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• ## Math Forum

Posted in math knowledge | | 1 Comment

Just saw this. SOSD (something like SPCA for dogs) is organizing an adoption drive tomorrow 22 Oct Sunday. So if you are interested to see the dogs and perhaps adopt one, you are free to attend (above One-North MRT Station).

I read on their Facebook that they are facing some problems due to too many stray dogs, their “enclosures are all full; we do not even have space in our quarantine unit to house any more dogs”.

They also do have dogs suitable for HDB, under this project called Project ADORE. If more dog lovers adopt instead of buy, the problem of stray dogs in Singapore can be solved humanely.

## New PR Singpass

Googling info on this is quite hard. Just to share what is the procedure. Basically you need to apply for a new Singpass based on your new PR NRIC, as the previous Singpass based on FIN will be invalid.

Also, most would soon encounter this problem: Your mobile phone is tied to the old Singpass account, and the system would not let you use it for the 2FA.

The solution (took quite a while for me to find this): (Source)

Q: I am a FIN holder who has been granted Singapore PR, how can I continue to use SingPass?

Ans: You will need to register for a new account using your NRIC number. Upon successful registration, your account details will be mailed to you within four working days. Click here for more details. Please note that one mobile number can only be registered with one SingPass account. If you have previously registered your mobile number in your existing account, and would like to use the same number for your new account, please email support@singpass.gov.sg with the following details:

Source: Singpass FAQ

Disclaimer: This info is dated 21 October 2017. The procedure may or may not change in the future. Also, please double check with the official website before taking any actions.

## Terence Tao Numberphile

Among current mathematicians, many people regard Professor Tao as the world’s finest… Opinions on such things vary, of course. Professor Tao kindly fielded some of our questions, including many submitted by Numberphile viewers. EXTRA FOOTAGE: https://youtu.be/48Hr3CT5Tpk (and more extras to come)

## “Actual” GEP Questions 2017 (from Forum)

Since the actual GEP papers are never released, the next best source is from those who have actually taken it and post on forums like Kiasuparents.

Some Maths questions my girl remembers.

“ In a fishing competition, five kids caught 50 fish in total. A is the winner – she got 12 fish. B and C caught the same number of fish and both are at second place. D is at fourth place. E came in last, got only 6 fish. How many fish did B get?“

( my girl couldn’t solve this one. )

“ The red ribbon is twice as long as the blue ribbon. The green ribbon is 2cm shorter than the blue ribbon. A red ribbon and two green ribbon together measure 16cm. How Long is the blue ribbon? “

( she managed to solve this one- but only after spending a lot of time on it. )

Review by mathtuition88: These two questions are not that hard. Can be solved by either model method or algebra.

Some tips from parents: English and GAT is actually harder to prepare than Maths:

Just sharing based on our experience last year. Of the 6 that were selected for GEP eventually from my child’s class, it seems English and GAT were the determining factors. For maths, a lot of kids are already very advanced and well – prepared nowadays. The majority of the balance 14 who went for round 2 found English harder than maths. According to them, English is somewhat like pitched at sec 1 and sec 2 standard, while maths was like up to P6 and Primary Maths Olympiad standard and more manageable. I think it was also more because anything can come out under the sun for English and you can’t really prepare for it. That’s what I heard last year.

## The State of Being Stuck

Nice story (with drawings) on Andrew Wiles and the Fermat’s Last Theorem.

Last year, I got the high school math teacher’s version of a wish on a magic lamp: a chance to ask a question of the world’s most famous mathematician.

Andrew Wiles gained his fame by solving a nearly 400-year-old problem: Fermat’s Last Theorem. The same puzzle had captivated Wiles as a child and inspired him to pursue mathematics. His solution touched off a mathematical craze in a culture where “mathematical craze” is an oxymoron. Wiles found himself the subject of books, radio programs, TV documentaries—the biggest mathematical celebrity of the last half-century.

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## Why do people get so anxious about math? – Orly Rubinsten

View full lesson: http://ed.ted.com/lessons/why-do-peop… Have you ever sat down to take a math test and immediately felt your heart beat faster and your palms start to sweat? This is called math anxiety, and if it happens to you, you’re not alone: Researchers think about 20 percent of the population suffers from it. So what’s going on? And can it be fixed? Orly Rubinsten explores the current research and suggests ways to increase math performance. Lesson by Orly Rubinsten, animation by Adriatic Animation.

Also view my previous post on Coping with maths anxiety.

Posted in math | Tagged , , | 1 Comment

## McCleary User’s Guide to Spectral Sequences (Errata)

(pg 455) When an element $u\in H_{n-1}(X)$ satisfies $ru=0$, then, by exactness, there is an element $\mathbf{\bar{u}\in H_n}(X;\mathbb{Z}/r\mathbb{Z})$ with $\partial(\bar{u})=u$. Should be $H_n$ instead of $H_{n+1}$.

## Talking Point 2017 – EP23

##### Thu 5 Oct 2017
23 MINS

By Channel 5 Published: 05 Oct 2017 Audio: English

Cast

Each year, only the top 1% of the primary school cohort will enter the Gifted Education Programme. Yet scores of parents send their children to preparatory classes in hopes that their child will ace the GEP Selection Exercise. Authorities frown on such courses. Learning centres say there’s overwhelming demand. Can a child be trained to be gifted? And should he? Talking Point gives you an inside look into how primary school students are being prepped to take a screening test for gifted kids.

There are 2 short films on the subject of PSLE, free on YouTube. Quite accurate about the lives of kids in Singapore currently. Do feel free to watch if you are interested.

It is truly a first-world problem (only kids in middle to high income families will suffer from this, as tuition is not cheap), but it does reflect the stress that children go through nowadays.

