Math Blog
Napoléon Triangle Visual Proof
Cédric Villani
Mathematician Cédric Villani (Fields Medal) is a MP in President Macron’s young party “En Marche”.
He introduced “Singapore Modeling Math” to French primary schools Arithmetic in 2017.
吴文俊 Wu WenJun
吴文俊，陈省身在 WW2昆明西南联大的弟子， 留法Strasbourg University, 兼任 博士生的tutor， 教导 法国未来的 大师Grothendieck (两人都是新数Bourbaki 学派 最后一批会员) 。
吴文俊在1975 文革后才研究 中国古代数学，从中得灵感，发明 电脑 机器化 AI 证明axiom-based 几何定理。得 1st batch Run- Run Shaw (东方Nobel Prize) $1 m Prize.
数学家清心寡慾不爱斗争，一心专注 “数学之美” ，其他生活繁琐的事(文革 批斗) 都看得开。所以多长寿 (Newton, 陈省身， Hadamard, 杨振宁, 也都90＋) ，吴文俊也高寿活到98岁。
French Baccalaureate Math Paper 2 (Analysis)
【「给我进来做题啦!」法国高考数学题难度如何？居然只有四道题？】
Baccalaureate Scientifique Math 2019 (Analyse).
Yet to see the Baccalaureate (S) Paper 1 “Algèbre” which is tougher on Abstract Algebra (Group, Ring, Field, Vector Space / Linear Algebra,…)
Integrate x^x
The integration is meaningless if
$latex displaystyle {int x^{x} dx}&fg=00aa00&s=3$
unless specifying the domain of defintion, eg. interval [0,1] :
$latex displaystyle {int_{0}^{1} x^{x} dx = frac {pi^{2}}{12} }&fg=aa0000&s=3$
Note: Gamma function proof by Feynman trick : differentiate under integral.
DEMO:
a^a^a^… a
$latex boxed{a = a^{a^{a^ {{…}^{a}}}}}&fg=aa0000&s=3$ $latex text {…. [A] } $
$latex text {Let } a = sqrt {2} $
Method…: Wrong !!!
Method 1 : Rigorous!
1) Prove [A] Convergent ?
2) If converge, find Limit ?
Method 2: by RMI Homorphism
View original post 1 more word
Book Marketing – Understanding the Importance of Branding
Book Marketing – Understanding the Importance of Branding
Branding in the library world is as important as the business world. This post identifies its importance to writers.
Branding is the nuanced art of creating a memorable impression on consumers by giving shape to your brand. Before it was defined as just a name, symbol, slogan, sign, or design. Now it is broader, with more aspects. It helps your customers and clients to distinguish your brand from other brands and know exactly what they can expect from you.
Ages ago, authors did not need to promote themselves on social media. Shakespeare never needed to promote Hamlet on Instagram, and Ernest Hemingway did not need to create dynamic content on Facebook to reach viewers.
But now reaching people without promoting yourself is quite impossible. But definitely, you need to know what to promote. And here ‘ME’ is not a satisfactory answer. You need to establish yourself and your literary work as a brand. That is why book marketing and branding are necessary for writers. Good branding helps you to connect with your audience, deliver your message, and create a positive value about your brand in your target audience’s mind. To learn more, keep reading.
A strong brand’s goals are to communicate the message effectively, personally resonate with your target demographic, inspire the customer to purchase, and build loyalty.
It Helps You Find Your Audience
Brands are easily tracked by the readers who are the main customers of writers. They buy brands. But branding is not always getting prioritized over your competitors. It is creating value for your customers. It is solving a problem.
Branding helps you to reach your consumers to get you connected with them. It exists to help you get recognized. When your readers discover your literary works, it motivates them spiritually and helps them solve their issues and receive mental peace. Brand recognition helps to create loyalty in customers and helps you live in their hearts and minds. Also, once you get a loyal fan base, they will also start marketing for you, which can build your audience even more.
It Tells the World What You’re About
Branding not only gets you loyal customers but also helps you to clearly deliver your message to them. A quality brand gives the consumers something to think about and helps them improve themselves as humans. Once they understand your value they will start reaching to you on their own. Because they value what you value.
A writer puts their soul into their literature. It is their form of communicating, and they definitely want people to know what they think. Branding plays a key role here in bringing together writers and readers. This makes the consumers feel like they’re a part of something significant and not just a cog in a wheel.
It Brings Your Purpose Into Focus
Strong branding helps you make a positive impression among your consumers. Every writer has a purpose. Some write fictional stories to make people understand what magic is inside their minds. Some write comedy stories to make people laugh. Some write biographies and historical books to educate people.
Some really want you to understand love by writing romantic novels. Genres play a big role in writers’ lives. If they can promote their piece well, it will bring in the target audience and fulfill the writer’s purpose.
Surely the world has witnessed thousands of love stories, but branding yours can get your story into the world.
It Gives You Guidance Going Forward
A well-executed brand has a lot to say other than just promoting. Even the greatest brand can even get better by rebranding. If you already brand your writings but want to add different features, values, and colors to them, you can. Rebranding is also very important in this ever-changing world.
Branding helps you to know your directions. It navigates you to make decisions and adapt to the new cultural changes. Ten years ago, love stories might have been really technologically far-fetched. It would be hard to relate to stories like that now. But if you incorporate technology and how to use it to enhance love, people will relate to it and to your writings. You need to brand yourself that way as well.
It Sustains Your Career Over the Long Term
It has already been established that branding helps you to reach out to your consumers and motivate them to buy your products. The stronger your brand is, the more it will expand and reach more people. The author of the Harry Potter series, J.K. Rowling, created her brand with uniqueness and kept on promoting herself to the world.
Even though the series ended quite a while ago, people of all ages still talk about it and appreciate it. A successful brand makes the readers keep coming. They not only still buy her books but also the accessories related to them. This actually helps to generate a huge business. Now not only does she make money, but people from all corners of the world make a living selling product related to her stories.
She not only created a platform for her career but also gave a platform to millions of other people to create theirs.
A Few Final Words
You may be convinced that you should brand your work. But it is not that easy, and you might not be as successful as you’d like for a long time. Still, never give up hope. Try to put out some kind of content on a daily basis. And since humans learn by doing, try to diversify your output and improve your techniques.
A brand doesn’t limit you. So keep exploring many aspects of life and publishing your thoughts about it. We hope these suggestions come in handy for you.
Never give up!
Gemini Referral Code
Gemini Referral Link: gemini.com/share/lvevmqvtn
Gemini Referral Singapore
For the referral code, you may just click on the following Gemini Referral Link directly!
There are rewards (such as earn $10 USD in bitcoin when when one trades $100 USD in 30 days) for using the referral code/link to sign up!
Gemini is a digital currency exchange and custodian that allows customers to buy, sell, and store digital assets. It is a New York trust company that is regulated by the New York State Department of Financial Services (NYDFS) and was founded in 2014 by Cameron and Tyler Winklevoss (the famous Winklevoss brothers who were cofounders of Facebook).
Gemini Commission Fees
One of the key benefits of Gemini is its low commission fees. It is highly competitive among all the brokers. For example the charges for using its Active Trader application is 0.35%. This is very low considering that many exchanges usually charge upwards of 0.5%. For example Binance SG charges 0.60%.
Due to the low fees of Gemini (Active Trader), it is useful for people who are either trading frequently or trading in small amounts.
It is important to always use Active Trader (rather than the basic interface), as it has lower fees.
Gemini Singapore Review
Gemini is extremely fast for signing up. You can signup online within minutes, using Singpass to fill in personal details automatically.
Funding is using Xfers FAST transfer, but it is not subject to the $30k annual limit since it is considered a direct Xfers transfer. For this reason, Gemini is a viable option for those who have maxed out the Binance SG Xfers annual limit.
The fund transfer speed via Xfers FAST is quite fast (pun unintended), usually within minutes.
The website interface of Gemini has an excellent design, and is extremely user friendly.
Gemini Minimum Deposit
There is no minimum deposit for Gemini, and there is also no minimum number of coins or tokens you need to purchase. One can buy as low as just a fraction of Bitcoin.
Is Gemini Safe?
This is the most frequently searched question. Firstly, Gemini is a New York trust company that is regulated by the New York State Department of Financial Services (NYDFS). The official NYDFS press release for Gemini can be found here.
Secondly, The New York Times has reported that Gemini is trusted by Ari Paul, of the hedge fund BlockTower Capital, who deals in virtual currency.[9] According to reports by both Bloomberg News and Fortune magazine, Gemini was the first exchange to launch bitcoin futures contracts in December 2017. Fortune reported that Chicago Board Options Exchange (CBOE) uses Gemini “as the basis for the daily settlement for the bitcoin futures”.[10]
With any investing, there is always some risk, so do your research carefully before investing using any exchange!
Gemini Invitation Code / Promo Code
Once again, if you decide to sign up for Gemini, do use the invitation code by just clicking on the following Gemini Referral Link directly!
Disclaimer: The opinions on Gemini expressed in this blog post is for general informational purposes only and are not intended to provide specific advice or recommendations for any individual or on any specific security or investment product. It is only intended to provide information on Gemini Referral Code. In particular, this blog post is not a substitute for obtaining advice from a qualified investment advisor.
The below YouTube video is a beginner friendly introduction and review of Gemini.
祖暅定理
Coinbase Referral
Coinbase Referral Sign Up
Hi – I’ve been using Coinbase which makes it really easy and safe to buy, sell, and store digital currency (like Bitcoin). Sign up now and get SGD 13.36 of free Bitcoin when you buy or sell at least SGD 133.63 of digital currency. Claim your invite now: https://www.coinbase.com/join/wu_t22
Coinbase is a listed company on Nasdaq, with ticker symbol COIN. As of March 2021, Coinbase was the largest cryptocurrency exchange in the United States by trading volume.
