Mathtuition88

Prime Numbers since Euclid 2300 years ago remains a mystery today…

Riemann’s Hypothesis is the Top Conjecture Unsolved in 21st Century.

https://theconversation.com/why-prime-numbers-still-fascinate-mathematicians-2-300-years-later-92484

Free Money from PayLah (Quick! Before it is fully redeemed)

Hey! You can get S$5 when you register for PayLah! with my Referral Code WILDOF087 (last 3 digits are numbers zero-eight-seven) by 31 December 2018. Download PayLah! from http://www.dbs.com.sg/paylah now and enter the above Code during sign-up before this offer is fully redeemed. T&Cs apply.–

PayLah! can be downloaded from Apple Store or Android store (Singapore). Getting your $5 should be instantaneous. Be sure to redeem it today since there is a cap of 40000 people who can redeem. (The offer is still available now, but who knows next week it may be fully redeemed.)

110 Nanyang Girls’ High students fall sick during boarding school programme

Quite worrying. Based on my personal experience and online research, food in Singapore cannot be left in room temperature for more than 4 hours, due to our hot and humid temperature. To be safe, food needs to be put in the refrigerator as soon as possible if not consumed immediately.

Hope all affected students get well soon.

Source: 110 Nanyang Girls’ High students fall sick during boarding school programme
Read more at https://www.channelnewsasia.com/news/singapore/110-nanyang-girls-high-students-sick-boarding-school-programme-10097196

Second Order Linear ODE Summary

Second Order Linear D.E. Summary

Homogenous D.E.
$y''+ay'+by=0$ .

Solve the Characteristic Equation: $\lambda^2+a\lambda+b=0$ .
Case 1) Two real roots $\lambda_1,\lambda_2$ : $\implies \boxed{y=c_1e^{\lambda_1x}+c_2e^{\lambda_2x}}$

Case 2) Real double root $\lambda$ : $\implies \boxed{y=c_1e^{\lambda x}+c_2xe^{\lambda x}}$

Case 3) Complex Conjugate root $\lambda_1,\lambda_2=-\frac{a}{2}\pm iw$ , where $w=\sqrt{b-\frac{a^2}{4}}$ : $\implies \boxed{y=e^{-\frac{a}{2}x}(c_1\cos wx+c_2\sin wx)}$

Non-homogenous D.E.
General solution of non-homogenous D.E.: $\displaystyle y=y_h+y_p,$ where $y_h$ is the general solution of the homogenous equation, and $y_p$ is the particular solution (with no arbitrary constants).

Method of Undetermined Coefficients (Guess and try method)
$y''+p(x)y'+q(x)y=r(x)$ .

Only works if $r(x)$ is polynomial, exponential, sine or cosine (or sum/product of these).

Polynomial: Try $y$ =Polynomial (e.g. $y=Ax^2+Bx+C$ or $y=Bx+C$ .)

Exponential ( $e^{kx}$ ): Try $y=ue^{kx}$ , where $u$ is a function of $x$ .

Trigonometric ( $\sin kx$ or $\cos kx$ ): Convert to complex differential equation by replacing $y$ with $z$ , replace $\sin kx$ / $\cos kx$ by $e^{ikx}$ .

Try $z=ue^{ikx}$ , where $u$ is a function of $x$ . After solving for $z$ , take real/imaginary part of $z$ for cosine/sine respectively.

Method of variation of parameters
$y''+p(x)y'+q(x)y=r(x)$ .

[Step 1)] Solve the homogenous D.E. $y''+p(x)y'+q(x)y=0$ .

Get solution of the form $y_h=c_1y_1+c_2y_2$ .

[Step 2)]
Let $\displaystyle u=-\int\frac{y_2r}{W}\,dx$ and $\displaystyle v=\int\frac{y_1r}{W}\,dx$ where $W$ is the Wronskian $\displaystyle W=y_1y_2'-y_1'y_2.$

Particular solution: $y_p=uy_1+vy_2$ .

General solution: $y=y_h+y_p$ .

Forced Oscillations
Let $F_0$ be the amplitude of the driving (external) force. If $F_0=0$ , by Newton’s Second Law, $m\ddot{x}=-kx$ , hence $\displaystyle \boxed{\ddot{x}=-\omega^2 x},$
where $\omega=\sqrt{k/m}$ . The value $\omega$ is called the natural frequency.

If $F_0\neq 0$ , then $\displaystyle \boxed{m\ddot{x}+kx=F_0\cos\alpha t},$
where $\alpha$ is the driving (external) frequency.