Look at the child’s timetable: https://youtu.be/FQB7ritn580?t=116. Completely packed from Monday to Sunday. (Quite realistic as I have seen real life examples of such scenarios.)

## More expat students catch the ‘tuition bug’ and other Educational News

 More expat students catch the ‘tuition bug’ The Straits Times Singapore has gained a reputation for being a “tuition nation”, with surveys … Mr Shaun Lim, a partner at Quintessential Education, said the “kiasu” …
 SUSS to weave social impact into all courses The Straits Times The Singapore University of Social Sciences (SUSS) will expand its … It provides an applied education approach that targets fresh school leavers and …
 NTU alumni to receive $1600 credits each to take up courses The Straits Times SINGAPORE – About 222,000 alumni of Nanyang Technological University (NTU) will receive$1,600 credits each which they can use for a wide …
 How can the public learn more about the history of Chinese education inSingapore? The Straits Times A new book by the National Library looks back on the development of Chinese education in Singapore, through more than a century’s worth of …
 How Singapore Encourages Lifelong Learning and Workforce Resilience The Diplomat SkillsFuture Singapore (SSG), for example, is a statutory board under the Ministry of Education that provides an array of lifelong learning and …

A self-study Russian mathematician, kicked out 3 times in high schools, expelled from Moscow University, all because he did not attend classes, preferred to self-study in a broader scope for his curiosity, at his own faster speed than the rigid curriculum and boring test-and-exams regime in classrooms.

He did the PhD in Harvard by invitation even he did not have a Bachelor degree, and he barely passed the Harvard’s QE (Qualifying Exams) in Algebraic Geometry, a field in which he made a revolutionary discovery few years later, and for which he was awarded the highest honor : Fields Medal.

This is the typical trait of the geniuses like Evariste Galois, Albert Einstein, Ramanujian, Hua Luogeng (华罗庚), Zhang YiTang (张益唐 – proved “70m Twin Prime Gap”) [#] , Chen Jingrun (陈景润, proved Goldbach Conjecture “1+2”) [##]… with self-motivated curiosity in their field of passion, with reading from the Masters’ works…

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## Univalent Foundation – Computer Proof of All Maths

The scary complex field of Math worried the mathematicians who would prove a theorem relying on the previous theorems assumed proven correct by other mathematicians.

A sad example was Zhang YiTang (1955 – ) who prepared his PhD Thesis based on a previous “flawed” Theorem proved by none other than his PhD Advisor Prof Mok in Purdue University. Unfortunately his Thesis was found wrong, and the tragic happened to Zhang as he had revealed the mistake of his PhD advisor who insisted his (Mok’s) Theorem was correct. As a result Zhang failed the 7-year PhD course without any teaching job recommendation letter from his angry advisor. He ended with a Subway Sandwich Kitchen job offered by his Chinese friend, sleeping in another Chinese music conductor’s house on a sofa. It was there he spent another 7 years thinking on Math, finally an Eureka breakthrough one 2013 morning in the backyard…

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## Motif (Motive 目的)

Below is an excellent intuitive explanation (in Chinese) of the abstract concept Motif by Grothendieck:

Brief summaryMotif is the source of all “beautiful things” expressed in different forms.

Example : God created Natural Numbers (N), we express N in different forms: Binary (0, 1), Decimal (0, 1, 2 …9), Hexadecimal (0,1, 2…9, a, b, c, …f), etc. However, the “Motif” behind these forms is they all follow : 1) Commutative Law ; 2) Distributive Law.

Similarly, in Algebraic Geometry applying the cohomology from Algebraic Topology: étale cohomology, crystalline cohomology, de Rham cohomology are the different forms (~ Binary, Decimal, Hexadecimal), factored throught the common “Motif” of the Universal cohomology (~N).

[My Analogy in IT Language]:
Motif is like Interface or Generic, it spells out only the specification, leaving out the implementation (method) for actual classes / functions…

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## Free Math Games For Everyone

Free Math Games For Everyone

Multiplication of big numbers, complex mathematical problems – there are so many issues that people can face not only at school but also in their everyday lives! People need math everywhere and always! That is why understanding the fundamental principles of math is not less important than being able to read or write! Going shopping or starting your own business – gaining the needed mathematical knowledge and being able to apply it in practice will come in handy for everyone, no matter where they go and what they do!

How to learn this subject? Just like any other science, it requires time and efforts to learn it! However, thanks to the modern technologies and the Internet, everything has become a bit easier today and now, it is enough to find a few useful resources to resolve any academic matters! Some of the most useful resources offer people not only to find the answers for their homework sheets and read the main rules but also to enjoy math games and learn while playing!

It is not a secret that children of a younger age, perceive the information much better if it is presented in a fun and engaging form, for example, while playing. This explains such a high demand for online educational games. However, not only kids can enjoy free maths games, in fact, many adults will also find such activities quite useful and fun!

What are the other benefits? The platforms that offer you to study maths online by means of playing games will help you to master all the possibilities of mathematics easily – you will learn how to add, subtract, divide and multiply. For kids, such activities will be useful for admission to the school. For adults, such activities can help fill in the gaps that they have in their knowledge!

Below you can find a list of top five free sources where you can learn mathematics fast and easily while enjoying an exciting game right from your browser in the online mode!

Math Playground

The website is convenient. There are many different categories, which make it simple to find suitable activities for everyone, while good graphics make the whole process really fun and enjoyable!

Math Game Time

This is one of the best platforms! All the games are organized by grade, but what really makes this site stand out is a wide range of additional opportunities like problem-solving, shapes and geometry, algebra or time and money games!

