotion by OCBC

There is a new ongoing promotion by OCBC bank:

OCBC Passbook and Statement Savings Accounts

Get S$54 cash credit with every S$5,000 in fresh funds deposited in an OCBC Passbook or Statement Savings Account, with no limit. Funds deposited must be maintained for 7 months.

Promotion is limited and ends 31 August 2019. Terms and Conditions apply. Insured up to S$75,000 by SDIC.


This is effectively a 1.85% p.a. interest, which is quite decent. This may be a good time to open an OCBC account for those who are interested.

Working: 54/5000 x 100% /7 x 12 = 1.85%

There is another promotion ongoing at the same time:

Open your first OCBC Statement Savings account and 
get S$20 cash credit.
Promotion is valid for Singaporeans and PR who open an OCBC account from 1 August – 31 December 2019. Limited to first 600 customers per month.
Source: OCBC
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Python Water Changer Singapore

I have checked all the aquarium shops at the famous aquariums at Clementi Blk 328 (also known as C328 LFS). They do not carry the Python Water Changer or similar products such as the Aqueon Aquarium Water Changer.

Hence, the most probable way of getting the Python No Spill Water Changer is through Amazon:

25 Foot – Python No Spill Clean and Fill Aquarium Maintenance System

I have personally purchased it and it arrived in good condition within a reasonably quick time. Some photos are attached below, with a stack of A4 paper as a size comparison.

There is also a related product by Aqueon that works basically the same way. According to online reviews it is also good, but possibly not as good as Python.

Aqueon Aquarium Water Changer – 25 Feet

The benefits of these water changers is that they can not only fill the tank (a simple hose can already do that), but they can also draw water out of the tank, without using electricity. Basically they use suction from the tap (siphon effect) to draw water out.

Not sure why Singapore aquariums (LFS local fish shops) do not import these products as it seems quite a time saver and reduces the need for carrying buckets.

Note that online stores (such as Qoo10 or Lazada) may appear to carry these items, but at a much higher price than if you purchase from Amazon directly. The reason is that they are from dropshippers — when you order from them, they will act as the middleman and order from Amazon to send it to you.

A video to demonstrate how it works:

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Avocado Egg (Deviled Eggs)

Cooking For Fun

I used 4 eggs and 1 small ripe avocado in this recipe. You can adjust it according to your preference, use more eggs, less avocado or less eggs and more avocado.

  1. Boil eggs till they are hard boiled.
  2. Cut each eggs into halves. Gently scoop out the egg yolk.
  3. Put egg yolk and avocado in a bowl, mash them with a fork. Ripe avocado will make it a lot easier. I just mash them coarsely, so there is still avocado chunks in it.
  4. Season with salt and black pepper.
  5. Squeeze in 1/2 lime juice, 1/2 tbsp mayonnaise.
  6. Mix well till fully combined.
  7. Scoop egg yolk & avocado mixture with a spoon and put into the egg white.
  8. You can sprinkle some more black pepper or smoke paprika powder.

They are super easy to make and healthy too.

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What Makes an Amazing Nursery? 3 Things You Should Look for When Choosing a Nursery

Sending your child to nursery can be a very stressful decision. In fact, it is probably one of the most important decisions you will have to make for your child after he is born.

After all, the learning environment that they are exposed to at such a young age can have a significant impact on their long-term development. As education is so crucial for all children, it is critical that you dedicate the appropriate amount of thought to finding the right nursery for your child.

To help you with the search (it can certainly be an overwhelming one!), here are three essential things to look for when looking for the right nursery for your child.

1. A nursery that offers a  safe and stimulating environment

First and foremost, you want to ensure that you are sending your child to a nursery that provides a safe and stimulating environment. Children who are under age three need to be cared for in a manner that is different to what is required for older children, which is why it is advisable to send your child to a  nursery that is safe and offers a stimulating environment where your child can develop and thrive.

Take, for example, a nursery which is one of the top nurseries in Dubai. Here, children are not only in a safe environment but also in one that encourages them to move freely. The facilities ensure that there is the appropriate space for all parts of the curriculum to happen, as well as areas where children can be creative and use their imagination. Interestingly, these areas are designed to link in with “real-life experiences.”

More than just classroom areas, you want your nursery to have outdoor play areas so they can move and explore, as well as an indoor area with equipment for them to develop their physical balance and coordination.

2. A nursery with a strong curriculum — this matters so much!

As you may be able to tell, the key to finding a great nursery is to ensure that it has a wide array of facilities and offerings. However, the most crucial offering it must have is a strong curriculum as it is the curriculum that will be the backbone of your child’s experience at the nursery.

If you are living overseas, you may want to look for a British nursery in Dubai (or its equivalent) to ensure that your child is receiving the similar standard of a core curriculum that is based on the UK national curriculum.

When choosing between nurseries, make sure to take into consideration whether or not the staff administers the curriculum to each child’s unique learning needs and if they have a whole array of books and supplies that embrace all aspects of the curriculum. Ideally, the nursery you choose will offer extra-curricular activities and art classes such as music and dance intended to help your child develop their language, movement, and rhythm skills.