There are actually free gifts of crypto on Coinbase, just by signing up and watching some videos. The gifts are usually small amounts of lower cap crypto.
Coinbase Commission Fees
- Coinbase charges a spread of about one-half of one percent (0.50%) for cryptocurrency purchases and cryptocurrency sales.
- Coinbase also charges a Coinbase Fee (in addition to the spread), which is around $0.99 to $2.99.
Coinbase Singapore Review
Coinbase is quite fast for signing up. You can signup online within minutes. Note that they may require some identity verification such as ID (NRIC or passport) and a document containing your address (utilities bill, or bank statement).
The mobile app of Coinbase also has an excellent design, and is extremely user friendly.
Coinbase Minimum Deposit
There is a very low minimum deposit for Coinbase (around $50 recommended), and there is also virtually no minimum number of crypto you can buy (can buy as low as $2).
Is Coinbase Safe?
This is the most frequently searched question. Firstly, Coinbase has been granted a license exemption by MAS (Monetary Authority of Singapore). Their MAS exemption can be found here.
Secondly, all digital currency that Coinbase holds in its online hot storage is insured. If Coinbase were to suffer a breach of its online hot storage, the insurance policy would pay out to cover any customer funds lost as a result.
Thirdly, Coinbase is regulated by SEC (U.S. Security and Exchange Commission). Their SEC license can be found here.
Lastly, for added security, there is 2-Factor Authentication option for Coinbase. Sometimes, there is 3-Factor Authentication (email authentication as well). You can set it up during registration, by providing your phone number and email.
With any investing, there is always some risk, so do your research carefully before investing using any broker!
Coinbase Invitation Code / Promo Code
Once again, if you decide to sign up for Coinbase, do use the invitation code by just clicking on the following Coinbase Referral Link directly! (Free Bitcoin from signing up using the referral link!)
Disclaimer: The opinions on Coinbase expressed in this blog post is for general informational purposes only and are not intended to provide specific advice or recommendations for any individual or on any specific security or investment product. It is only intended to provide information on Coinbase Referral Code. In particular, this blog post is not a substitute for obtaining advice from a qualified investment advisor.
The below video is a very detailed review and tutorial on Coinbase (2021 updated).
Modern Math Education : Time for Reform
Modern Math Foundation : Set + Logic (Equivalence Relation).
A level (H2 level) / International Baccalauréat Math should study the big red square box (Number System, Set Theory, Logic).
All STEM university Year 1 & 2 study these 3 Math foundations : Algebra, Analysis & Vector Space.
The Math major university Year 3&4 study more : real /complex analysis, Topology, Galois Theory, graph theory, etc…
新数启蒙 (1-5) – 给16岁以上的中学生
This “Modern Math” Introductory Course is based on the French Baccalaureate “Modern Math” for 16+ years old, simplified & customized for local students in Chinese.
（1）集合： 等价关系 Equivalence Relation
（2）集合与集合的关系：映射 Mapping
(3) 新数 历史： Bourbaki 学派
（4）由外向内看代数结构 : 域Field，环 Ring，群 Group，向量空间 Vector Space
(5) 域 Field : 足球场
Tiger Brokers Referral: OAEMZD
Tiger Brokers Referral: OAEMZD
For the referral code, enter “OAEMZD” when prompted, or you may just click on the following Tiger Brokers Referral Link directly!
Currently, there are multiple rewards for joining Tiger Brokers:
- 10% off coupon to purchase a share of Tesla (this alone can be worth around $60 USD)
- 5 commission-free trades
- stock voucher of up to 100 SGD (depends on initial deposit of funds)
My Dear Friend,
Sign up and join Tiger Brokers using my following link: https://www.tigerbrokers.com.sg/activity/forapp/invitflow-intl/signup.html?template=invite202011&lang=en_US&invite=OAEMZD.
We both stand a chance to receive stock vouchers of up to SGD 100.
Best Regards!
Tiger Brokers Review
Previously, we have written an in-depth review of Tiger Brokers, including ease of use, reliability, and more. Do check it out!
Disclaimer: The opinions on Tiger Brokers expressed in this blog post are for general informational purposes only and are not intended to provide specific advice or recommendations for any individual or on any specific security or investment product. It is only intended to provide information on Tiger Brokers Referral Code. In particular, this blog post is not a substitute for obtaining advice from a qualified investment advisor.
Toy poodle playing with poodle toy
Charlie the toy poodle loves his new toy (which is also a poodle)!
Dogs have a good life, all they do is eat, play, and sleep!
Last few months to mine Free Pi Coins (Referral Code: math88pi)
Pi Network Invitation Code: math88pi
I am sending you 1π! Pi is a new digital currency developed by Stanford PhDs, with over 10 million members worldwide. To claim your Pi, follow this link https://minepi.com/math88pi and use my username (math88pi) as your invitation code.
It is literally the last few months to mine Pi Coins, Mainnet is launching in estimated Q4 2021 which is just a few months away.
Pi Network has a halving procedure in place, similar to Bitcoin. Basically it means that, the mining rate will reduce by half when a certain milestone is being hit (usually in terms of number of members). Eventually, the mining rate may even hit zero. This means Pi Coin eventually has a finite supply, just like Bitcoin.
We have a detailed review of Pi Network and Pi Coins in a previous blogpost.
Pi Wallet will be released on 31 March 2021
On the Pi Network’s official Twitter page, they announced that they will be releasing the Pi wallet on the Testnet with Test-Pi on March 31, 2021.
This is quite an achievement, Testnet is usually just one step behind Mainnet. For example, Ethereum has several Testnets such as Rinkeby Testnet. The Testnet can act as a test or experiment to see if there are any bugs, before rolling out the Mainnet which contains the actual Pi coins.
Pi network vs Bee network
In the previous blogpost, we detailed some reasons why Pi network is likely to be legit.
Unfortunately, the same cannot be said for Bee network:
- Bee network is created by anonymous/unknown people.
- Bee network is just a “clone” of Pi Network in many ways, up to their White Paper.
- Not sure if Bee network is a legitimate blockchain project, or just one that is trying to ride on the waves of Pi Network.
Hence, currently, we recommend Pi Network but not Bee Network.
Disclaimer: The opinions on Pi Network expressed in this blog post is for general informational purposes only and are not intended to provide specific advice or recommendations for any individual or on any specific security or investment product. It is only intended to provide information on Pi Network Referral Code. In particular, this blog post is not a substitute for obtaining advice from a qualified investment advisor.
Pi Network Referral Code: math88pi
In view of the upcoming Pi day (3.14), this topic of Pi Network is quite appropriate. In this blog post, we will share about Pi Network, what it is, and more.
Pi Network Invitation Code: math88pi
I am sending you 1π! Pi is a new digital currency developed by Stanford PhDs, with over 10 million members worldwide. To claim your Pi, follow this link https://minepi.com/math88pi and use my username (math88pi) as your invitation code.
Pi Network Review
Pi Network is an upcoming blockchain, with idea similar to Bitcoin, but yet with certain differences:
- Pi Network uses the Stellar Consensus Protocol, while Bitcoin uses Proof of Work.
- Pi Network is currently still in the early phases, meaning that it is not available on the “Main Net” yet, or on any exchange. Bitcoin is already very established as of 2021, even recognized by major institutions and banks.
Is Pi Network Safe / Is Pi Network Legit
While it is impossible to answer with 100% certainty, one can list at least 3 reasons why Pi Network is legit:
- Pi Network is listed on the Apple App Store. It is known that “Apple evaluates every app in detail before it’s available in the App Store to make sure that it doesn’t contains viruses.”
- Pi Network is created by real known people (Stanford PhDs: Dr. Nicolas Kokkalis and Dr. Chengdiao Fan) who put their real name upfront. Their identities are verified by Stanford Daily, which is the official student-run, independent daily newspaper serving Stanford University.
- No money is involved in using Pi Network app. No credit card details are needed. Hence, it is impossible that Pi Network is trying to scam money since no money is involved.
Is Pi Network Worth Anything
This is another popular question, on whether Pi Network is worth it. Firstly, Pi Network only takes few seconds per day, to tap the mine button. Hence, the total time wasted is very minimal.
Secondly, once Pi Network goes live on the Main Net, it has to be worth something non-zero. Many YouTubers have analyzed its worth (Pi Network price predictions), the below video has quite a mathematical estimate of what Pi Coin is worth.
Pi Network Referral Link: https://minepi.com/math88pi
Pi Network Invitation Code: math88pi
Pi Network Mining
Pi Network coins are able to be mined on a mobile phone. They are very unlike the Proof of Work algorithms which require massive amounts of electricity and computing power. In fact, the coins can be mined without WiFi or running in the background.
What is happening at this stage is actually “pre-mining”, which is consistent with the Stellar Consensus Protocol (SCP):
Pi Network differs from traditional cryptocurrencies in that the coins are “pre-mined” or pre-generated from the start. When you initiate mining on the Pi Network app, you are simply being a distributed a set amount of coins per hour. Because the coins are pre-generated, your phone doesn’t do any heavy computational tasks, and power impact is minimal.
Disclaimer: The opinions on Pi Network expressed in this blog post is for general informational purposes only and are not intended to provide specific advice or recommendations for any individual or on any specific security or investment product. It is only intended to provide information on Pi Network Referral Code. In particular, this blog post is not a substitute for obtaining advice from a qualified investment advisor.
Google Pay Referral Code: pm3yp1a
Google Pay Referral
Join me on Google Pay and you’ll earn $3 when you opt in to Google Pay offers and rewards and make your first payment (min. $10)! Terms apply. Download the app and use my referral code pm3yp1a to get started. https://g.co/payinvite/pm3yp1a
Google Pay Referral Code: pm3yp1a
Actually, one can just send $10 to your family member/friend to and fro, in order to earn the cashback rewards. There are also some kind of “Huat Pals” game to be played to get additional rewards.