Cool Math Games

There are many strategy and logic activities. Also, on this platform, you can find some exciting and useful “skill games” that are aimed at developing the basic mathematical skills, and they can come in handy not only for the children but also for the whole family!

Unlike the previous platforms, this website offers a wide variety of fun educational activities on numerous subjects, including spelling, reading, science, etc. All the games are bright and colorful. This creates a pleasant atmosphere and will be especially interesting for younger kids. The highest age for games specified on the site is 12. However, some of them will also be useful for grown-ups!

Learning Games For Kids

Although from the first glance it seems like this site is created exclusively for children, I am sure that adult users will also find something interesting and useful for them! There is a wide range of choices. All activities are divided by their goals and grades, and there are also addition and random math activities; such divisions help to navigate through the website with ease and find exactly what you were looking for! There are also many other possibilities. The site also features many vocabularies, art, science, health, brain, literature, and some other activities!

There are just a few sources of many! You can look for more opportunities on the Internet. Find out what options you have – test a few games from different platforms to compare their efficiency, and, without a doubt, you should find something suitable for yourself! Also, if you are enjoying playing on the go – there are numerous applications for tablets and smartphones that you can use at any time and from any place, which will be convenient for busy people!

Final Words

Why is math so important in our lives? It is one of the basic sciences that every person should understand. It does not mean that each of you needs to become well-versed on this subject because if you lack certain skills that are needed to cope with your homework, you can always hire a tutor or turn to www.customwriting.com for academic help. However, having the necessary knowledge base is a must! Without it, you will find it difficult to do the most usual things like count the change in the grocery store, and thus, you will feel less confident!

## How to prepare for ASEAN Scholarships Pre-U Entrance Test

Recently I received an email from a reader (name removed for anonymity). Just posting here in case it is useful to other readers. Good luck for those interested in applying for the scholarship!

I am a 16-year old Malaysian student and I am interested in applying for the ASEAN scholarships for Malaysian Pre-University One Scholarships, yet I am lost as to how to prepare for the entrance tests(especially the mathematics test) and thought that i could ask you since I’ve frequently browsed your website for a while and have read that you’re experienced in the O’level and A’level fields of mathematics.

If you wouldn’t mind, I have a few questions to ask:
1. How should i prepare for the entrance tests?(as in what should i study/focus on for the Math entrance test)
2. Is it necessary for me to learn the SEAB A-levels/ JC syllabus? If yes, what textbooks would you recommend me buying in order to prepare for the exam?
3. What is the difference between IGCSE Additional Math syllabus(I’m in the IGCSE class in my school) and the Singapore O’level syllabus?(I’d like to know what I’d possibly be lacking in)

It would be most helpful if you could answer my questions. I hope to hear from you. Thank you!

Thanks for visiting my website.

1. I think you should focus on the Additional math / Elementary math for O Levels.

2. I don’t think JC syllabus should be necessary as that is usually taught for 17-18 year old students, which should be beyond the scope of the pre-university exams.

3. Overall it should be the same, but there may be some small differences. You may check out this new syllabus: http://www.seab.gov.sg/content/syllabus/olevel/2017Syllabus/4047_2017.pdf

For example, for the Singapore syllabus, there is this sum of cubes/differences of cubes formula that is tested: https://mathtuition88.com/2014/10/27/sum-of-cubes-a-maths-tuition/

For practice questions, you may want to check out this set of papers (with solutions): https://sellfy.com/p/l4w2/

They are representative of what is tested in the Singapore A Maths syllabus.

## Song of Simple Group

Group Theory is abstract, but the song…

The lyrics to the song can be found in “Contemporary Abstract Algebra” (Seventh Edition) by Joseph A. Gallian

(ISBN 978-0-547-16509-7) pages 422 & 423.

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## One of the world’s most influential math texts is getting a beautiful, minimalist edition – The Verge

https://www.theverge.com/2017/9/2/16247282/euclids-elements-kroncker-wallis-math-text-beautiful-minimalist-kickstarter

Little print-edition of Math Classics: Euclidean 《The Elements》(几何原理) – the second printing by volume after 《The Bible》.

The Euclidean Geometry was less emphasised in Secondary school from 1970s in the world (80s in Singapore) to be replaced by Vector Geometry (UK/USA) and Abstract Linear Algebra aka Vector Space / Affine Geometry (in France). It was a pedagogical mistake now these countries recognise – never “Throw the baby (Euclidean Geometry) together with the bath water (Old Maths )”.

IMO Competition usually has 2 out of 6 problems in Euclidean Geometry but no modern math or Calculus, reason being to cater for 100+ countries still with Classical Math. That’s why the Asian countries – South Korea (2017 IMO Champion), China (2nd IMO 2017), Vietnam (3rd IMO 2017) , HK, Taiwan, Thailand, – with old syllabus are top IMO but not the Advanced countries (France, UK, other European, Japan, USA, Singapore…).

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## Zhihu 知乎: 环Ring, 域Field, (半Semi-)群Group, 幺半群 MonoId

[葛利流，数学科技]

(I) 环和域

“环”最好的例子: 整数(Integer) 记作 Z (德文Zahl) 是个环。 他研究 Clock Arithmetic 时钟 是个 Modular Arithmetic (Mod 12)运算, 比如 15 = 3 mod 12

Hilbert 的得意女弟子 Emile Noether 把 环论 发扬光大, 创造 “Noether Ring”。

Hilbert 发现 “环”有个重要性质是含有 “理想” (Ideal) – 理想 * 任何”外面”的东西 还回来”里面”。

0 * 任何Z数 => 回来 “0家族里面”

(II) 群 Group / 半群 Semi-Group / 幺半群MonoId
Group 群 有4个性质 C.A.N.I.
C: Close 封闭性
A: Associative 连续性
N: Neutral (or Identity = Id) 幺元
I: Inverse 逆元

Semi-Group 半群 只有2个性质: C.A.