3. A nursery that encourages creativity

Undoubtedly, the best way for young children to learn is through play-based approaches.

More than just helping them gain basic knowledge, creative play promotes children’s social, cognitive, and physical development. Furthermore, activities that encourage children to be creative assist them in developing essential skills needed to interact, work, and cooperate with other human beings — yes, even at their age!

Therefore, when you are looking at potential nurseries, make sure to ask the staff how they utilize play and what they do to encourage the development of creativity. Additionally, you can ask them specifically how they structure the time for individual children’s interests. Last, but not least, pay attention to whether staff talk frequently to the children, even the younger ones, as this is critical to the development of the children’s communication and language skills.

Have you recently started looking at nurseries for your child? If so, what challenges are you facing when trying to identify which is the right one?

Alternatively, if you have already been through the process, what tips do you have to share with other parents who are currently struggling?

Let us start a conversation in the comments below!

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From poor in math to Quantum Physics

Math Online Tom Circle

She is a Cambridge PhD in Quantum Computing.

How to learn Quantum Mechanics on your own :

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Data Science: 5 Statistics & Math tools

Math Online Tom Circle






5. PCA = Pricinpal Component Analysis


1. Probability & Statistics

2. Linear Algebra (Matrix, Eigenvectors, Eigenvalues)

3. Optimisation : eg. Gradient Descent, etc.

4. Discrete Math in Computing

(想看更多合你口味的内容,马上下载 今日头条)

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林群院士:怎样学好数学?How to learn Math well ?

Math Online Tom Circle


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)" :


…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。


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Singlish Math : Toa-Cah-Soh大脚嫂

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,


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) 。尤其讨厌 “三角恒等式” (Trigonometric Identities Proof) 证明,用死记的公式纠缠地 (messy) 变来变去,"剪不断, 理还乱",考试差点不及格 (60%)。

80年代 英校数学老师发明一个记忆妙招 :Singlish TOA CAH SOH 大脚嫂👍

Who says Singlish is useless? Our Sec 3 Math students are Top PISA (#1) in the World !

Another smart Singlish Math Chant:

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Primary School Math

Math Online Tom Circle

Given: 3 circles of radius 2
Find: Shaded Area?


Sum of 3 angles in the triangle

= π = 1/2 (2π) =1/2 circle

=> its Area = 1/2(π. 2^2) = 2π = Sum of 3 arcs’ area

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The World’s Most Beautiful Equation : Euler’s Identity

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.

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Dunman High DSA

Dunman High DSA Tips

Dunman High is a good school that has a very good school culture. It is strong in several CCAs (Co-curricular activities). Its Chinese Orchestra is exceptionally good (and large in terms of numbers), in fact most likely the top in Singapore among Secondary Schools, throughout the history of Singapore.

DSA Interview May be Conducted in Mandarin

According to reliable sources in, Dunman High may well conduct the DSA Interview in Chinese, as a surprise, to test how the child reacts. This is also in line with the strong Chinese culture in Dunman High.

Quote 1: Hi All, congrad (sic) to all parents who have already got confirm CO. For those who are still going through the interviews just wanted to give a heads up to DD that are interviewing for SAP schools. My DD went to interview at DHS for sport and was asked to do the interview in Mandarin which caught her off guard. Unfortunately, she was only able to converse 50% of the interview in Mandarin but we were proud that she persisted instead of freezing up ..”
Source: Kiasuparents

Quote 2: “Yes, Dino.

Dunman High interview for DSA both Western music and Chinese music section, were conducted in Mandarin. I shared this at DHS website … start=3990

My friend’s child is a Singapore citizen. Luckily, child could converse in Mandarin fluently. On that day for music interview, other candidates were very nervous. One interviewee asked politely, if others can go first, before his (her) turn, because he (she) was so nervous, wasn’t ready. He (she) was still flipping through and reading his (her) interview notes.

Come to think of it, how about the other way round ? Not sure if interviewers at DHS interview candidate in English, ie. the other way round instead, if the DSA applicant (interviewee) happen to be a foreigner, from China, just to test and assess their level of proficiency in English Oral conversation ?

Hence, the conclusion is that the student needs to brush up more on Chinese / Mandarin skills (possibly reading some idioms or poetry) in order to prepare well for the Dunman High DSA Interview.

A favorite DSA Question may be to ask “What is your favorite Chinese book?“. It is good to make sure that your child has read at least one Chinese book and can conduct a decent conversation about it.

Related Sites

Since Dunman High can conduct its DSA Interview in Chinese/Mandarin, it is reasonable to expect that many SAP schools with strong Chinese culture may well do the same. The key idea may be to surprise the child so as to take him/her out of any home-prepared preparation, and make it more natural as opposed to memorizing a pre-determined script written by the parents.

For instance, some of the SAP schools with strong Chinese culture are:

  • Singapore Chinese Girls’ School (IP) DSA
  • Catholic High School 公教中学 DSA
  • Chung Cheng High School (Main) 中正中学 (总校) DSA
  • Hwa Chong Institution 华侨中学 DSA
  • Nan Chiau High School 南侨中学 DSA
  • Nan Hua High School 南华中学 DSA
  • Nanyang Girls’ High School 南洋女子中学校 DSA
  • River Valley High School 立化中学 DSA

The above schools are all good schools that either already have DSA or may be soon in line to adopt a DSA (Direct School Admission) program.