Google Pay Referral Reward 2021
The current referral reward for Google Pay in 2021 is $3, but there are many other cashback rewards:
- Earn $2.5 cashback on your next movie at Shaw
- Send money to friends & earn up to $10 twice a week
- Earn $2.5 cashback on your next movie at Golden Village
- Order food on Google Pay and get $2.5 cashback
- Scan to pay in stores and earn up to $10 twice a week
- Free Upsized Meals from Burger King on Google Pay
- and more…
Download the app and use my referral code pm3yp1a to get started!
https://g.co/payinvite/pm3yp1a
Payoneer Referral Link
Payoneer Referral Link: http://tracking.payoneer.com/SH2nV
Payoneer Referral Link
Payoneer Referral Link ($35 sign up bonus): http://tracking.payoneer.com/SH2nV
Payoneer is the “Israeli PayPal”, specializing in B2B online payments. Typical users include sellers/freelancers who earn on international platforms such as Amazon, Fiverr, Airbnb, and wish to transfer their USD earnings to local bank accounts.
Payoneer often has lower fees than PayPal, as well as better customer service. For instance, Payoneer has a 4.4 rating on Trustpilot, versus Paypal’s dismal 1.2 rating.
Payoneer is one of biggest tech companies in Israel. In 2019, Israel’s former chief economist of the Ministry of Finance Yoel Naveh joined Payoneer, leading Payoneer’s working capital division.
Payoneer Referral Link ($35 sign up bonus): http://tracking.payoneer.com/SH2nV
Soundtech Digital Timer Manual
Soundtech MDT-269 Manual PDF
This is one of the good automatic digital timers in the SG market. It is very suitable to use as a timer for aquarium lights.
The manual is not found online, and it is not exactly obvious how to set it without looking at the manual. Hence, we have uploaded the manual below.
Soundtech Digital Timer Manual PDF: Soundtech Timer Manual
Soundtech Mini Digital Timer Manual
Please read the following information carefully before using this timer.
• •Countdown Function
• Automatic Reminding
• Up to 20 ONIOFF settings day, 140 ON/OFF settings per week
• Summer/Winter time optional
• 24 hours and 7 day S Programming application
2 NY button- set the day of the week;
3 HOUR button – hour setting;
4 CLOCK button- real-time setting;
5 button- push and release to set or
change programmed on and off times;
6 button -push and release to
manually switch AUTO OFF, ON, AUTO
ON, or OFF at any time.
7 RESET button – clear all the programs and real time with a sharp object such as a pencil;
8 MIN button- minute setting;
9 button – clear a program setting;
10 CTD button – set the countdown tire.
LCD Display Are* Introduction:
1. Real -time;
2. MO TU Day of the week;
3. Mode -AUTO OFF, ON, AUTO ON, OFF
4. SUMMER time;
Setting Present Time:
4
1. Press ‘CLOCK’ and ‘DAY’ at the same time to get the correct day.
2. Press ‘CLOCK’ and ‘HOUR’ at the same time to adjust hour time.
3. Press ‘CLOCK’ and ‘MIN’ at the same time to set the minute.
4. Press ‘CLOCK’ for 3 seconds to choose SUMMER TIME or not. One hour will be added under SUMMER state.
Initial Operation:
The timer uses rechargeable batteries that need to be charged before the timer
functions can work. Before attempting any programming, plug the timer into a power outlet and switch on. Allow around 10 minutes for the initial charge.
Use a pointed object, such as a pen or pencil, to clear the memory by pushing the RESET button.
Countdown Setting:
I In timing state press CTD Countdown button, LCD display “countdown 0:00 00”
2 Press”HOUR””MlN”button respectivel to set countdown time.
(long press CTD Countdown button to clear the setting)
3 Press CTD Countdown button again to start the count mode and another pressing can
make it a pause. Press CLOCK button to get back to real-time state.
Note : During countdown mode, press CLOCK button to show current time and back to countdown mode in 3 secondS automatically. If press CTD Countdown button during 3 seconds, the countdown mode stop.
At the end of the countdown, the buzzer sound out. and will be stopped automatically after 1 minute. If a button is pressed during this time, the buzzer sound will stop
Programming;
1. Press SET button once, the display will now show “ON 1” mode.
2. Press respectively to set the days, hour and minute
you required. While each push of •DAY* button will cycle through the following options,
• Each separate day
• All 7 day of the week
• Working days only
• Weekend
• Monday to Saturday
• Monday, Wednesday, Friday
• Tuesday. Thursday, Saturday
• Monday, Tuesday, Wednesday
• Thursday, Friday, Saturday
3. Once the “ON’ time is set, press SET button once. The display will now
show •OFF 1′
4. If you wish to clear a programme setting, push the RST/RCL button. Pushing
the RST/RCL button again will reinstate the setting, which only the displayed
setting will be affected.
5. Repeat the step 1 to 3 for ON2/OFF2,
ON2010FF20.
If no operation is applied to the timer for about 20 seconds, it will get back to the
Real-time display automatically.
Press the MANUAL to set the timer to your desired operation mode. Each push of
this button will cycle through the following settings which are shown on the display:
AUTO ON— OFF.
AUTO OFF: Timer is switched off and will switch ON at next programmed ON time.
ON: Overrides all programming and switches the timer permanently on.
AUTO ON: The timer is switched ON and will be switched OFF at the next
programmed OFF time.
OFF: All programming is overrode and tt e time is switched permanently off.
• For indoor use only.
• Connection must be to the voltage requirements as specified in the rating label
located on the product.
• Do not immerse timer in any liquid, expose to weather, moisture, temperature
where it is too high or too low, or where it can be collided or shaken easily.
• DO not disassemble this timer by yourself.
• Clean the housing and the LCD with soft cloth, do not wash it with the corrosive chemical reagent and suds.
Converted from PDF to text via: https://ocr.space/ (This OCR free website is surprisingly good.)
7 Best article rewriter to use in 2021 [Free & Paid]
You might hear that “CONTENT IS KING” but it is only when it is unique. This content can help you to fulfill your requirements.
For instance, the students can spin the assignments when getting out of the ideas and similarly, the bloggers can spin the blog posts if found with plagiarism.
There are numerous article rewriters that are available for free over the internet but not all the rewriters are capable of having efficient working to meet your expectation.
Below, we have reviewed 10 article rewriters that are effective in spinning or rewriting your document.
1. WordAi
One of the top-ranked and most efficient article rewriters is WordAi. The WordAi is based on modern technology including artificial intelligence which makes the rewriting better.
Some of the best features of the WordAi are mentioned below:
- This article rewriter/paraphraser creates the content that is enriched in human-readable and this way, the content becomes appropriate for the SEO
- It is one of the popular tools for rewriting because it helps individuals to spin the article in bulk
- It uses artificial intelligence to find the relation between the sentences and this way, it generates the new article at its best
- It integrates the plagiarism checker “CopyScape” to directly checks the plagiarism once the article is rewritten
- Comparable to the efficiency of its working, this price of this website is quite affordable and most of the students are already using it for their assignments and thesis
There are different options for spinning your article on this tool. For example, it features the options of very readable, readable, unique, very unique.
The tool would create the content according to your selected option and there is no limitation of words on any of the options.
2. Prepostseo article rewriter
https://www.prepostseo.com/article-rewriter
Prepostseo not only offers article rewriter instead it offers several other SEO and education tools. An article rewriter is one of the famous tools that this website offers and this tool is amongst the best in the market.
The most amazing fact about this tool is that it offers free usage to all without any limitations. This is the reason why most freelancers, students, marketers, and bloggers love this website.
Below, we have mentioned some of the best features of this online tool that makes it efficient and between the top.
- The article rewriter of this website has different variations including Simple, Advance, and Beta (based on artificial intelligence)
- The artificial intelligence version of this tool is quite efficient because it generates content that is highly readable and it improves the sentence structure thus selecting a more effective selection of words
- There are different options for adding the content for rewriting including pasting the content, uploading from the device, and cloud storage (Google Drive, OneDrive)
- This article rewriter is also usable through an android article rewriter for free
- Once you rewrite an article, it will allow the user to change the selection of words by entering the word of your own or selecting the word by the suggestion of the tool
- The working of this tool is amazing as it keeps the original meaning of the writing
The article rewriter doesn’t require any registration nor it requires any subscription. This tool is accessible instantly and without any cost. The user doesn’t need to enter the details for the credit card instead they just need to open the tool and enter their text to proceed.
3. Spin Rewriter
The Spin rewriter is another amazing article rewriter that works for changing the majority of the words of a context along with the maintenance of the content.
The Spin Rewriter tool is famous because of the ELN technology which helps to offer unique content when you spin the original content.
This technology makes the spinning more efficient and meaningful. For instance, when you enter the text into the tool, it will change most of the words of the content but it will not change the actual thoughts of the content.
The Spin Rewriter is the favorite tool for marketers and businessmen. Not only this, it converts the complex sentences into a human-readable tone which makes it according to the search engine as well as easy to understand for all types of readers.
This tool is not free instead but it’s not too expensive. The plan of this tool starts from the=$47/month while you can also buy the permanent subscription by paying $495 for just a single time.
4. Chimp Rewriter (Desktop Version)
This is another amazing article rewriter tool that works based on artificial intelligence and Machine Learning. The Natural Language processing of this tool makes this tool easy to understand your writing and then convert it into a fresh copy.
The rewritten articles from this tool contain the same ideas that of the original article and this way, this tool doesn’t affect the quality of your writing. Instead, it increases the quality by selecting the best words for maintaining the meaning as well as improving the understanding of the writing.