Monoid 么半群 : C.A. + N (= Id) => Mono + Id

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## 2017 PSLE Math Question

Answer: 10 (Yes!) but why ?

…(see explanation here )

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## Garlic Butter Lobster

1. Put lobster in boiling water for 4 mins.

2. Take lobster out and soak it into cold water.

3. In a bowl, add in minced garlic.

Then chopped chili, parsley and sprinkle salt. Mix well. Then add in butter. Stir them.

4. Cut lobster into halves.

5. Spread garlic butter onto lobster.

6. Heat a skillet on the stove. When it becomes smoke hot, put the lobster in with the butter side down.

7. Heat a bit then turn them over.

8. Place lobster in a plate. Pour garlic butter over it.

My husband loves it.

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## Train delay: Students given full duration for paper (PSLE English Language and GCE O-level Music Performing)

Fortunately, students affected by the train disruption are given the full duration for their respective papers. It would have been quite a traumatic experience though.

Source: Straits Times

SINGAPORE – No exam candidates were affected by the train delay on the East-West Line on Thursday (Sept 28) morning, said the Singapore Examinations and Assessment Board (SEAB) in response to queries from The Straits Times.

As at 8.30am, no schools have informed SEAB that candidates sitting the PSLE English Language and GCE O-level Music Performing examinations were affected by the disruption, said the exam board.

Earlier in the morning, the Ministry of Education said that students who are affected by the train delay on EWL do not need to submit an excuse letter and will be given the full paper duration.

## Online Technology News Media Teknologi & Internet

The following is a new Online Tech News site: onlinetech.news.

Category: Media Berita Internet

Keywords related to the site:

Online Technology News Media Teknologi & Internet
Berita harian internet
Berita harian internet
Situs berita internet
situs berita teknologi
Berita online
teknologi online
berita teknologi
berita online
berita internet
situs berita teknologi
situs berita online
situs online

## Travel Advisory: Volcanic Activity in Bali

On 22 September 2017, Indonesian authorities raised the alert-level for Mount Agung on Bali island to level 4 (Awas or Warning) due to an increased possibility of a volcanic eruption within 24 hours. Indonesia’s National Disaster Mitigation Agency has warned residents and tourists to stay 9 kilometres away from the crater and up to 12 kilometres away to the north, northeast, southeast and south-southwest.

Given the possible eruption of Mount Agung, Singaporeans should defer non-essential travel to the affected areas at this juncture. Volcanic eruptions could result in ash clouds that could severely disrupt air travel. Singaporeans currently in Bali should monitor these developments closely and avoid Mount Agung and its vicinity. They are advised to take all necessary precautions for their personal safety, monitor the local news closely and heed the instructions of the local authorities, such as to be ready to evacuate at short notice. They should also purchase comprehensive travel and medical insurance and be familiar with the terms and coverage.

Singaporeans are advised to stay in touch with your family and friends so that they know you are safe. Singaporeans travelling overseas are also strongly encouraged to e-Register with the Ministry of Foreign Affairs at https://eregister.mfa.gov.sg/, so that we can contact you should the need arise. Those in need of urgent consular assistance may contact the Singapore Embassy in Jakarta or the Ministry of Foreign Affairs Duty Office at:

Embassy of the Republic of Singapore in Indonesia (Jakarta)
Jln H R Rasuna Said, Kuningan, Block X/4, KAV No 2,
Kuningan, Jakarta Selatan 12950
Tel: + 62 (21) 2995 0400 or +62 811 863 348 (24-hours)

Ministry of Foreign Affairs Duty Office (24-hours)
Tanglin, Singapore 248163
Tel: 6379 8800, 6379 8855
Email: mfa_duty_officer@mfa.gov.sg

## PSLE Chinese Listening Exam (mrbrown) Very Funny!

Recently, there is a PSLE Chinese Listening Exam that does not make sense.

Question: Student A bought a new clothes. Student B asks Student A: “You bought new clothes?” Student A said: ” No, it is sewn by my mother, do you think it is beautiful?” Student B said: It is very beautiful, I didn’t knew your mother could sew?”.

What did Student A say next?

1) My mother will sew clothes for me whenever she is free.
2) My mother does not like to spend money to buy clothes.
3) My mother just started learning how to sew.

I am totally puzzled by this question. The three options seems equally plausible. How are we supposed to know which is the truth?

Answer is option 3 by the way.

## Recommended Books for Spectral Sequences

So far the most comprehensive book looks like McCleary’s book: A User’s Guide to Spectral Sequences. It is also suitable for those interested in the algebraic viewpoint. W.S. Massey wrote a very positive review to this book.

A User’s Guide to Spectral Sequences (Cambridge Studies in Advanced Mathematics)

Another book is Rotman’s An Introduction to Homological Algebra (Universitext). This book is from a homological algebra viewpoint. Rotman has a nice easy-going style, that made his books very popular to read.

The classic book may be MacLane’s Homology (Classics in Mathematics). This may be harder to read (though to be honest all books on spectral sequences are hard).

Posted in math | Tagged , | 1 Comment

## Interesting Facts about Green’s Theorem

Firstly, Green’s Theorem is named after the mathematician George Green (14 July 1793 – 31 May 1841). Something remarkable about George Green is that he is almost entirely self-taught. He only went to school for one year (when he was 8 years old). His father was a baker, and George helped out in the bakery. Later, at the age of 40 he went to Cambridge to get a formal degree, but even before that he had already discovered Green’s Theorem. It is a mystery where did George Green learn his mathematical knowledge from. (During his time there was clearly no such thing as internet.)