Hence, for the above schools, it is wise to prepare and practice the DSA Interview in both languages — English and Chinese.

Bad News for Purely English-Educated Kids

This is another bad news for purely English-speaking kids who are not good in Chinese (Mother Tongue), since they may be disadvantaged in the DSA Interview which is conducted in Chinese/Mandarin.

Under the new PSLE System, we have already analyzed that the most disadvantaged students are the English-Educated Kid and the Math/Science Whiz.

It may not be too late though, to brush up on one’s Chinese. Usually children can pick up languages very fast compared to adults. The preparation may need to start at least several years before the DSA Interview.

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Free Software for Meta Analysis (OpenMeta Analyst)

Open Meta Analyst Review

Open Meta-Analyst ( is a free software developed by professors in Brown University, for Meta Analysis.

Previously we reviewed another free software RevMan5. RevMan5 is very good at doing meta analysis with placebo control groups. What it is not very good at is doing single arm meta analysis, that is, for clinical trials without a control group.

Open Meta Analyst can do single-arm meta-analysis, with the benefit that it seems even easier and more user-friendly than RevMan (which is already quite good with a GUI).

There are some YouTube tutorials on how to use Open Meta Analyst to do analysis on RCTs (Randomized Clinical Trials) and more.

The user manual for Open Meta Analyst can be found at The good thing about Open Meta[Analyst] is that it supports both Windows and Macintosh.

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How to do Forest Plots using Software

According to many online reviews, an easy way to do Forest Plots (Forrest Plots) is supposedly to use the free RevMan software. RevMan (currently RevMan5) can be downloaded here. RevMan is a software geared towards medical statistical analysis.

RevMan is said to be the easiest method since at least it has a graphical user inferface (GUI). For total beginners, before even doing the Forest Plot, we need to learn how to enter the data into RevMan.

Overall, I think RevMan should be one of the easiest ways to do Forest Plots or meta-analysis. Furtheremore, the software is completely free. However, there is still a significant learning curve.

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Spicy Sticky Rice Cake (Tteokbokki)

Cooking For Fun

It’s a Korean style dish. I love almost all the food made from sticky rice.

For the sticky rice cake, I bought from supermarket. It’s vacuum pack. Sticky rice cake is very hard and dry. So first, I need to soak them in water and separate them. To make it easier, I also boil them in water for several mins until they get really big and fat and soft. Soak them in cold water and drain.

Prepare sauce: 2 tbsp Korean chili paste, 1/2 1 tbsp light soy sauce, 1/2 1 tbsp sugar, 1 tbsp syrup. Mix them well.

  1. Heat a pan. Add in a little oil. Saute 2 cloves of chopped garlic and slices of 1 onion till aromatic.
  2. Add in sauce, and pour in 1/2 1 cup water/stock. Stir to let the sauce dissolve evenly.
  3. Put in drained rice cake and sausage slices. Boil till sticky rice cake…

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Math High-Pay Career in Data Science

Math Online Tom Circle

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 the “4th Industrial Revolution” , ie Mind Automation by Machine Learning and its ‘Mother’ Artificial Intelligence.

The 3 top jobs (by order of pay) :

1. Data Scientist (US $120K) :

Skills : Math (Stats, Linear Algebra, Calculus, Probability, & potentially Algebraic Topology / Homological Algebra) + A. I.

Mathematician PhD preferred.

2. Data Architect / Engineer (US $100K)

Skill: IT, especially in Big Data technologies

3. Data Analyst / (US $65K)

Skills : IT, Business

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Walnut Banana Bread

Cooking For Fun

Banana is one of my husband’s favorite fruit. But sometimes, He forgot to eat them, and banana got ripe very quickly. So I would use them to make smoothie or cake or bread.

This summer when we went back to my hometown, we brought so many walnut back. My mom just cracked them and store the shell-removed walnut in 2 large containers. My husband likes walnut, so he adds some in his yogurt. Yet, we still have a lot. So I tried to bake something with walnut and banana.


Bananas 2

butter 1/2 cup

white sugar 1 cup

eggs 2

vanilla 1/2 tsp

flour 1 cup

baking soda 1 tsp

salt 1/2 tsp

cinnamon powder 1/2 tsp

chopped & toasted walnut 1 cup

  1. Preheat oven to 170 Degree C.
  2. Cream butter and sugar together till light and fluffy.
  3. Add in 2 beaten eggs and vanilla. Stir well.
  4. Add in…

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A Programmer’s Regret: Neglecting Math at University – Adenoid Adventures

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 “Proof” : Propositions as Types, HoTT

Abstraction: Monoid, Category


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IMO 2019

Math Online Tom Circle


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】

Two observations:
1. Why almost all Chinese in top China, USA, Canada, NZ, Singapore teams?
Either Chinese chase the wrong Math (IMO) education, or the western Math Power countries (UK, France, Germany…) are RIGHT to ignore IMO education?
2. Singapore team skewed heavily in 2 schools: RI (5) + HCI (1). Also 0 girl.