The Chimp Rewriter supports almost all languages and this tool is popular worldwide. Whether you are willing to remove the plagiarism or you are wishing to have more effective writing, you can easily use this rewriting tool.
The tool is supportive to rewriter and along with that, you can instantly clear all the grammar mistakes in your writing.
The chimp rewriter is not a free tool nor it offers a free trial. To use this, there are two pricing plans including $15/month and $99/year.
5. Ai Article Spinner
Ai Article Spinner is another tool for rewriting and the most amazing part of this tool is that it is an entirely free tool for everyone. Whether you wish to rewrite thousands of pages, this tool will help you without spending a penny.
This tool has joined the market of artificial intelligence as they have integrated the AI-Based algorithms for making qualitative content for the original writing.
With this tool, you can easily generate content that is plagiarism-free and holds the same meaning as it had in the original context.
There are three modes of rewriting including Good, Better, and Best. This article rewriter is worth it for the bloggers and marketers because this tool features the improvement in the sentence structure.
Not only the sentence structure, but it also replaces the words with the most appropriate synonyms, and this way, it keeps the original ideas of the writing.
6. The Best Spinner 4
The Best Spinner 4 is a premium tool that offers different unique features for all types of professionals. The Best Spinner 4 have a built-in seed and PLR articles which makes it more efficient for the one that has to produce more article in less time.
It not only makes your content unique but also helps to get some high-quality pictures relevant to your article as a bonus. These pictures can be used for any purpose and you won’t face any copyright issues.
The Best Spinner 4 is best for the one that works for content production. For example, this tool also features the conversion of text to audio.
The accuracy of this spinner is quite high because it generates better revision by using the latest technology.
7. Spinner Chief
The most amazing thing about Spinner chief is the availability of an article rewriting tool for the online web version as well as for downloading on Desktop.
The most unique feature of this application is that it offers team collaboration with the help of the Team collaboration version of this tool.
With the option of importing the file into multiple formats including DOC or TXT. It also features the grammar checker along with the rewriting tool while all of the grammatical errors are cleared automatically.
For web owners, this application also features the API which can be integrated with a lot of tools or websites.
This tool also offers a free trial, as well as the newly launched version (Spinner chief 6), which is available for just $6. The premium packages are quite affordable for students and bloggers. The packages start from $175 for lifetime usage.
Buying property off plan
Obviously the prices of buying your property off plan will vary. Factors that can increase the price of your off plan property are location, the size of the property, access to local towns/cities and airports and the legal fees.The size of the property can effect the price, larger properties cost more than smaller ones to build.The location of your spanish property can effect the price that you pay. The location can effect the price of your off plan property, if it in a tourist area then it may cost more to build there however it can also generate good renting prospects as some properties in the south of spain only need to be rented out for around 18-20 weeks a year in order to cover the mortgage, that leaves you with a minimum of 32 weeks in the sun. One point you should always keep in mind when looking at the price of a property is the lawyers costs, the registration costs and the notary costs. This can range from being anywhere between 5% and 10% of the original cost of the property.
Best property in Mallorca – https://yes-mallorca-property.com/
Advantages of Buying Off Plan:
Some advantages that you can find from buying your spanish property off plan are:
That you only pay the amount that the property was valued at when you first signed the contract for example should you buy a house for €100,000 and then by the time that the property has been built it has increased in value to €130,000 you still only have to pay €100,000.
Should you change your mind about the area or the property then usually you have the option to sell your property prior to completion and the writting of the deeds (escritura). However before you sign the contract to start building your property you should ask if this service is available to you because it is not always.
Buying an off plan property is usually about 30% cheaper than buying a ready built or resale property. It is generally much simpler to buy off plan in terms of searching for the right property for you. This is because you can see straight off what the property is going to be like through arctitectual drawing unlike when you go to view a resale house they can be very diferent to what they look like in picures on the website or prospects. Also with off plan buying you have can change the aspects of the house that are not to your taste or that you had imagined to be different in your dream house.
There can be advantages to buying your property off plan but through “ready made” plans. By doing it this way you can get all the benefits of buying off plan but there is less stress placed upon you to come up with a design for your property. The downside to this is that there may well be quite a few properties that look very similar to yours. It does also mean that there should be less cost with architects because the plans are already there.
Tiger Ang Pow
Tiger Brokers has launched the Lunar New Year campaign (Tiger Ang Pow). Click on the “Open” button via the campaign page below to initiate an Ang Pow opening mission and share the 88 SGD stock voucher with friends together!
Click on “Open” button link below:
Besides, the referral promotion is also available. When your friend registers with your invitation code and opens an account successfully, both you and your friend will get 5 commission-free trades for stocks denominated in USD or HKD. When your friend makes the initial deposit, both you and your friend will get a stock voucher of up to 100 SGD.
Disclaimer: The opinions on Tiger Brokers expressed in this blog post is for general informational purposes only and are not intended to provide specific advice or recommendations for any individual or on any specific security or investment product. It is only intended to provide information on Tiger Brokers Ang Pow. In particular, this blog post is not a substitute for obtaining advice from a qualified investment advisor.
GameStop Short Interest
GameStop Short Squeeze is recently a very hot topic in the USA, and refers to the short squeeze of the stock of the American video-game retailer GameStop and other securities that took place on various stock exchanges, causing major financial consequences for certain hedge funds. It has been reported in many news outlets, including CNBC, BBC, and Reuters.
There are a few free sites to check out the GameStop current short interest, or the GameStop short interest today. Short interest is the number of shares that have been sold short but have not yet been covered or closed out. A related concept, short interest ratio, represents the number of days it takes short sellers on average to cover their positions, that is repurchase all of the borrowed shares.
GameStop Short Interest Data
- One of the sites to check out the current GameStop Short interest is:
https://isthesqueezesquoze.com/. It uses data from Ortex or S3Shortsight. - Another site is the Twitter Page of S3 Partners, which is a FinTech company. They often publish the statistics for GameStop (GME) short interest on a daily basis.
- A third source is Ihor Dusaniwsky’s Twitter Page. Ihor is the Managing Director of Predictive Analytics at S3 Partners. He posts GameStop Short Interest information on a regular basis, including some explanations to beginners.
Note that there are two ways to calculate short interest (SI):
- SI = shares shorted / (float). This value can exceed 100%.
- SI = shares shorted / (float + shares shorted). This includes the “synthetic longs” created by short selling, and will be a value between 0% to 100%.
GameStop Short Squeeze
Do also check out the Twitter Page of Michael Burry, where he posts information about GameStop Short Squeeze, GameStop Gamma Squeeze and more. Michael Burry is a famous investor and inspired the main character in the movie “The Big Short”.
Secondary 1 Chinese Exam Papers
中一华文试卷, 中一高级华文考卷
There seem to be very few Sec 1 Chinese / Higher Chinese Exam Papers available online, be it free or for sale. Similarly, Secondary 2 Chinese Exam Papers are equally rare.
The only resource online we can find is: https://padlet.com/hogtiggy/1FG_HCL
It contains Secondary 1 HCL MYE (Mid Year Exam) Revision Materials 2017, which is still relatively recent. There are also lists of Chinese vocabulary for different chapters, as well as tips for Chinese Oral Exam. Do download the PDF and Zip files while it is still online!
On the opposite spectrum, Secondary 4 ‘O’ Level Chinese or Higher Chinese Exam Papers are very common, almost every site has it, it is very easy to find.
For example, there is a 292 page PDF document on Smile Tutor full of free Secondary Four Higher Chinese Exam Papers from various schools such as Cedar, Victoria, or Nanyang Girls’ High School:
https://smiletutor.sg/wp-content/uploads/2020/10/Sec4_Higher_Chinese_2016.pdf
If you find any Secondary 1 or 2 Chinese Notes/ Exam/ Test paper materials, do comment down in the comment section below! It will help many readers who are searching for free Chinese Exam Papers (Secondary 1 or Secondary 2).
Related posts:
Ethereum in real life (Duke University is teaching Ethereum)
Ethereum has started to see many actual use cases in real life. For instance, major companies like Amazon, Microsoft, Google, Visa are all starting to adopt Ethereum as part of their real life usage.
Ethereum has started to appear in education as well. Duke University (one of the top universites in the USA), has started teaching modules of “Ethereum and Smart Contracts” as part of the syllabus.
Course description (Ethereum and Smart Contracts course in Duke University):
“Learn how to develop smart contracts and decentralized applications on the Ethereum Blockchain as well as history and trends of Ethereum itself. Ethereum is the most promising decentralized smart contract platform, and blockchain developers are in high demand. Learning these skills will give you a leg up in the blockchain world, especially in the Ethereum ecosystem. We will cover Ethereum (the platform), Solidity (the programming language), Truffle (the developer framework), and web3.js (the front-end library). Preference: some blockchain/cryptocurrency understanding. Prerequisite: basic programming skills.”
Trinity College of Arts and Sciences at Duke University
Ethereum Book
Learning blockchain technology should be a very marketable skill in the near future. Currently, there are two main ways to learn it, through online courses or through books.
Mastering Ethereum: Building Smart Contracts and DApps
The book above is authored by Dr Gavin Wood, who was the creator of the Solidity language and cofounder of Ethereum.
Ethereum Real Life Applications
Recently, the blockchain Ethereum is starting to gain widespread acceptance, many major companies such as Microsoft, Google, Amazon are already using it.
In terms of publicity, Ethereum is still behind its more famous cousin “Bitcoin”, but that should change in the near future. In fact, many people have postulated that a “flippening” may happen where Ethereum takes over Bitcoin as the cryptocurrency with the largest market cap.
In this blogpost, we list the real life applications and uses of Ethereum, using official sources as far as possible. That is, if Google is using Ethereum, we will try to point to the official Google website instead of a third party news site. Otherwise, we will only use very reliable third party sources such as Forbes, etc.