It is unclear to historians exactly where Green obtained information on current developments in mathematics, as Nottingham had little in the way of intellectual resources. What is even more mysterious is that Green had used “the Mathematical Analysis,” a form of calculus derived from Leibniz that was virtually unheard of, or even actively discouraged, in England at the time (due to Leibniz being a contemporary of Newton who had his own methods that were championed in England). This form of calculus, and the developments of mathematicians such as LaplaceLacroix and Poisson were not taught even at Cambridge, let alone Nottingham, and yet Green had not only heard of these developments, but also improved upon them.
-Wikipedia

One of the applications of Green’s Theorem that I find interesting is finding the area of the ellipse: https://www.whitman.edu/mathematics/calculus_online/section16.04.html. (Scroll down to Example 16.4.3). I find the proof very neat, you may want to check it out.

## Pierre-Simon de Laplace; French Newton

To increase your interest in mathematics, let me introduce the French mathematician Pierre-Simon de Laplace, also known as the “French Newton” or “Newton of France”. He helped to calculate projectile motion for Napoleon’s artillery. Laplace was also the examiner for Napoleon when he entered military school. Laplace also invented “Laplace transform” and “Laplacian” which will be useful in advanced engineering calculations.

Some quotes:

In September 1785 Laplace subjected Napoleon to a rigorous examination in differential equations and algebra as well as the practical applications of mathematics.
Book on Napoleon

The French Revolution began in 1789. Laplace was fortunately situated for avoiding its dangers, in part because, like Lagrange, his talents were found useful in calculating artillery trajectories. Napoleon esteemed Laplace, and after the Revolution showered him with honors.
https://www.umass.edu/wsp/resources/french/personnnes/laplace.html

Napoleon himself was good at math, he proved a theorem called Napoleon’s Theorem. Napoleon was “close friends with several mathematicians and scientists, including Fourier, Monge, Laplace, Chaptal, Berthollet, and Lagrange.”

Napoleon also made the following quote:

The advancement and perfection of mathematics are intimately connected with the prosperity of the State. — Emperor Napoléon Bonaparte.

Hope the above interesting facts increase your interest in math.

## 5 Skills Students Need To Cope With School Pressures

According to an article published by the American Psychological Association (APA), many teenagers in the USA say they experience stress in patterns comparable to what adults go through. Teenagers also report higher stress levels than adults during the school year.

Tutors from Leaps ‘n Bounds, a learning center in Dubai, also observe that teen stress is not just confined to adolescents in certain countries; it is slowly becoming a widespread issue.

Teen stress can be caused by different factors including the pressure to perform well (or at least to pass) academically and in sports, and to have a great social life. In school, adolescents constantly face tough academic demands and responsibilities and experience social pressure.

Unfortunately, these challenges spill over even after the afternoon school bell rings, which can cause teenagers to feel even more stressed.

## Dealing with Teen Stress

For teenagers to learn how to effectively deal with school pressures, they need to develop and rely on key personal skills. These include:

### 1.    Time management

All teenagers today always seem to be swamped with numerous activities: assignments, studying, extracurricular activities and sports. They need to find time for their friends, too.

Because teenagers need to have enough time to go through and complete these activities, they need to learn how to manage their time properly. Time management is an important skill they need to develop. This skill pertains to their ability to plan and control how they spend the hours in their day to complete their tasks and accomplish their goals.

With proper time management, teens will be able to establish which tasks to prioritize and how to set their goals, and learn how to monitor where their time actually goes. As such, they will be able to avoid the stress of not having enough time on their hands to finish their assignments, complete their projects, meet their friends, and see their maths tutors in Dubai, if they have additional weekly tutorial or learning sessions.

### 2.    Setting realistic goals

Being number one in the class and, at the same time, for example, being the captain of the school football team are goals worth working hard for. However, overachieving teens tend to feel more pressure. When they fail or feel they didn’t perform up to expectations, they may develop low self-esteem and other negative feelings and attitudes.

Teenagers, therefore, are encouraged to lower their goals or set more realistic ones so that they can achieve more. By doing so, teens will also avoid pressure and boost academic success.

### 3.    Positive coping skills

Coping skills are daily strategies and activities everyone uses or relies on to deal with, work through, or process emotions. Examples of positive coping skills include exercising, meditating, talking with friends or other family members, and having healthy hobbies such as reading and gardening.

Teenagers need to develop and practice positive coping skills instead of negative ones so that they will learn how to deal with stress through healthy ways. Positive coping strategies increase long-term resilience and well-being.

Negative coping techniques such as smoking and using drugs, on the other hand, may provide temporary relief from difficult emotions and pressure but lead to substance dependency and abuse.

For teenagers to effectively withstand adversity and deal confidently with daily stress and other challenges, they need to choose and apply positive coping strategies.

### 4.    Self-care

For teens to better cope with pressure, they also need to have strong, healthy bodies. Teenagers, therefore, need to get enough sleep and rest, have a well-balanced diet, and get the right amount of exercise their bodies they need every day.

Adolescents need to take some time to pause from the relentless pace of everyday life and enjoy some creative activities that will help keep them from dwelling on or stressing over school pressures. This, in turn, will help them lower their stress levels.

### 5.    Optimism

Generally, stress is precipitated by stressful thinking. As such, teens can avoid stress and its negative effects by changing the way they think. When they have a positive mental attitude, they will have stronger coping strategies, better health, and a more stable, less stressful emotional life.

Adopting a positive way of thinking also helps teens complete their work and handle all their responsibilities. If they consistently think they won’t finish something or they don’t have enough time on their hands, they will lack the motivation to complete what they already started or even begin their task.