【解读中美数学奥赛并列第一,敬请期待对话美国队总教练 | 袁岚峰】

(想看更多合你口味的内容,马上下载 今日头条)

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Math Online Tom Circle


10 Math Videos:

  1. The Joy of Math
  2. The Joy of Stats
  3. The Joy of Logic
  4. The Code
  5. A Brilliant Madness
  6. The Great Math Mystery
  7. How Long is a piece of string
  8. Hunting the hidden dimension
  9. Dimension: A walk thru mathematics
  10. The secret life of chaos

(想看更多合你口味的内容,马上下载 今日头条)

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What to read to fall in love with Math

Math Online Tom Circle

Find the last 2 in Singapore NLB libraries:
“The Joy of X” , “How to bake Pi”

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Forest Plot Correct Spelling and what is “Forrest Plot”

The original spelling is “Forest plot”, the name refers to the forest of lines produced.

In September 1990, Richard Peto joked that the plot was named after a breast cancer researcher called Pat Forrest and as a result the name has sometimes been spelled “forrest plot”. Source:

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Ribs & Seaweed Soup

Cooking For Fun

My husband doesn’t like seaweed. But I think seaweed is really good for health. Yet, he doesn’t say no to seaweed soup. So I made this soup for him.

  1. Since I used dry seaweed, I soaked them in water till softened before I started cooking.
  2. In a deep pot, add in ribs and enough water. Bring to boil and skim the soup to remove all the dirt.
  3. Good soup takes long time. I put all the ribs in a slow cooker, with seaweed, corn, shiitake, red dates and some ginger slices.

Also pour in the water after boiling the ribs. Add more water if you want.

I cooked it for 2 hours. And just season with salt.

My husband loved it very much.

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Choosing which statistical test to use

The top video on YouTube on how to choose an appropriate statistical test.

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New PSLE System favors “All Rounders” over “Specialists”

Singapore Maths Tuition

The new PSLE system clearly favors “all-rounders” over “specialists”.

Scenario 1: Math-Whiz VS All-Rounder

Imagine a Math/Science-whiz with

Math:100 (AL 1)
Science: 98 (AL 1)
English: 84 (AL 3)
Chinese: 84 (AL 3)

Total marks: 366   (Approx. 275 T-score)
Total AL: 8

With a “all-rounder”:

Math: 90 (AL 1)
Science: 90 (AL 1)
English: 90 (AL 1)
Chinese: 90 (AL 1)

Total marks: 360 (Approx. 270 T-score)
Total AL: 4

The Math/Science whiz (total AL 8) will be getting double the score of the “all-rounder” (total AL 4), effectively eliminating his chance of entering the top schools. The irony is that the total marks of the Math/Science Whiz is a considerable 6 marks more than the “all-rounder”.

Under the old system, both are likely to get around the same T-score (approx. 270+), with the Math/Science whiz having a higher T-score.

Scenario 2: English-Educated Kid VS All Rounder

This scenario is…

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Mushroom Sauced Chicken Chop With Penne

Cooking For Fun

  1. Prepare a boneless chicken leg. Cut it slightly to prevent curling up while cooking. Season it with salt and black pepper.
  2. Heat a pan. Usually I don’t add in oil, cos chicken leg contains fat. So Just sear the chicken with skin side down. Fry with medium-low heat for 3-5 mins or till skin turns golden. Flip it over and fry the other side till brownish too.
  3. Chicken out into a plate. There will be some oil left in the pan. Just use it to saute 1 chopped garlic clove. Then add in mushroom slices. Stir fry till aromatic.
  4. Pour in 1/2 cup stock. Simmer for 3 mins.
  5. Add in 1/4 cup milk, also season with salt, pepper and mixed dried herbs.
  6. Put Chicken back into the pan. Simmer for 10 mins to let it completely be cooked.
  7. Condense the soup by adding starch water. Keep stirring to reduce the…

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Convert Excel to LaTeX

This tool is a lifesaver if you are trying to convert Excel tables to LaTeX format.

LaTeX tables are notoriously difficult and tedious to write manually. If you already have an Excel (or .csv) table, you can easily change it into LaTeX format using the website above.

Just go to File -> Paste table data. You can literally copy and paste your excel table into the online tool, and it will convert to LaTeX format for you. It will take no more than a few seconds!

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SCGS Mathematics

SCGS (Singapore Chinese Girls’ School) follows the IP system, with students having the option to continue to Eunoia Junior College, the newest JC.

SCGS IP Mathematics

SCGS IP Mathematics is still split into E Maths (Elementary Mathematics) and A Maths (Additional Mathematics). Content-wise, it is quite similar to O level Mathematics, except that the order of topics taught can be quite arbitrary and up to the school teachers.

SCGS Math Exams

On paper, SCGS has few “exams” and has totally eliminated the midyear exams. In actual fact, there are still numerous tests just that they don’t use the word “exam”.