Amazon Ethereum Blockchain
This is very recent news, on Dec 21 2020. Amazon Managed Blockchain now supports Ethereum. With Amazon Managed Blockchain, AWS (Amazon Web Service) customers get secure networking, fast and reliable syncs to the Ethereum blockchain, durable elastic storage for ledger data, encryption at rest and transport, and secure access to the network via standard open-source Ethereum APIs.
Official Amazon Ethereum Blockchain news: https://aws.amazon.com/about-aws/whats-new/2020/12/amazon-managed-blockchain-supports-ethereum/
Google Cloud & Ethereum
Ethereum can inter-operate with Google Cloud’s enterprise cloud data warehouse (BigQuery) via oracle middleware (Chainlink). At a high level, Ethereum Dapps (i.e. smart contract applications) request data from Chainlink, which in turn retrieves data from a web service built with Google App Engine and BigQuery.
Official Google Cloud & Ethereum news:
https://cloud.google.com/blog/products/data-analytics/building-hybrid-blockchain-cloud-applications-with-ethereum-and-google-cloud
Ethereum Blockchain as a Service on Microsoft Azure
Microsoft and ConsenSys (a blockchain software technology company) are partnering to offer Ethereum Blockchain as a Service (EBaaS) on Microsoft Azure so Enterprise clients and developers can have a single click cloud based blockchain developer environment. The initial offering contains two tools that allow for rapid development of SmartContract based applications: Ether.Camp – An integrated developer environment, and BlockApps – a private, semi-private Ethereum blockchain environment, that can deploy into the public Ethereum environment.
Official Microsoft Ethereum news:
https://azure.microsoft.com/es-es/blog/ethereum-blockchain-as-a-service-now-on-azure/
Visa Ethereum
Visa announced it is connecting its global payments network of 60 million merchants to the U.S. Dollar Coin (USDC) developed by Circle Internet Financial on the Ethereum blockchain.
Visa didn’t quite announce it on its official Visa website, but we can see that Visa is actively recruiting engineers with Ethereum and Solidity (the programming language on Ethereum) experience.
Visa is actively recruiting engineers with Ethereum experience:
We’re seeking a strong developer experienced with Ethereum and blockchain architecture to be a part of
team tasked with building distributed application. Our ideal candidate has built and released distributed
applications, has worked with the Ripple, R3, Ethereum and/or Bitcoin blockchain, and has experience with SolidityMultiple Positions are available in Austin, TX and Foster City, CA locations
Source from Official Visa website: https://usa.visa.com/careers/job-details.jobid.743999664785893.deptid.934140.html
Ethereum JP Morgan
The Blockchain Center of Excellence at J.P. Morgan leads efforts for Distributed Ledger Technology applications, actively researching blockchain use cases to develop in-house technology and pilot solutions across lines of business within J.P. Morgan.
The program also manages strategic relationships and investments with key vendors and consortia, including Enterprise Ethereum Alliance (EEA). The Enterprise Ethereum Alliance is a member-led industry organization whose objective is to drive the use of Ethereum blockchain technology as an open-standard to empower all enterprises.
Official JP Morgan Ethereum news:
https://www.jpmorgan.com/insights/technology/blockchain
Other Ethereum use cases
A full list of companies using (or interested in using) Ethereum can actually be seen on the Enterprise Ethereum Alliance website, under the members section. We can see that many big name companies are part of the Enterprise Ethereum Alliance, including:
- Accenture
- Baidu
- Dell (Boomi)
- Ernst & Young
- Intel
- PricewaterhouseCoopers LLP
- Standard Chartered Bank
- VMware, Inc.
It is interesting to note that 2 of the “Big Four” accounting firms, Ernst & Young and PricewaterhouseCoopers are interested in Ethereum and smart contracts, which could potentially change the accounting industry.
According to Business Times Singapore, 80% of current accounting tasks will soon be done by machines, displacing humans in most junior finance roles.
Calendar 2021 Singapore
Printable Calendar 2021 Singapore
Free printable 2021 calendar Singapore available for download in the link below.
In the 2021 Monthly Calendar Singapore (printable) attached above, we see that Chinese New Year falls on 12 February, which is a Friday. Hence there is a long weekend stretching from 12 February (Friday) to 14 February (Sunday).
Another long weekend we can see in the Singapore calendar 2021 with public holidays, is the Good Friday long weekend starting on 2 April 2021 (Friday) to 4 April 2021 (Sunday).
The next long weekend is potentially the Labor Day long weekend, as can be seen in the above Singapore calendar 2021 with public holidays. Labor day (1 May 2021) falls on a Saturday, hence it is up to one’s employer to offer a day off-in-lieu.
The second last official long weekend should be the National Day public holiday, ranging from 7 August (Saturday) to 9 August (Monday).
Lastly, the last long weekend in 2021 according to the printable calendar is Christmas, ranging from 25 Dec 2021 (Saturday) to 26 Dec 2021 (Sunday), and potentially 27 Dec 2021 (Monday) if there is a off-in-lieu.
The above printable calendar is generated by Calendar Labs.
NIO ES8 Aluminium: Li Bin’s Genius Aluminum Strategy (no other country can copy NIO!)
Summary: There are only 3 countries in the world that can make more than 10 million all-aluminum Electric Vehicles per year. NIO happens to be in one of them that can make 100 million per year, and Li Bin has taken full advantage of this fact. No other country can copy NIO at a large scale since there is simply not enough aluminum (unless heavy imports are done which will further drive up the price of aluminum).
Two of the above 3 countries have to use up their entire aluminum production to achieve 10 million all-aluminum cars, which is not practical since there are other important uses for aluminum besides cars.
NIO ES8 Aluminium
NIO’s CEO Li Bin has made the genius decision for the NIO ES8 to be completely aluminum, or to be precise, the ES8 uses 96.4% aluminum, the highest percentage of aluminum used in an all-aluminum body in mass production worldwide.
The clear benefit of aluminum over steel is that it is lighter. The NIO ES8 uses an all-aluminum frame, which is about 40% lighter than traditional steel bodies (density of steel 7.8 g/cm3> aluminum 2.7 g/cm3).
With a lighter body, an all-aluminum car would be able to travel further than a steel car per unit of battery power. It is very clear that an all-aluminum car is superior to a steel car.
The NIO ES8’s body-in-white weight is 13.6% of the total vehicle weight, which is 2460 kg. That means, the weight of aluminum in one NIO ES8 car is approximately 13.6%x2460 = 335 kg.
The genius of Li Bin’s strategy is that no country can copy this all-aluminum strategy on a large scale, as shown in the calculations below. To further add to this, Li Bin must have thought and planned for this very early, well before the factory of ES8 was built.
How many All-Aluminum Cars can each Country make per year
The yearly aluminum production of each country is taken from Wikipedia: List of countries by primary aluminium production.
China produces 36,000,000,000 kg of aluminum in a year. Since one NIO ES8 contains 335 kg of aluminum, that means that:
China can make 36,000,000,000/335 = 107 million aluminum cars per year
Similar calculation for India, India produces 3,700,000,000 kg of aluminum in a year. Since one NIO ES8 contains 335 kg of aluminum, that means that:
India can make 3,700,000,000/335 = 11 million aluminum cars per year
We do the other calculations in the table below. Note that India and Russia have to use up 100% of their aluminum in order to exceed the 10 million aluminum cars target per year. Other countries cannot make more than 10 million all-aluminum cars even if they use up all their aluminum production.
| Rank | Country/Region | Aluminium Production (thousands of metric tons) | No. of Aluminum Cars per Year (millions) |
| 1 | China | 36,000 | 107 |
| 2 | India | 3,700 | 11 |
| 3 | Russia | 3,600 | 11 |
| 4 | Canada | 2,900 | 9 |
| 5 | United Arab Emirates | 2,700 | 8 |
| 6 | Australia | 1,600 | 5 |
| 7 | Bahrain | 1,400 | 4 |
| 8 | Norway | 1,300 | 4 |
| 9 | United States | 1,100 | 3 |
| 10 | Saudi Arabia | 932 | 3 |
Shaoqing Ren NIO: The Genius of Autonomous Driving
Ren Shaoqing NIO – Top Researcher in Autonomous Driving
Not many people know this, but NIO car manufacturer’s head of AI, Ren Shaoqing (任少卿) is an absolute genius in the field of autonomous driving. In this blog post, we will detail facts about Dr Ren Shaoqing and his research in self driving and autonomous driving technology. We will also introduce other top researchers in the field of autonomous driving. All our sources are from Google Scholar and other trusted sources.
Ren Shaoqing NIO – the secret weapon of NIO Autonomous Driving
Everyone knows that the main trumps of electric vehicles are clean energy, and autonomous driving. NIO has managed to hire the top researcher in the field of autonomous driving. They are quite low profile about it, not many people know about this at the moment.
Just click on the Google Scholar (Autonomous Driving) link, it will show you the full ranking of the top researchers in the field of autonomous driving, ranked by the official Google Scholar algorithm according to citation count.
Just look at the top researcher in the list, it is Dr Ren Shaoqing of NIO, with a whopping 111,396 citation count (as of Dec 2020). Citation counts are a way of measuring the impact of a researcher’s work. Basically, the more citation counts means the more people are noticing and citing the researcher’s papers. Ren Shaoqing’s citation count of 111k is typically 10 times more than a Full Professor at most universities.
In terms of quantity of citations, it is clear that Ren Shaoqing (NIO’s head of AI), is at the top of the game. How about quality of research?
Dr Ren Shaoqing’s research quality is top notch as well!
Ren Shaoqing NIO – Achievements in the field of Autonomous Driving
- First author paper at NIPS (Conference on Neural Information Processing Systems), which is one of the best conferences in computer science. The paper’s topic is “Faster R-CNN: Towards real-time object detection with region proposal networks”. Real-time object detection is very related to autonomous driving, it helps the car detect objects and obstacles in real time.