At resonance (when $\alpha=\omega$ ), $\displaystyle \boxed{x=\frac{F_0t}{2m\omega}\sin(\omega t)}.$

Joseph Fourier is Still Transforming Science

Math Online Tom Circle

Key Words: 250 years anniversary

Yesterdays: Fourier discovered Heat is a wave , Fourier Series, Fourier Transformation, Signal processing…
Today: IT imaging JPEG compression, Wavelets, 3G/4G Telecommunications, Gravitational waves …
Friends / bosses: Napoleon, Monge… Egypt Expedition with Napoleon Army.
Taught at the newly established Military Engineering University “Ecole Polytechnique”.
Scientific Research: Short period but intense.
Before Fourier died (wrapped himself in thick carpet in hot summer), he was reviewing another young Math genius Evariste Galois’s paper on “Group Theory”.

https://news.cnrs.fr/articles/joseph-fourier-is-still-transforming-science

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10 Things You Don’t Know About Albert Einstein

Source: Thoughtco

Some of the 10 facts are:

He Loved to Sail
Einstein’s Brain
Einstein and the Violin
Presidency of Israel

For those interested in the theory of relativity (special and general), which is the main core of Einstein’s research, do check out this book Relativity: The Special and the General Theory, 100th Anniversary Edition. Highly rated on Amazon, it is one of the few books that tells the story of Einstein and also includes real scientific content.

Drawing Chemistry Diagrams in LaTeX

The web application “mol2chemfig” is very amazing. (http://py-chemist.com/mol_2_chemfig).

Especially the search function, where one can just type the name of the chemical and out comes the chemfig code where it can be pasted to LaTeX. The mol2chemfig package needs to be imported in LaTeX before the code can be compiled. Alternatively, one can just save the PDF image (vector graphics) generated by the web app.

Below is a screenshot of what is happening:

Linear First Order ODE, Bernoulli Equations and Applications

Linear First Order ODE
DE of the form: $y'+P(x)y=Q(x)$ .

Integrating factor: $R(x)=e^{\int P(x)\,dx}$ .
$\begin{aligned} R'&=RP\\ Ry'+RPy&=RQ\\ (Ry)'&=RQ\\ Ry&=\int RQ\,dx \end{aligned}$
$\displaystyle \boxed{y=\frac{\int RQ\,dx}{R}}$
(Remember to have a constant $C$ when integrating the numerator $\int RQ\,dx$ .)

Integration by parts
$\displaystyle \boxed{\int uv'\,dx=uv-\int u'v\,dx}$

Acronym: LIATE (Log, Inverse Trig., Algebraic, Trig., Exponential), where L is the best choice for $u$ . (This is only a rough guideline.)

Bernoulli Equations
DE of the form: $y'+p(x)y=q(x)y^n$ .

$y^{-n}y'+y^{1-n}p(x)=q(x)$

Set $\boxed{y^{1-n}=z}$ .

Then $(1-n)y^{-n}y'=z'$ . The given DE becomes
$\displaystyle \boxed{z'+(1-n)p(x)z=(1-n)q(x)}.$

Fundamental Theorem of Calculus (FTC)
Part 1: $\displaystyle \frac{d}{dx}\int_a^x f(t)\,dt=f(x)$

Part 2: $\displaystyle \int_a^b F'(t)\,dt=F(b)-F(a)$

Hyperbolic Functions
$\begin{aligned} \sinh x&=\frac{e^x-e^{-x}}{2}\\ \cosh x&=\frac{e^x+e^{-x}}{2}\\ \cosh^2 x-\sinh^2 x&=1\\ \end{aligned}$
$\begin{aligned} \frac{d}{dx}\sinh x&=\cosh x\\ \frac{d}{dx}\cosh x&=\sinh x\\ \frac{d}{dx}\sinh^{-1}x&=\frac{1}{\sqrt{x^2+1}}\\ \frac{d}{dx}\cosh^{-1}x&=\frac{1}{\sqrt{x^2-1}} \end{aligned}$
$\displaystyle \int \tanh(ax)\,dx=\frac{1}{a}\ln(\cosh(ax))+C.$

Uranium-Thorium Dating
Starting Equations:
$\displaystyle \begin{cases} \frac{dU}{dt}=-k_U U\implies U=U_0e^{-k_Ut}\\ \frac{dT}{dt}=k_UU-k_TT. \end{cases}$

$\frac{dT}{dt}+k_T T=k_U U_0e^{-k_Ut}$

$R=e^{\int k_T}=e^{k_T t}$ .

$\displaystyle \boxed{T(t)=\frac{k_U}{k_T-k_U}U_0(e^{-k_Ut}-e^{-k_Tt})}$

$\displaystyle \boxed{\frac{T}{U}=\frac{k_U}{k_T-k_U}[1-e^{(k_U-k_T)t}]}$

Louis-Le-Grand, un lycée d’élite 法国(巴黎)精英学校: 路易大帝中学

Math Online Tom Circle

Lycée Louis-Le-Grand is the best high school (lycée) for Math in France – if not in the world – it produced many world-class mathematicians, among them “the Father of Modern Math” in 19th century the genius Evariste Galois. (See also: Unknown Math Teacher produced two World’s Math Grand Master Students ), Molière, Victor Hugo, 3 French Presidents, etc.

Its Baccalaureat (A-level) result 100% passed with 75% scoring distinctions. Each year 1/4 of Ecole Polytechnique (France Top Engineering Grande Ecole) students come from here.

More surprisingly, the “Seconde” (Secondary 4) students learn Chinese Math since 6ème (PSLE Primary 6).