For example, a sample syllabus for SCGS’ A Math Block Test for Secondary 3 students (around July) is:

  1. Simultaneous Equations
  2. Surds
  3. Indices
  4. Logarithms
  5. Quadratic equation of expressions (alpha and beta)

The syllabus for the E Math Block Test is:

  1. Quadratic Equations
  2. Linear Equality / Inequalities
  3. Indices and Standard Equations
  4. Coordinate Geometry
  5. Graphs of Function and Geometry (including quadratic graph, curve sketching and graphical solution, and graphs in practical situations)
  6. Area & Volume of similar figures and solids
  7. Congruence and similarity
  8. Applications of Trigo (Angles of Elevation and Depression), Trigonometric ratios of acute and obtuse angles (excludes bearings and 3d shapes)
  9. Lower Secondary Algebra
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Braised Pork & Rib Soup Bento

Cooking For Fun

The rule of my husband’s bento: there must be at least 1 meat dish.

This time, I tried pork.

  1. Prepare soup. Cos soup is time-consuming. I can let the soup on the stove while preparing other dishes. Wash ribs. Put them in a pot and add in enough water. Bring to boil. Skim the soup to remove all the dirt. Simmer for 30 mins. Add in carrot and corn. And simmer for another 20-30 mins.
  2. Pork belly in the pot. Enough water in and bring to boil. Take the pork belly out and wash clean. Cut into small chunks. Heat a pan. Add in a little oil. Sear the pork belly till brownish. Add in light soy sauce, dark soy sauce and sugar. Stir fry evenly. Add in enough hot water, also bay leaves and star anise. Lid on and simmer for about 20 mins. Lid off and reduce the…

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Applications of Sig Fig Calculator

Applications of Sig Fig Calculator


Mathematics is all about presence of mind and high standard conceptual knowledge. These days, you have technological tools to perform the critical steps and provide you with 100% correct answers. When you talk about significant figures, students and other users normally make mistakes when they are not aware of the rules. If you don’t know about the regulations of determining significant figures, it would not be possible to come up with the correct answer.

·       Looking at an example


Consider that you have the number 25020. How many significant digits does this number have? If someone does not have complete information about the rules, he would be confused about whether zero would be significant or not. On the other hand, someone who is clear about the rules would not have any trouble in reaching the correct answer.


In accordance with the regulations of significant figures, the zero between 5 and 2 would be significant. This is simply because it is placed between two significant numbers. The zero that is present in the end would not be counted as significant because there is no whole number after that. It is all about being aware of the correct regulations.


Using Sig Fig calculator to determine results without stress


It takes a considerable span of time to determine the significant digits in a number. Even if you are well aware of the regulations, it is not an easy task after all. The use of a quality online calculator is an amazing option for users. The following points explain how you can benefit from this tool easily.

  • Put your time to better use instead of counting the significant digits in a number. The Sig Fig calculator would complete the task in a much simpler manner. No effort is needed from the user. He does not have to sit and apply logic to determine the correct count of significant digits. When you enter the required number, the tool would determine the significant digits. In addition to that, you can round off a number to the number of significant digits as per your need. To find out more Math Calculators visit

Conversions done through a fast process

Determination of significant figures and rounding off are time consuming steps. If you have less time available, it would not be simple to get the conversion done in due course of time. The use of an online calculator provides a complete assurance that no time would be wasted.

  • Quickness is a major plus point of this tool. Unlike a lot of other tools present online, this tool is much faster. It does not make the user wait or go into the non-responsive mode when the conversion is being done. The moment you enter a number and its rounding off digit requirement, the calculation would be completed in few seconds.

No apprehensions about limited usage

Most users do not prefer technological tools because they do not want to spend money on paid versions. This is actually a dilemma for most people. First of all, it is hard to find a completely free tool. Although a lot of options promise to be free but the user determines the actual condition when he starts using them. This calculator is completely free and no conditions are applied on the users.

Plus points for students

Even the thought of solving an assignment on significant figures can prove to be scary. These questions require a lot of concentration because students have to apply logic, implement the rules and perform other important steps to complete the questions. The Sig Fig calculator is a beneficial tool for all the students who want to submit correct assignments in due course of time.

  • This calculator determines the significant digits in the number you want to round off. For instance, if you want to round off 256202, the tool would show that there are sig significant digits in this number. Similarly when you round it off, the number of significant digits would be shown again. In an overall manner, this tool provides immense help to students. First of all, they do not have to complete any calculations without using a tool. Similarly, they are able to complete multiple calculations in quick time.


  • This calculator is quick and does not have a long processing time like a lot of other applications. Once you enter the input, the related calculations would be performed in a quick manner. You can be absolutely sure about the correctness of the results. However, you can only rely on the results if the calculator is dependable.



Significant figures in a number are determined after using certain rules. For instance, in the number 23604, zero would be counted as a significant number because it is present between two significant digits. The use of a quality Sig Fig calculator is a good alternative for students because it helps them in saving time and producing accurate calculations.

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Gain Higher Grades through Well Written Assignments

Gain Higher Grades through Well Written Assignments

One thing is for sure that the human being of the past was a better human being compared to the human being of today. The age that we live in is called ‘space age’. We have the most modern and state-of-the-art innovations at our disposal. We have the facility of the most modern equipment. How easy and quick it is for us in a various matter of life. The machine has made life extremely easy for us. Two decades back it took days in solving the various calculations. Now, computers have helped us in solving the most difficult of the calculations. Similarly, the ease of contact with the help of cell phones has made communication flawless.