- CVPR Best Paper Award, 2016. CVPR is the premier annual computer vision event comprising the main conference and several co-located workshops and short courses. His co-authored award winning paper is titled “Deep Residual Learning for Image Recognition”.
- ImageNet Large Scale Visual Recognition Challenge (ImageNet) Competition Winner Award, 2015
- COCO Detection Challenge Winner Award, 2015
- Microsoft Research Asia Fellowship, 2014
- National Scholarship of China, 2010
In case, if anyone is thinking that Dr Ren Shaoqing is just an academic nerd with no business experience, that would be totally wrong! He has business and startup experience as well, he co-founded an autonomous driving software startup Momenta.ai, which grew into unicorn (private company with a valuation over $1 billion) in three years, aiming to help people live a better life with improved safety and efficiency of driving through artificial intelligence.
More of Ren Shaoqing’s achivements in autonomous driving and self driving can be found on his personal website.
Some of the comments on Ren Shaoqing’s personality can be found on Chinese website Zhihu (Chinese version of Quora):
这里的“年轻”除了长相上的嫩，也包括为人处世——完全没有架子。他是个很儒雅的人，手下的团队跟他也很亲近。少卿做事风格看起来不紧不慢、慢条斯理，但论及“拼”，他也是超拼。记得有一段时间，他白天一整天的时间都花在各种会、各种面试上，一直会持续到凌晨十二点之后。这时他也不着急走，而是继续干些得静下心来才能干的工作。早期他主要负责视觉感知研发方面的工作，后来负责了一段时间高速路自主巡航相关的项目，我走的时候还是在负责感知研发。
Translation:
Ren Shaoqing is a young guy, he is very humble with no airs. He is a very refined person, and his team is very close to him. Shaoqing’s style of doing things does not seem to be hurried, his style is slow and steady, but when it comes to “fighting”, he is also super persistent. I remember that there was a period of time when he spent the whole day in various meetings and interviews, which lasted until after 12am midnight. At this time, he did not leave office in a hurry, but continued to do some work that could only be done by calming down in the quiet of the night. In the early days, he was mainly responsible for the research and development of visual perception. Later, he was responsible for the projects related to autonomous driving on highways for a period of time. When I left, he was still responsible for the research and development of visual perception.
Source: https://www.zhihu.com/question/414025403/answer/1408847709
Other Top Researchers in Autonomous Driving
Other than Ren Shaoqing of NIO, there are also other genius top researchers in the field of Autonomous Driving. Interestingly, the third highly ranked researcher in Autonomous Driving (Dr Zhou Xing) is also affiliated to NIO!
We compile some of the top researchers in autonomous driving in the table and barchart below.
Top Researchers in Autonomous Driving and Computer Vision
We list 15 top researchers (with more than 1000 citations) in the field of autonomous driving and computer vision. Notice that #1 and #3 on the list are from NIO!
| Rank | Name | Citations |
| 1 | Shaoqing Ren (NIO) | 111396 |
| 2 | Andrew Blake (Samsung) | 57258 |
| 3 | Zhou Xing (NIO, Stanford) | 36267 |
| 4 | Raquel Urtasun (Uber, University of Toronto) | 34264 |
| 5 | Andrej Karpathy (Tesla) | 32692 |
| 6 | Jonathan P. How (MIT) | 31601 |
| 7 | Gang Wang (Alibaba) | 16240 |
| 8 | Uwe Franke (Daimler Mercedes-Benz) | 13485 |
| 9 | Fisher Yu (ETH Zurich) | 13150 |
| 10 | Dmitri Dolgov (Google) | 8381 |
| 11 | Markus Enzweiler (Daimler Mercedes-Benz) | 7917 |
| 12 | John M. Dolan (Carnegie Mellon University) | 7206 |
| 13 | Forrest Iandola (Tesla) | 6277 |
| 14 | Xinzhou Wu (XPENG) | 5787 |
| 15 | Tianjun Xiao (Tesla) | 2588 |
We can see from the barchart above that all 15 researchers (ranging from NIO, Tesla, XPENG) are very excellent in their field, producing research with more than 1000 citations in the field of autonomous driving or closely related fields like computer vision.
It is clear that Ren Shaoqing is one of the brightest stars in this exciting new field of Autonomous Driving!
Ren Shaoqing – the 21st Century Zhuge Liang of Autonomous Driving
Based on Ren Shaoqing’s personality (devoted and extremely hardworking 鞠躬尽瘁, but yet calm and unhurried) and achievements in autonomous driving, he bears close resemblance to a legendary character in Chinese history: Zhuge Liang.
In Chinese history or legend, Zhuge Liang was a famous military strategist and inventor. He is said to invent the first self-driving (or self-walking) cow, called the Wooden Cow Flowing Horse (木牛流马). It was said to be able to walk by itself and was used to transport grain during the Northern Expedition.
Hence, Zhuge Liang can be said to be the father of autonomous driving or self-driving, according to legend. Will Ren Shaoqing (NIO’s head of AI) become the Zhuge Liang of the 21st Century and invent the perfect autonomous self-driving car?
NIO Book
Currently, there is no NIO book available as history is still being written! We will definitely add them here if books on NIO become available. For a deeper insight into Electric Vehicles and Autonomous Vehicles, there are several great books on Amazon.
Elon Musk: Tesla, SpaceX, and the Quest for a Fantastic Future
(New York Times Bestseller!)
Autonomous Vehicles: Opportunities, Strategies and Disruptions: Updated and Expanded Second Edition
(Autonomous vehicles will change our fundamental lifestyles and create what are perhaps the most significant opportunities of this century!)
Autonomy: The Quest to Build the Driverless Car―And How It Will Reshape Our World
(Autonomous Vehicles are said to be the innovation that promises to be the most disruptive change to our way of life since the smartphone!)
NIO Car Battery Swap Videos
Interesting real life video of NIO car battery swap. Interestingly, the NIO car BaaS battery swap center in Shanghai is right next to its competitor Tesla’s Supercharger! The battery swap section is right at 8:55.
The above YouTube channel is a reliable and unbiased one, not set up specifically to promote NIO. It has been around for years, showing how the channel’s owners who are just in their 40s “retire” in Malaysia. They are currently back in Shanghai, not sure if it is permanent or just temporary to avoid the COVID situation in Malaysia.
By the way, in the video, the people are discussing how a house in Shanghai costing 6 million RMB (or almost 1 million USD) is “cheap”! This shows how rich the people in Tier 1 cities in China are, buying an electric car is no big deal for them, as long as the quality is good.
The video above is another authentic video from a real life NIO owner, performing battery swap in another Tier 1 city in China, Shenzhen. The entire battery swap process takes around 4.5 minutes, provided there is no long queue. This is just as fast or even faster than refilling petrol.
Battery swap can be considered as a moat of the company NIO. It is not easy for other car companies to suddenly switch to battery swapping since that would involve significantly redesigning their car or factory.
NIO cars can also charge the battery the conventional way, in addition to battery swapping. Another advantage of battery swapping is that older NIO car models can easily “upgrade” to a newer battery, for example from 70 kWh to 100 kWh.
Check out NIO’s CEO Li Bin launching the new 100 kWh battery in the video below, just recently in November 2020. The 100 kWh battery is on par with Tesla’s Model S.
Tesla vs NIO (NIO is the only other company to follow Tesla’s “Master Plan”)
Tesla is a famous company founded by billionaire genius Elon Musk. Elon Musk is the CEO and founder of multiple high-tech companies such as Tesla, SpaceX and Open AI.
It is highly recommended for gifted kids and parents to read about Elon Musk and his unique childhood and personal traits. Currently, there is a promotion where you can listen to the bestselling audiobook free if you Try Audible Plus
Elon Musk: Tesla, SpaceX, and the Quest for a Fantastic Future
NIO vs Tesla
Firstly, we introduce the founder of NIO, Li Bin, as a comparison to Tesla’s Elon Musk. Li Bin was born in a poor cow farmer’s household in Anhui, China. His home did not have electricity until he was around 10 years old. His brilliance was noticed early in life, where he emerged the top scholar in the Anhui province in the Gaokao exams and entered the best university in China, Peking University. In Peking University, he majored in sociology, and minored in law and computer science.
Before NIO, Li Bin has founded or cofounded multiple successful companies, including:
- Bitauto (易车), a leading provider of internet content & marketing services, and transaction services for China’s automotive industry.
- MoBike, a bike sharing platform in China.
Under Li Bin, NIO is the only other EV company to follow Elon Musk’s tried and tested Master Plan:
Tesla’s “master plan”, as iterated by Musk in 2006 was: Build sports car. Use that money to build an affordable car. Use that money to build an even more affordable car. While doing above, also provide zero-emission electric power generation options.
Source: Wikipedia
NIO EP9
The first step of Tesla’s “master plan” is to build a sports car. NIO has already built the EP9 car which is one of the world’s fastest supercar. It has broken multiple records, and can reach a top speed of 350 km/h.
NIO EC6
True to the “Master Plan”, NIO has next built more affordable cars, such as the latest NIO EC6. The EC6 is a fully-electric mid-size luxury crossover SUV, just announced in late 2019 by NIO.
NIO vs Tesla China
NIO is initially aiming for a share in China’s enormous EV (Electric Vehicle) market, which is the world’s biggest market for EVs. Subsequently, it has plans to expand into Europe and the rest of the world.
NIO does not have its own factory currently (it has a joint factory with the state-owned JAC Motors in Hefei). This may change in the future. The JAC-NIO factory is impressive, and has up to 97.5% automation rate. Note that Apple also doesn’t have its own factory, hence not having a factory can’t be said to be a fatal flaw of NIO.