Teenagers only have a few more years before they enter another important phase in their lives: adulthood. But they can still enjoy all the experiences that come with adolescence and, at the same time, cope with all their school work and other activities without all the stress by simply developing the right skills.

AUTHOR BIO

Bushra Manna is one of the founders and Principal of Leaps and Bounds Education Centre – Motorcity. She has 20 years’ experience teaching the British and American curricula internationally at primary level – early middle school level, ages 4-12. Bushra believes in imparting deep learning to a child and not just rote learning, which is why she recommends the Magikats programme at her centre, to promote a genuine understanding with its multisensory, differentiated and interactive approach within a small group setting.

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## Best Online Resources to Improve Your Math Skills

Best Online Resources to Improve Your Math Skills

Although Maths is a compulsory subject in all the educational institutions all over the world, many students consider it as a complete waste of time and skip this issue, claiming that they prefer not mathematically oriented disciplines but only social sciences. But will it really help you in your future or it is just something you have to learn because everybody does it? Math, as well as other exact sciences, is essential for the intellectual development of a person from early years, it helps to develop intelligence and better your critical, analytical, deductive and prognostic abilities together with improving your abstract thinking. Very often people understand the importance of logic and algebra when they are already adults and try to make up for lost time, but do not know where to find a qualified help quickly. We think that a man is never too old to study, that is why we have selected the best online sources to improve your knowledge of numerous subjects:

• Online courses

There are plenty of courses available on the web, which can offer math courses online at low prices or even for free. Online learning is a trendy way of getting new knowledge and experience nowadays, but still, there are people, who prefer old and traditional methods and say it is useless and wastefulness. But, if you keep up with the times, you can visit such sites as Academic Earth, Edx, TED, University of the People, Coursera and others and get a unique experience in exploring new things from universities all over the world, just sitting on your sofa and holding a laptop.

• Online libraries

For those, who still hesitate, exist online libraries, where you can download books you need and dive into learning by yourself. Of course, there is nothing better than a smell of a written word, but the theme of books varies depending on the site, and mostly they have a plethora of them available for free, so everybody could find the one he needs. The one drawback of using web libraries is that you have to organize an academic process yourself, thus have good time-management and organizational skills. Nevertheless, if you are a person, who is self-motivated and can move towards the goal on your own, this type of e-learning is exactly what you need. Among the most popular web libraries are The Online Library, Harvard Library, Wiley Library, Open Library and others.

• Online Tutors

There are different types of school teachers, some of them focus on the needs of each student, other – use discipline as a key to successful learning, but the thing that is common for all of them, is strict correspondence to the school program, established in the country. School program doesn’t care whether the student understood the material he had just learned, or he still needs time to master it. This is the time when online tutors come to stage. If you need to learn math or other subjects that you have missed at school or simply improve them, they can assist you as they are 100% students oriented and can present the material according to the students’ abilities and needs.

• Online lessons

This type of lessons is a perfect variant of distance learning for those, who are limited on time and want to master something quickly and get great results. Individual classes can take place in the form of face-to-face conversation by means of various apps or programs such as Skype and other video calls. Among the advantages of this type of e-learning is easy access – you can learn from home and build up your own learning schedule, also there is wide choice of tutors available on the Internet, no matter how far away they are, different educational content – video and audio which you can find for free on the web and, of course, you can choose the subject or skills you want to level up – it could be mathematics assignment writing, organic chemistry, etc.

There are plenty of ways how to study maths online, and it depends on which directions of studying will you choose, the pros and cons of each method based on your goal and preferences. The one thing you should remember is that it is never late to gain new knowledge or skills. As Benjamin Franklin once said, “An investment in knowledge pays the best interest.”

## An ancient Babylonian tablet known as Plimpton 322

Source: NY Times

One of my favorite YouTube Math Professors, Norman Wildberger, has made a historical math discovery: that the ancient Babylonian tablet known as Plimpton 322 is actually a trigonometric table.

“It’s a trigonometric table, which is 3,000 years ahead of its time,” said Daniel F. Mansfield of the University of New South Wales. Dr. Mansfield and his colleague Norman J. Wildberger reported their findings last week in the journal Historia Mathematica.

Check out my other blog posts on Prof. Norman Wildberger:
1) Algebraic Topology Video by Professor N J Wildberger

## Garry Kasparov Masterclass Review

Garry Kasparov Teaches Chess is the latest Masterclass by World Champion Garry Kasparov. I am sure that even from the trailer, you can see that it is of exceptional quality.

According to the FAQ, “the class will test players with a US rating of 1300-1700 and include more advanced concepts and examples that will benefit 1800+ rated players”. Most amateur players will fall under this range.

# Morse Theory.

An old joke, as most of my academia-related ones are. The young scholar says to his teacher how amazing it was in the old days, when people were foolish, and thought the Sun and the Stars moved around the Earth. How fortunate we are to know better. The elder says, ah yes, but what would it look like if it were the other way around?

There are many things to ponder packed into that joke. For one…

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## Education and the Blockchain – Should We be Teaching Blockchain in Schools?

It goes without saying that tech progress is moving at a rapid pace. Futurists point to Moore’s law – the idea that tech capabilities double every two years – as evidence for tech’s expansion into nearly every facet of our lives.

Teaching Technology

Education has seen its own dramatic tech advances. Kids can learn math from gamified apps while riding in the backseat of the family minivan. Students can hire an online algebra tutor and learn from anywhere via Skype. Aspiring students can virtually attend free Ivy-league classes (Massive Open Online Course, or MOOC) with millions of other learners of all ages and backgrounds. And NASA now collaborates with high school students in inventive hardware and robotics projects.