Yet, humanity has lost the basic manners. The invention of the internet is one of the most brilliant achievement today. But, it has also opened a door to hacking. Extremely important data of various companies and countries have been hampered by the hackers. Millions of dollars have also been looted by them from the bank accounts of the people.

Internet is an open forum, anyone can come up, use it and write. The important thing is that your writing must be informative and user’s oriented. You have to go through from a Grammar Check process every time when you write assignments. It will helps you improve your quality of writing. There is no barrier to any class, color, religion, race, identity, etc. You are a butcher located in Mozambique, or a farmer in Bihar, or a businessman from Canberra. You are most welcome to market your skills, talents, and your products on the internet.

Simultaneously, it has opened a door to plagiarism. For example, you write about the finest tourist spot in the world, but later your content used in your site is copied by your competitor and used as it is. Consequently, you cannot grow- the Google algorithms will not let you and the competitor who plagiarized reach to the top of SERPs.


Importance of Quality Writing

Each and every person is creative somehow. The fact that nature has blessed every individual with a unique fingerprint. It suggests that not just the fingerprint but you can differ from even your twin brother in different traits, ideas, school of thought. You can be a supporter of a different ideology, however, your twin sister can be a proponent of some other ideology.

If you try you can be extremely unique, you would not need to copy the concept and idea of anyone else. It can be best analyzed from the fact that unique ideas have been a key to major innovations in history. People became renowned because they were able to generate a theory or philosophy different from their contemporary people.

From Avicenna to Newton, from Leonardo Da Vinci to Shakespeare, from Jean-Jacques Rousseau to Karl Marx. You will find a commonality that they all differ from each other. Had they been talking about the same ideas they would never have achieved the fame.

Threat to uniqueness

It is good to be positive but one must also analyze the academic corruption which has spread globally. Every idea once written on a piece of paper become an intellectual property right. It means that it is protected by international law as well as the domestic law of your country.

Billions of people have not heard of it, so they feel that anything that they see and read on the internet or in the books can be copied in their material as it is. Not even thinking that it is considered as plagiarism and the original writer has a right to sue cheater in the court of law. Plus, SERPs are highly affected on the internet.

The article which you post on your blog can become worthless for you if you do not follow proper techniques. The first thing that you need to do yourself is to be as original as you can. Don’t copy anything! You can read the blog written by another person, get an idea from him or her. In order to write something you also need to read a lot of material.


Higher grades and Educational Tools

Pre Post SEO know that you are a hardworking candidate, you need to submit university assignments. Sometimes daily and sometimes on a weekly basis. So, be it an assignment in the form of a report or a final semester thesis we suggest you make use of our grammar checker.

The benefits of using our grammar checker are that you will get access to not just grammar but also the plagiarism checker. We know that you believe in producing originality but sometimes during research you might mistakenly copy content from a blog. Otherwise, sometimes your words and sentences can also match.

So, we will also show you the texts with which your material matches. You can also read that text and make changes to yours. Plus, our grammar checker will point out all the errors which you made in your written material. Pre Post Seo understands that you will never deliberately make the Grammar mistakes.

The teacher is extremely strict in some cases. Especially, if you are in your post-graduation and you make wrong use of articles in English. Life has become so busy that it is difficult to keep on reading grammar book daily. One forgets the usage of tenses and many other things.

Teachers are already in academia. They remain in touch with their field of study and with linguistics. The usage of plagiarism and grammar checker designed by highly skilled technicians of Pre Post SEO will make you feel that not only your paper is corrected. But, your English will also improve.

Just to explain to you how good we are in terms of delivering quality work. When you will type your content on our checker. There are chances that the following mistakes will appear:

  • Mistakes in placing the comma.
  • Mishandling the colon and commas.
  • Subject-verb mishandling.
  • It’s used instead of Its, or vice versa.
  • Dangling modifier.
  • Wrong
  • Improper vocabulary used.

All the people make these common mistakes on a daily basis, but we will correct it. In order to overcome them use our checker to build your credibility in front of your teachers. Furthermore, we just gave you an example of a student. If you are of a different profession, feel free to use it. It is yours now. Good Luck!

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Sweet & Sour Ribs (糖醋排骨)

Cooking For Fun

  1. Wash ribs in water. Put all the ribs in a deep pot. Add in enough water. Bring it to boil for 3-5 mins. Take out all the ribs and rinse under water.
  2. Heat a pan with a little oil. Stir fry drained ribs till they turn a bit brownish.
  3. Add in ginger slices and green onion. Stir fry till aromatic.
  4. Drizzle in 1 tbsp cooking wine. Stir fry till ribs dry again.
  5. Prepare sauce: 1 1/2 tbsp light soy sauce, 1/2 tbsp dark soy sauce, 2 tbsp vinegar, 3 Tbsp rock sugar (you can reduce or add more sugar according to your taste). Pour sauce into the pan.
  6. Stir fry to let the ribs be coated with sauce.
  7. Pour in enough hot water can cover all the ingredients. Turn to low heat and simmer for 30-40 mins.
  8. Lid off. Turn to high heat and reduce the sauce.
  9. When sauce is…

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Singtel Dash $3 Cashback and other Promos

Hi! Get up to $3 cashback when you make your 1st transaction via Singtel Dash! Sign up with this link now – .T&Cs apply.