NIO Future Plan and Potential
NIO’s future plan is to produce more models of cars, including two sedans (ET5 and ET7), as well as a minivan (EF9) and another SUV (ES7).
NIO focuses a lot on good service, and provides several unique services, most notably BaaS (Battery as a Service). BaaS allows NIO cars to swap their batteries, which is currently much faster than charging. In addition, most Asian countries, including top tier cities in China, simply do not have enough space for a charging station for each household. Hence, BaaS will be a great differentiating factor which gives NIO an edge over its competitors.
As for NIO’s potential, just watch this video on top 30 most industrialized countries in the world. NIO is the premier high end electric vehicle manufacturer in China, and all signs are pointing to it having a great potential in the future (if things go smoothly).
NIO Moat
A moat is a key competitive advantage that sets a company apart from its competitors. NIO’s first moat is its unique BaaS. Since a car’s model cannot easily change (due to the factories’ fixed specification), should BaaS battery swapping become the trend, NIO will be the sole company that provides it and will have at least a few years’ lead ahead of its competitors.
NIO’s second moat is its infrastructure and domestic home ground advantage. NIO’s autonomous driving system is naturally trained in China’s traffic conditions. Even in the event of slightly inferior autonomous driving technology (which is still highly debatable), the end result would still be better than a top driving system trained in another country’s very different traffic conditions, including different driver behavior and different road signs.
NIO backed by government
Many signs have shown directly or indirectly that NIO is backed by the government. Firstly, JAC Motors with whom NIO has a joint factory with, is a Chinese state-owned automobile and commercial vehicle manufacturer.
Secondly, NIO is the first car company to cooperate with State Grid EV service to build 100 charging and battery swap stations by 2021. This is good news for NIO since the State Grid EV being owned by the State/government has good potential to select excellent locations for the battery swap stations which will further strengthen’s NIO’s BaaS network.
Chinese 3AD Arithmetics 东晋. 刘徽 《九章算术》更相减损术
Please explain the Number Theory behind this trick :$latex boxed{frac {a } {b}= frac {frac {a}{b-a}}{frac {b}{b-a}}} &fg=aa0000&s=4$
Example: $latex 246 – 205 = 41$
$latex boxed {frac {205} {246}= frac {frac {205}{41}}{frac {246}{41}}=frac{5}{6}&fg=0000aa&s=3}$
…
Example:
27759 – 10227 = 17532 = 2 x 8766 = 2 x (2 x 4383) = 2 x 2 x (3 x 1461) = 2 x 2 x 3 x (3 x 487 )
$latex boxed {frac {10227} {27759}= frac {frac {10227}{1461}}{frac {27759}{1461}}=frac{7}{19}&fg=00aa00&s=3}$
Explanation:This method is from《九章算术》295AD 刘徽（曹魏/东晋），he invented the “Limit” 割圆法 method with 95-polygons to get the world’s best pi = 3.1416
https://zhidao.baidu.com/question/109475024.html
更相减损术证明：
Bézout’s Theorem :
For a, b CO-PRIME, ie gcd (a, b) = 1
There exist integersxandysuch thatax+by= 1
DBS Multiplier Interest Rate Changes
DBS Multiplier Changes
DBS Multiplier has officially announced some changes, effective 1 January 2021. Do check out the official PDF document here.
We also attach the screenshot below for the reader’s convenience.
DBS Multiplier Review
Well, it is clear that the DBS Multiplier changes are not good! Most of the interest rates are heavily affected, especially for the average Singaporean saver. This is not unique to DBS though, most banks in Singapore have slashed their interest rates, including Citibank, CIMB, and others.
For savers who have less than 3 categories transactions (Credit Card Spend, Home Loan Instalments, Insurance or Investments), most likely his/her interest rate will drop to below 1% p.a. This is a halving of the previous interest rate.
DBS Multiplier Minimum Balance
Note that DBS Multiplier has a relatively high minimum balance of S$3,000, and there is a service charge of S$5 if average daily balance falls below S$3,000.
DBS Multiplier Alternative
If you are looking for an alternative to DBS Multiplier, do check out our previous blog post Gigantiq Promo Code: MATH88. Basically, Gigantiq is a capital guaranteed savings plan that offers interest rate of 1.8% p.a. (previously 2% p.a.). This is much higher than all banks currently, including fixed deposits. Gigantiq is backed by Etiqa, which is the insurance branch of Maybank, the largest bank in Malaysia.
【数学科普】：函数概念的四重境界 Bourbaki Definition of “Function”
为啥法国数学这么强，平民的算数这么烂 ？
结账的算数：€ 313.5
华人：[给] €323.5 – [找] €10 ＝€313.5
法国人: [给] €320 – [找] ？＝€ 313.5
{? ＝€ 6.5 是这样算的 ：313.5+0.5 [凑整]＝314.0, 然后 314＋6＝320，得[找] 0.5＋6 ＝6.5}
Proof Pi Irrational
“这个人”并不存在，但他却是20世纪最伟大的数学家之 – Bourbaki
Geometry Proof : Sum of Squares
Spyder Typing Delay
Recently, the Spyder IDE faced serious typing delay or lag. Basically, after entering something using the keyboard, it takes almost half a second for it to appear on the screen. The issue can also be described as a typing lag in Spyder.
This seems to have been triggered by the installation of Big Sur OS.
Spyder slow on Mac
After intensive googling, we stumbled upon this Github page detailing several possible solutions.
The one that worked for us was installing pyqt and pyqtwebengine. Basically, type the following commands in the terminal:
pip install PyQt5 pip install PyQtWebEngine
The above solution should be very safe since it is just installing Python packages.
Spyder lagging
The above solution helped to solve the troubling issue of Spyder lagging. Since Spyder uses Qt for its GUI, it is critical to keep the various Qt related packages updated / at the correct version. This may be the reason why installing PyQt5 and PyQtWebEngine helps to remove the lag in Spyder.
Spyder very slow
There seems to be many reasons, other than the above, that can result in Spyder being very slow. One tip that is useful, is never update to the latest version of Spyder, Mac OS, or Anaconda immediately once it is released, unless it is absolutely necessary. Most of the bugs appear in the newest releases, and can cause multiple problems including making Spyder very slow. By updating at a later date, most of the bugs would have been solved by then and it is a much safer approach.
Previously, updating to the latest Spyder 4.1.5 also caused several problems, including lag, slowness or even Spyder simply just crashing.
My All 2020 Mathematics A to Z: Wronskian
Great interesting post on Wronskian, which is widely used in the study of differential equations. Wronski is an eccentric genius, who was once forced to leave his post at the Marseille Observatory after his theories were dismissed as “grandiose rubbish”, according to Wikipedia.
Today’s is another topic suggested by Mr Wu, author of the Singapore Maths Tuition blog. The Wronskian is named for Jzef Maria Hone-Wroński, a Polish mathematician, born in 1778. He served in General Tadeusz Kosciuszko’s army in the 1794 Kosciuszko Uprising. After being captured and forced to serve in the Russian army, he moved to France. He kicked around Western Europe and its mathematical and scientific circles. I’d like to say this was all creative and insightful, but, well. Wikipedia describes him trying to build a perpetual motion machine. Trying to square the circle (also impossible). Building a machine to predict the future. The St Andrews mathematical biography notes his writing a summary of “the general solution of the fifth degree [polynomial] equation”. This doesn’t exist.
Both sources, though, admit that for all that he got wrong, there were flashes of insight and brilliance in his work. The St Andrews…
View original post 1,534 more words
What happens if you fail PSLE?
The PSLE (Primary School Leaving Examination) is a momentous event in the Singapore education system, where all Primary 6 (12 year old students) sit for the national exam that will determine their future secondary school (or even beyond, in the case of Integrated Programme).
PSLE is not everything
Despite the overall importance of PSLE, it has to be noted that PSLE is not everything. There are countless stories of late developers who later pursued successful careers, despite a bad PSLE Score.
Read about the miracle story of a student who scored 181 for PSLE (technically still a pass grade, but considered not so good), but later entered NUS Medicine, the most prestigious course in Singapore.
PSLE fail go where?
This seems to be a frequently asked question. There are still many options, one of them is NorthLight School, which was featured in the Straits Times. NorthLight School is a specialized school that takes in students who fail their PSLE. Each year, the intake of NorthLight School is around 200 students.
In 2009, Assumption Pathway School was also set up to take in students who fail PSLE, ensuring that students have a place to go to further their education.
After graduating from NorthLight School or Assumption Pathway School, around 45% of students go on to enter Institutes of Technical Education (ITE). After that, they can move on to Polytechnics.
What happens if you fail one subject in PSLE?
Unlike O levels, where there are quite severe consequences for failing critical subjects like ‘O’ level English or Maths, there is no penalty specifically for failing a certain PSLE subject.
According to experienced parents at Kiasuparents, the only problem of failing one subject in PSLE is that it will drag down the overall PSLE T-score. It has been estimated that failing one subject in PSLE would most likely cause the overall score to be below 200 (which can still enter many neighborhood secondary schools).
PSLE takes into account all 4 subjects. So even if you failed English or Chinese or any subject, it doesn’t matter. what matters is your combined score that determine whether you go express or normal academic.
Source: Kiasuparents
Hence, if the student does well for other subjects, it is not a big problem for failing one subject in PSLE, be it failing PSLE English, failing PSLE Chinese, or failing PSLE Math.
Bad PSLE results
It is actually quite rare to fail PSLE outright (around 98.4% of students pass and make it to secondary school). However, it is quite common to get a ‘bad’ PSLE results or a lower score than one expects.
When one gets a bad PSLE result, or fail PSLE (one or all subjects), the important thing for the student is not to get overly disheartened. It could well be the case that the student is a late developer, or that certain negative events out of the student’s control have impacted the student’s family, which resulted in the bad PSLE results.