The most significant advance in computer-based education isn’t AI or virtual-based learning or even big data – it’s the blockchain. Blockchain has its origins in cryptocurrency, i.e. Bitcoin. The blockchain is essentially a way of managing data transactions – and it’s considered a radical disruption of traditional banking.

Plus, its applications in education – both virtual and classroom-based – have the potential to change everything about schools, from instruction to student achievement.

Exposure Versus Creativity

In the US, three-quarters of children have access to a smartphone. But on its own, that’s not necessarily a good thing. Kids who simply learn to operate a phone, just downloading and playing games, become consumers. The future lies with creators.

US Department of Labor statistics tell us that 2020 will bring with it 1.4 million computer specialist job openings. But American universities produce woefully inadequate numbers of graduates in the right fields – enough to fill a mere 29% of the jobs.

So what’s wrong with the picture? Why the big gap? There are many societal reasons we could point to, but one thing seems to stand out. We’re teaching tech literacy the wrong way.

Textbook-style curriculum may have its place, but not in tech ed. When kids are taught to memorize coding sequences and churn out the same answers to the same textbook questions, there’s no creative spark. No outside-the-box thinking.

In the best way, blockchain is wildly unconventional. To advance the world-changing potential of anti-dogmatic thinking, we need to encourage kids’ inventiveness. If the educational focus is on robot-like achievements rather than innovation, where will we find our climate change-tackling problem solvers?

We’ve labeled a generation of kids “tech-savvy” without giving them the tools to move from consumption to creation. It’s a waste of their brain power to hook kids on the addictive side of tech without pulling back the curtains and showing them the remarkable inner workings. Children and teens want to know how things work.

One solution? Teach tech like art. Coding has more in common with drawing than accounting. Yes, there is a necessary foundation in understanding digital languages and principles – but without encouraging creativity, we’re creating a generation of the same brain. Even gamified learning, if done improperly, can be perilously bland.

Tackling the Education Gap

There are few key components of a sound approach to teaching creative thinking around technology.

1. Let it be accessible. Kids will shy away from a big learning curve – learning and doing need an intimate relationship.
2. Remove the achievement roof. Learning platforms and educational approaches which employ standardized tests as the litmus for success – and for what the content can achieve –inhibit creativity. Rather than saying “do this to produce this result,” what if we said, “here are your tools – now, what can you create?” Consider The Lego Movie’s message of the importance of imagination – for future tech innovation, we need makers, not managers.
3. Embrace a shifting curriculum. In other subjects, things might stand as eternal truths; the Magna Carta will always have been signed in 1215. But in technology education, things move at a blistering pace. A particular tool or lesson may become quickly outdated, so the educational format needs flexibility, just like the subject it teaches.

Blockchain is set to change the world. But as we continue to encounter environmental and societal problems, we need amazing minds to solve them. Revolutionizing how we teach technology education might be the answer we didn’t know we needed.

## Mathematical Functions vs Programming Functions

Key Points:

• Pure Function
• Partial Function
• Total Function

View story at Medium.com

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## Symmetry, Algebra and the “Monster”

Very good introduction of Modern Math concept “Group” to secondary school math students by an American high school teacher.

https://www.quantamagazine.org/symmetry-algebra-and-the-monster-20170817/

Summary:

• Symmetry of a Square
• Isometry (*) or Rigid Motion (刚体运动) = no change in shape and size after a transformation
• What is a Group (群 “CAN I” ) ? = Closure Associative Neutral Inverse
• Monster Group = God ?
• String Theory: Higgs boson (玻色子) aka “God Particles”

Note (*): “保距映射” (Isometry），是指在度量空间 (metric space) 之中保持距离不变的”同构“关系 (Isomorphism) 。几何学中的对应概念是 “全等变换”

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## Math Problem Solver – SymboLab

A new alternative to the UK Mathematica’s “Wolfram Alpha” online tool:

http://www.makeuseof.com/tag/not-wolfram-alpha-solve-math-equation-symbolab/

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## Son of taxi driver among this year’s President’s Scholars

Mr Lee Tat Wei lives in a four-room flat in Woodlands. He and his older brother went to neighbourhood schools. His father is a taxi driver and his mother works as a part- time sales assistant.

Despite his humble background, the 19-year-old said he has never felt shortchanged. “My parents gave me an environment that money couldn’t buy. They never pressured me to get straight As. They taught me to live in the moment,” said the Anglo-Chinese School (Independent) graduate who had a perfect score of 45 for his International Baccalaureate diploma exams.

Mr Lee, who is one of the five recipients of the President’s Scholarship this year, will be going to read liberal arts at Yale University.

## I’m a Rare Breed: An Elite Chess Player Who’s Open About His Faith

A nice interview by Wesley So, one of the top chess grandmasters from Philippines.

On the small planet where elite chess players dwell, very few people worship Jesus Christ. If anyone discovers that you’re one of those “superstitious,” “narrow-minded idiots,” you’re likely to see nasty comments accumulate on your Facebook fan page. On a regular basis, I receive emails from strangers lecturing me about the dangers of following Jesus. Out of pity or disgust, they wonder how I, the world’s second-ranked chess player, can be so “weak-minded.” I have been assured that identifying openly as a Christian will interfere with sponsorship, support, and invitations to events. I have been told that spending time reading my Bible, praying, and going to church will inevitably weaken my performance. People plead with me to at least keep quiet. They say thanking God publicly makes me look ridiculous. So why did I make such a risky move?

From Wikipedia:

As a young player, So’s aggressive and tactical style of play caught the attention of a former Philippine chess champion, International MasterRodolfo Tan Cardoso. Cardoso said of So:

“The young lad…would sacrifice a queen or any other pieces in his arsenal to get a winning attack….He cannot afford decent training given by well known GM-coaches and has to rely on his pure talent…before competing.”