For those using Singtel postpaid, do note that paying with Singtel Dash essentially means free 1GB data every month! Download Singtel Dash now if you haven’t already!

Signup here:

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Zong Zi Again!

Cooking For Fun

There are still some bamboo leaves left in my fridge since last time I made zongzi (sticky rice dumplings). Last Wednesday was my resting day. No work, no need to go out. So I decided to use some to make Zongzi. And also because I really missed zongzi, could’t wait to have some.

This time, I only used sticky rice, no red bean. And for the filling, I went with the simplest one – red dates.

Only when I went to college in Fujian did I know that not all the people in China have simple zongzi with only sticky rice and red date inside. People in Fujian have the meat zongzi, with pork, mushroom, peanut, beans inside. And according to the different color, they call the meat ones Hongzong (red zongzi), and our simple ones Baizong (white zongzi).

After trying so many types of zongzi, simple white zongzi are…

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WordAds Appeal Successful

Recently, I managed to appeal successfully for WordAds to be run on my other site Previously, it was rejected a few years ago in 2016 due to insufficient traffic.

The appeal process is quite simple: simply log in to and click on “Please contact us if you would like an update on your application.” below your previously failed application.

For the appeal to be successful, I think that there needs to be at least a significant upwards trend in your traffic. Personally, I had a 500% increase in traffic over 3 years.

If your appeal is successful, a mail will be sent (for me it was within the same day):

Happy to help you. I’ve checked your site stats and it seems that you were on track to be approved next week, so I just put that through for you today instead. You can now finish setting up WordAds via or the new “WordAds” section under your blog at

I hope that helped. Come back if you have questions. We are happy to help you anytime 🙂

Good luck for anyone trying to apply for WordAds!

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Soy Sauce Chicken & Tamago Yaki Bento

Cooking For Fun

Actually I cooked half soy sauce chicken. It’s quite simple and can be done by rice cooker.

  1. Put the half chicken (approx. 300-400g) in a big bowl. Sprinkle a little oil and light soy sauce. Massage the chicken to let the oil and soy sauce evenly spread. Let it marinate for 30 mins.
  2. Brush oil to the bottom of rice cooker. Put in 3 or 4 ginger slices, 1 or 2 stalk of green onion. Chicken on ginger and green onion.
  3. Pour in 1/2 cup water, 1/4 cup light soy sauce, 2 tsp dark soy sauce, and 2 tsp sugar.
  4. Cover the lid, press cooking button. When it’s done, flip the chicken over. Cover the lid and press button again.
  5. When it’s done again, don’t open the lid immediately. Let it be tightly closed for another 10 mins. After that, it’s ready to serve.

For tamago yaki:

Beat 2 eggs…

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New Math applied in Modern Physics

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】


  • 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 Theory : 范畴学
  • Group Theory : 群论
  • Algebraic Topology : 代数拓扑


1. Four “Physics” Revolutions aided by Math

Math is applied to explain the Nature (Physics) :

Calculus (Differential Equation) : Newtonian Physics

Riemann Geometry : Einstein General Relativity

Partial Differential Equation: Maxwell Electro-Magnetic Field

Linear Algebra (Matrix) : Quantum Mechanics

Group Theory: Physics / Chemistry Symmetry


Category Theory : Topological Order of the long-range Quantum Entanglement

Algebraic Topology: Topological Insulator (2016 Nobel Prize Physcis)

2. The 5th Physics Revolution aided by New Math tool : Category Theory

3. Category Theory = “Structural Relationship” Math

4. Algebraic Topology

(想看更多合你口味的内容,马上下载 今日头条)

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5G Polar Codes Dr. Erdal Arikan

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 of polar coding as the channel coding technique for control channels for 5G communications system may have put Huawei at the forefront in the 5G race(27 Gbps in 2016).

1 Gbps = 1000 Mbps

5G Basic Explained:

Part 1: The Math behind 5G Polar Codes


Part 2:

Part 3:



$latex displaystyle F = begin {bmatrix}
1 &…
1 & 1

$latex A =
a_{11} & a_{12}& ldots & a_{1n}
a_{21} & a_{22} & ldots & a_{2n}
vdots & vdots & ddots & vdots
a_{n1}& a_{n2} &ldots & a_{nn}
$$latex B =
b_{11} & b_{12}& ldots & b_{1n}
b_{21} & b_{22} & ldots &…

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“Poisson Distribution Intuition (and derivation)”

Math Online Tom Circle

“Poisson Distribution Intuition (and derivation)” by Aerin Kim 🙏

Poisson was a 19CE French mathematician, or Statistician, who invented the Poisson Distribution.