Do check out this other inspirational story, of a student who scored 105 for PSLE, but later graduated from NUS with a Master of Architecture degree. The important thing is not PSLE grades (PSLE is not everything), but rather the character traits of a student such as being determined and hardworking.
Related posts:
PSLE 2020 Results and PSLE Cut Off Point 2020
The 2020 Primary School Leaving Examination (PSLE) results will be announced on 25 November 2020 (Wed). Given the ongoing COVID-19 situation, students will receive their results from their respective primary schools – in their individual classrooms instead of gathered as a cohort in the school hall – from 11.00am on 25 November 2020.
Source: MOE Website
PSLE 2020, 2021 Cut off point
The exact cut off point is not out yet, but based on previous years’ cut off points, we give some estimates of the PSLE 2020 Cut off point (for entry to secondary school in 2021).
IP schools cut-off point
The most popular schools are definitely the IP (Integrated Programme) schools, since they are the most prestigious, and also students get to skip the O Levels which is a major source of stress for the students and their parents.
IB schools are also very popular, since it is well known that the IB syllabus is easier to score than the ‘A’ levels.
‘S’ Tier IP Schools PSLE Cut off point
The ‘S’ Tier IP and IB schools are:
- Hwa Chong Institution
- Raffles Girls’ School (Secondary)
- Methodist Girls’ School (Secondary)
- Nanyang Girls’ High School
- Raffles Institution
These are the top elite schools in Singapore. MGS (Methodist Girls’ School) COP has risen to this level in recent years, while HCI, RGS, RI, NYGH are the traditional top 4 secondary schools. In order to have a secure chance of entering these schools, the estimated COP or cut-off point is around 260, not considering affiliation. In certain years, a high 250s score such as 258 or 259 may also suffice, but it is quite risky.
‘A’ Tier Secondary School PSLE Cut-off point 2020
The ‘A’ Tier top secondary schools are:
- Dunman High School (IP)
- National Junior College (IP)
- CHIJ St. Nicholas Girls’ School (IP)
- Anglo-Chinese School (Independent) (IB)
- Catholic High School (IP)
- Cedar Girls’ Secondary School (IP)
These schools are very close to the ‘S’ Tier elite schools mentioned above. For these schools, traditionally, a score of around 255 and above is the usual COP or cut off point.
Note that some of the above good schools also have an ‘O’ level track whose COP (Cut-off point) is typically around 5 points lower, or around 250.
PSLE Express Cut off point 2020
Historically, the PSLE cut off point for express stream is around 188. For example, the following schools (express stream) have their PSLE cut-off point set at 188, for the 2020 secondary school intake:
- Assumption English School
- Bartley Secondary School
- Bedok Green Secondary School
- Bendemeer Secondary School
- Boon Lay Secondary School
- … and many more, all the way to Yuhua Secondary School and Yuying Secondary School.
Read our previous blog post on the frequently asked question of: Express vs Normal Academic for borderline PSLE score.
Money Saving “Lobang” (Tips):
- Save up to 30% of your electricity bill by switching to Ohm!
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My All 2020 Mathematics A to Z: Velocity
V for Velocity! Excellent exposition on velocity, and especially on phase space by Nebus Research blog.
I’m happy to be back with long-form pieces. This week’s is another topic suggested by Mr Wu, of the Singapore Maths Tuition blog.
Art by Thomas K Dye, creator of the web comics Projection Edge, Newshounds, Infinity Refugees, and Something Happens. He’s on Twitter as @projectionedge. You can get to read Projection Edge six months early by subscribing to his Patreon.
Velocity.
This is easy. The velocity is the first derivative of the position. First derivative with respect to time, if you must know. That hardly needed an extra week to write.
Yes, there’s more. There is always more. Velocity is important by itself. It’s also important for guiding us into new ideas. There are many. One idea is that it’s often the first good example of vectors. Many things can be vectors, as mathematicians see them. But the ones we think of most…
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What Are the Best Online Math Tutoring Websites?
What Are the Best Online Math Tutoring Websites?
Many people find math to be a difficult subject to excel in as compared to any other subject. However, it is not the case at all. Math only needs one to have a positive attitude, an excellent tutor, and lots of practice. It is quite an interesting subject to learn and proves to be handy on many different occasions.
Looking for a tutor online to help you figure out your math problems can be quite a daunting task. It is relatively easy to get the wrong service provider when you need to find help for your child. You need to check the best online math tutoring websites, which will help you find the best services online for your child or student. It is quite common to find a service provider who will not give you the value you desire online. It would help if you took into account reviews, which will guide you to make the best decision.
The Best Online Math Tutoring Websites
Here is a list of the best available math tutoring websites online:
1. Princeton Review
The Princeton Review is recognized as one of the best platforms in the tutoring arena. The platform does not only provide tutoring services but also helps with the completion of the assignment. The service providers offer students different options during the signing up process. There is a one-time option available that grants students tutoring over a period of time and a monthly subscription.
For students who require regular tutoring, the monthly subscription costs $40 per hour, $80 per two hours, and $115 per three hours. If you would like a more flexible schedule, you can opt to pay $350 for 10 hours or $950 for 30 hours.
2. Chegg
This is an excellent site for math tutoring services as the services are available 24 hours. The student is automatically matched with the suitable instructor after keying in the problems they have. The user can opt for a live class, text, or audio.
For an off-chat lesson, the class costs $11 and $20 for unlimited chat lessons for a month. For those who would like a video call subscription, they will pay $30 for a month. You should also check out Math videos on YouTube to help you learn more and faster.
3. Learn To Be
This is an NGO based site that aims to provide equal opportunities to all students. Students fill in an application and detail the issues they need assistance with. Within seven days, the site will reach out to the student with a suitable tutor to arrange an online meeting.
This is a great service provider as it does not cost the student anything. A portion of the money donated to the site is responsible for helping students access algebra tutoring services or paying the tutors.
4. Revolution Prep
It is quite famous for having tutors available for most of the day. The site uses highly interactive sessions to teach students math. They aim to make the subject fun to develop a positive attitude towards the subject. The sessions incorporate flashcards, posters, and other tools.
The tutoring services cost about $1398 for every 12 hours, and their group sessions cost $499 for 12 hours. Each group has four to eight people.
5. Prodigy
This is an exceptional site if you prefer a one-on-one session with your tutor. The site offers different levels of maths by tutors who are suitable for your needs. The company’s goal is to enable each student to achieve their highest potential.
The site charges £30 per half an hour, and it’s discounted to $24 if you pay for three classes or more. You can also opt to pay for five classes at $120. During each first session, the tutor, parent/teacher, and the student discuss the service’s goals.
Conclusion
Math is quite a phenomenal subject to study that can lead to a very prospectus life. There are plenty of options available to choose from when it comes to studying the issue. There are online group classes, individual tutoring, and even in-person course. The available platforms, schedule, optimal studying style, and budget will influence which platform you will use. The list above will guide you in selecting the best service providers so you can be the math guru you were meant to be.
Function Continuous =>? Differentiable
【高等数学】变限积分与变量分离
This young Chinese Math student is quite rigorous :
Given f(x) CONTINOUS function,
Is it wrong to f'(x) right away?
Differential Theorem
Differential Theorem
If f differentiable at point a => f continuous at point a
Converse not true !
‘Differentiability’ stronger than ‘Continuity’
Are all Continuous functions Differentiable ? False!
Counter-example (by Weierstrass):
$Latex f(x)=Sigma{b^n}cos(a^npi x)$ n ∈[0,8], a= odd number, b∈[0,1], ab > 1+3Π/2
f(x) Continuous everywhere (cosine), but non-differentiable everywhere!
Note: Weierstrass Function is the first known fractal. (e.g. Snowflake Koch’s curve).
Plot of Weierstrass Function (Photo credit: Wikipedia)
Note: What it means a curve (function) is :
1. Continuous = not broken curve
2. Differentiable = no pointed ‘V‘ or ‘W‘ shape curve
吴军《数学之美》：数学模型帮您实现认知跨越
20CE 中学数学教育 (陈建功)
20世纪（1950s -1970s）的中国数学教育改革是迎合WW2 战后工业化, 影响我们中学数学 Secondary School Math (13-18 岁) 。
21世纪 (2000s – 2030s) 迎合的是 工业 4.0 (AI, Big Data, IoT, Fintech… )，中学数学改革 是什么呢？
陈建功 (1893-1971) 和 师弟 苏步青是二战前 留学日本派的数学教育家 （微分几何），建立浙江大学和复旦大学数学系 – 与 陈省身 的 留法/德/美 “南开”派，华罗庚的留英/俄 “清华” 派 三派鼎立，融合成特有的 中国数学派 。
这三本数学（中三/中四）书是我们 70s年代 新加坡华文中学的课本 (文言文) ：
- 欧氏几何 (Euclidean Geometry)
- 范氏大代数 (Henry Fine ［*］ Algebra)
- 葛氏平面三角 (Granville Trigonometry ［＃］)
Note ［*］: Henry Fine was the Founder of the Princeton Institute of Advanced Study (IAS) , who hired the first professor – Albert Einstein.
［＃］This 《葛氏平面三角》(Granville Trigonometry) text book was arcane and translated in ‘old’ Chinese (文言文).
Jewish / French Math vs German Math
The French “Bourbaki” School of Abstract Math (based on Set Theory as Foundation of ALL Math) influenced the…
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日本战后数学教育家 远山启
远山启：用数学照亮人性与自由
日本战后的＂新＂数学：把抽象化转成 平易化。出了一群 Fields Medalists, 数学教育家 (这位 远山启，Shimura, ), 科普作家 结城浩 (《Math Girls》Series : Galois Theory, Fermat’s Last Theorem, etc. )…
Mathtuition88 