## UK Textbooks à la Chinese / Singapore Math Style

[Original Financial Times Article] Google: UK maths books fail DfE test

$latex boxed {text {The Ideal Math = (Chinese + English) * French }}&fg=aa0000&s=3$

UK, USA, France are copying Chinese Math (from which the “Singapore Modeling Math” derived) in Primary schools, this proves my above-mentioned “Ideal Math” formula is correct. The 2 Asian countries were top in 2015 PISA Math Test for 15-year-old students, while UK was ranked 27th.

It remains to see if China / Singapore reciprocate the French Math theoretical foundation rigor in High Schools (Junior Colleges) and in the first 2 years of undergraduates for STEM (Science, Technology, Engineering, Math) students.

Compared with Fields Medals (equivalent to Nobel Prize in Math), the picture is reversed – where USA, France and UK are top. The secret lies in the formula : the multiplying factor – (* French), ie the math theoretical foundation notably…

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## How (not) to memorise mathematics

Many excellent Math students after leaving universities more than 10 years forget 90% of math they learned, save some primary school arithmetics – few could do Singapore PSLE Modelling Math or solve quadratic equations.

The “Story-Telling” memory technique via “Signposts” can be used to reconstruct math from first principles:

https://medium.com/@fjmubeen/how-not-to-memorise-mathematics-98fef71aefcf

Note: Lewis Carroll: the author of “Alice in wonderland”

Cambridge Professor Tim Gowers (Fields Medalist) suggested the similar pedagogy of “Memorise by First Principles”.

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## The Ring Z/nZ, Fermat Little Theorem, Chinese Theorem (French)

Revision: Modulus Arithmetics

(1/2) Fermat Little Theorem

(1/2) Chinese Theorem

(Note: This is the “RING” foundation of “The Chinese Remainder Theorem” which deals with remainders )

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## The scientist nuns: In pursuit of faith and reason

Source: Aleteia

Making a career out of science, just like joining a religious order, requires dedication and discipline. Some tireless souls have managed to do both.

In 1965, Mary Kenneth Keller became the first woman to obtain a PhD in Computer Science. She was also a nun.

Born in Cleveland, Ohio, in 1913, Keller entered the Sisters of Charity of the Blessed Virgin Mary in Dubuque, Iowa, in 1932. Eight years later, she professed her vows, before obtaining B.S. and M.S. degrees in mathematics from DePaul University in Chicago, where she became fascinated by the incipient field of computer science.

As a graduate student, she spent semesters at other schools, including New Hampshire’s Ivy League college Dartmouth, which at that time was not coeducational. For her, however, the school relaxed its policy on gender, and she worked in the computer center, where she contributed to the development of the BASIC programming language that became so instrumental to the early generation of programmers.

## Ideal Math Education

$latex boxed { text {Ideal Math Education } = (C + E) * F}&fg=aa0000&s=3$

C = Chinese 中文 = Primary school Arithematics sans “Algebra” (= Singapore Modeling Math). Abacus-Algorithmic thinking.

E = English = Secondary School Math

F = Français (French) = High-school / Baccalaureate & University Math = Theoretical, Abstract
=> Rigorous Math Philosophy for Advanced Concepts
=> New frontier Scientific Research.

Why (C+E) ?
C + E = Basic Math Foundation.

Why * F ?
If multiply by Theoretical F, like flying with added wings (如虎添翅)。

However,
if (C+E) -> 0 (less applied), or
if F -> 0 (lack theories),
then Total Math Education -> 0.

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## Theorem of the Day

Just to recommend this excellent website: Theoremoftheday where they feature one mathematical theorem each day.

The nice thing is that each theorem is a one-page summary, good for getting acquainted with the theorem, and subsequently you may read it up in more detail.

The website does have a XML feed, though it would be nice if there were a email subscription (with weekly emails).

## How to win Sir Roger Penrose’s Chess puzzle (that computers can’t solve)

Despite chess computers being very highly rated and winning virtually all human grandmasters, there are still certain positions that the computers can’t solve.

Sir Roger Penrose has documented one of them here:

Chess engines will state that black is winning by a large margin, when in fact White can easily draw, or even win!

Drawing should be easy. Just move the king around (without moving the c6 pawn). The only black pieces that can move are the dark-squared bishops, which can’t checkmate your king.

Winning should be only possible if Black plays badly, e.g. Bishops all give up control of the c7 square. Then c7 followed by c8=B or c8=Q is checkmate!

Very nice study by Sir Penrose that illustrates the weakness of computers!

## Math Olympiad (Primary Schools) 一筐鸡蛋

1粒1粒拿，正好拿完。
Remove 1 by 1, nothing left in basket.

2粒2粒拿，还剩1粒。
Remove 2 by 2, one left in basket.

3粒3粒拿，正好拿完。
Remove 3 by 3, nothing left in basket.

4粒4粒拿，还剩1粒。
Remove 4 by 4, one left in basket.

5粒5粒拿，还差1粒才能拿完。
Remove 5 by 5, short of one to complete.

6粒6粒拿，还剩3粒。
Remove 6 by 6, 3 left in basket.

7粒7粒拿，正好拿完。
Remove 7 by 7, nothing left in basket.

8粒8粒拿，还剩1粒。
Remove 8 by 8, one left in basket.

9粒9粒拿，正好拿完。
Remove 9 by 9, nothing left in basket.

At least how many eggs are there in the basket?

[Hint] This is a Chinese Remainder Problem (韩信点兵“)

—— [Solution] —–

Let there be minimum X eggs in the basket.

Remove 1 by 1, nothing left in basket:
X = 0 mod (1) …[1]
=> trivial & useless !

Remove 2 by 2, one left in basket:
X =…

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