Note: “Applied” Math vs “Pure” (aka Modern / Abstract) Math

Poisson, being an Applied Math expert in the French Science Academy, did not understand the “abstract” Math paper submitted to him by the 19-year-old Evariste Galois in “Group Theory” for the “Insolvabilityof Quintic Polynomial Equations“. Poisson rejected the paper commenting it was too vague, destroying the final hope of Galois to make his invention the “Modern Math” known to the world. The dejected poor Galois died at 21 after a duel during the chaotic era of the French Revolution.

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China Gaokao 2019 Interesting Math Question

Math Online Tom Circle

Gaokao = Baccalaureate = GCE A Level

…[Solution scrolled below]

Let Ф = 0.618

… Golden Ratio Ф = 0.618

defined as:

“Head to Throat” vs “Throat to Navel” = a/b = Ф ,


“Head to Navel” vs “Navel to bottom of Legs” =(a+b) / c= Ф

Knowing :

Head to Neck = 26 cm &

Legs = 105 cm

Find the height (H) ?

Note: The tricky part is to know “the neck is below the throat” & “the legs start some distance below the navel”, hence 2 inequalities :

a <…

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Viral Chinese 2019 Gaokao Question

Math Online Tom Circle

Gaokao 高考 = Baccalaureate = Cambridge GCE A-Level


f(x+1) = 2f(x)
tells the height = f(x) double when x moves to x +1
=> periodicity is 1

Like Sine or Cosine curves have periodicity of 2π.
sin (2π + A) = sin (A)

Ref: More complicated curve drawing by French Method.

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Math Online Tom Circle


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: by Van der Waerden (Noether的学生: Artin, Waerden)

2. Number Theory 史上第一本数论启蒙书:

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Simple groups, Lie groups, and the search for symmetry

Math Online Tom Circle

Math History | NJ Wildberger


  1. Normal subgroup
  2. Quotient Group
  3. Finite Simple Group: Z5, D5,…
  4. Tesselation (regular)
  5. Platonic solids

… Two families of Group :

  1. Symmetric Groups: Sn
  2. Linear Group: GL(n) = M, det M ≠0

An = Alternating Group

[even permutation, det = +1]

n>=5, An is a Simple (non-commutative) Group

Lie Groups :



Simple Lie Groups : Matrix Group M

  1. Special Linear Group: SL(n), det M = 1
  2. Orthogonal Group: O(n), $latex M. M^T = I$
  3. Symplectic Group : Sp(2n)

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Alibaba “Damo” Global Math Competition

Math Online Tom Circle

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 Century, established ShaoLin Monastery, also invented Chinese Kongfu.

Problem 1

Hint: Answers in the above link.

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RSA Encryption – Number Theory

Math Online Tom Circle

Background knowledge:

1. Group

2. Cardinality : Euler Totient Function


A linguistic remark: The Latin word “totiens” (or “toties”) means “that/so many times”.

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Homotopy Type Theory: Vladimir Voevodsky

Math Online Tom Circle

A self-study Math genius Vladimir Voevodsky, Fields Medalist, Russian.

Voevodsky borrowed idea from Computer Science (“Interface” =hide implementation details) to Math, and vice-versa, from Math to Computer Science :
Homotopy Type Theory (HoTT)

Result: Computer to prove math theorems.

Computer Science Idea:

  • Hiding Implementation Detail
  • Black Box “Interface”
  • Type (类) : Boolean, Integer, String, … (stronger structure than "Set" 集合)

Math Idea (Abstract Geometry : Algebraic Geometry) :

  • Homotopy (同伦)
  • eg. Cup ~ Donut, both are homotopic or same “Type” (in Computer)
  • Isomorphism is Equality “=”
  • Homotopy Type Theory (HoTT):
    • Univalent Theorem: both objects are considered “=” if they are isomorphic (prove if 1-to-1 correspondence 对应)

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Characters, Symbols and the Unicode Miracle

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 characters of all human’s languages (Chinese, Japanese, Arabic, Korean,…)

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Learn Calculus With These Four Online Courses

Math Online Tom Circle

Four Online Free Calculus Courses:

2. “Calculus Made Easy” (1910 )

3. “Essence of Calculus” (12 short videos, with Chinese subtitle)

4. [Best👍] “Calculus” (MIT Prof Gilbert Strang)

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Teriyaki Chicken with Pan-Seared Portobello Mushroom

Cooking For Fun

Teriyaki Chicken:

1. Prepare a whole boneless chicken leg. Sprinkle a little salt and black pepper.

2. Use the back of knife to hit chicken a bit.

3. Heat a pan on stove. When the pan is hot, put the chicken inside with skin side down. Flip over when the skin turns golden brown. Fry the other side till brown, too.

4. If there is much oil after sear, you can pour the oil out.

5. Add in 1 tablespoon light soy sauce, 1/2 tablespoon dark soy sauce, 1 tbsp sugar and 1 tablespoon honey. Let the chicken be coated with sauce.

6. Pour in hot water just enough to cover the chicken. Cover the lid and simmer for a while.

7. Remove the lid. Turn to high heat to reduce the sauce.

Portobello Mushroom:

Remove the Portobello mushroom’s stem first and wash clean.

1. Heat a pan. Cut in…

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