Note: Louis Le Grand (= Louis 14th). He sent the Jesuits (天主教的一支: 耶稣会传教士) as the “French King’s Mathematicians”(eg. Bouvet 白晋) to the 16-year-old Chinese Emperor (康熙) KangXi’s Court.

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How to draw polygons with angles (LaTeX Tikz)

Just learnt some amazing angle-drawing techniques using LaTeX Tikz.

Although cumbersome to code, the benefit of using LaTeX to draw diagrams is that it matches the font of your document, and is easier to customize and edit. Also, it is “vector graphics” in the sense that even if you zoom in, it is in perfect resolution.

Important: In order to use Tikz to draw angles you need to load the following packages:

\usepackage{tikz}
\usetikzlibrary{calc,patterns,angles,quotes}

Sample Tikz code for drawing the above figure (polygon angles)

\begin{figure}[htbp]
\begin{center}
\begin{tikzpicture}
\coordinate (v0) at (-2.2,1.2);
\coordinate (v1) at (0,0);
\coordinate (v2) at (2.2,1.8);
\coordinate (v3) at (0,3);

\filldraw
(v1) circle (2pt) node[align=left, below] {$v_1$}
-- (v2) circle (2pt) node[align=center, below, right] {$v_2$}
-- (v3) circle (2pt) node[align=left, above] {$v_3$}
-- (v0) circle (2pt) node[align=left, above, left] {$v_0$}
-- (v1);
\pic [draw, -, "$\alpha_0$", angle eccentricity=1.5] {angle = v1--v0--v3};
\pic [draw, -, "$\alpha_1$", angle eccentricity=1.5] {angle = v2--v1--v0};
\pic [draw, -, "$\alpha_2$", angle eccentricity=1.5] {angle = v3--v2--v1};
\pic [draw, -, "$\alpha_3$", angle eccentricity=1.5] {angle = v0--v3--v2};
\end{tikzpicture}
\caption{}
\label{fig:quad}
\end{center}
\end{figure}

Clearly, the code can be modified for any polygon be it triangle, pentagon, etc. Also, if you are curious how to post source code in WordPress.com, it is by surrounding your source code with [ code ] [/ code]. It also supports a “lang=” option, see more at https://en.support.wordpress.com/code/posting-source-code/.

Bukit Batok / Hillview Maths Tuition

Please contact us for one-to-one Maths Tuition at Bukit Batok / Hillview area.

Nearby areas such as Clementi / Jurong East are also suitable.

Patient and dedicated Maths Tutor.

Senior Wrangler: Singapore Prime Minister

Math Online Tom Circle

Senior Wrangler is the First position in the Math Tripos in Cambridge. Singapore Prime Minister Lee Hsien Loong was the Senior Wrangler in 1973, the first Singaporean student with such great honors, among other senior wranglers like Arthur Cayley (Group Theory), J.J. Sylvester (Inventor of Matrix, private tuitor of the “inventor of Nursing” Florence Nightingale), J.E. Littlewood (partnered in a twin research team with G.H. Hardy), Frank Ramsey (Ramsey’s Theorem), Stokes, Pell, etc.

Some great mathematicians like Bertrand Russell (Logician, Nobel Litterature Prize) , G.H. Hardy (20th century greatest Pure Mathematician, mentored 2 geniuses: Indian Ramanujian and Chinese Hua Luogeng 华罗庚*) were not Senior Wrangler. Prof Hardy hated Math Tripos syllabus (revealed in his autobiography: “A Mathematician’s Apology“).

1914 Brian Charles Molony
1923 Frank Ramsey
1928 Donald Coxeter
1930 Jacob Bronowski
1939 James Wilkinson
1940 Hermann Bondi
1952 John Polkinghorne
1953 Crispin Nash-Williams
1959 Jayant Narlikar
1970 Derek…

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Topological Data Analysis

Math Online Tom Circle

Three Key Ideas:

Cloud of Points
Filter function: f (x,y,z) –> x
Cluster: Overlapping bins
Draw network:

Vertices: clusters
Edges: connecting lines between clusters.

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Crash course in Category Theory

Math Online Tom Circle

Key Point:

Haskell & any FP compiler don’t check the Category Theory proof if your codes (eg. fmap) follow Functor’s Laws (eg. Preserve structure, identity) or Monad’s Laws !

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God’s Book of Perfect Proof

Math Online Tom Circle

https://www.quantamagazine.org/gunter-ziegler-and-martin-aigner-seek-gods-perfect-math-proofs-20180319/

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Canadian mathematician Langlands wins Abel Prize

Math Online Tom Circle

http://www.thehindu.com/sci-tech/science/canadian-mathematician-langlands-wins-abel-prize/article23304119.ece/amp/

Michael Bishop’s Science

Math Online Tom Circle

Michael Bishop (Nobel Medicine 1989)
School Science subjects should be taught in this sequence (unless in single ‘Combined Science’):
1st Physics
2nd Chemistry
3rd Biology

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Mind over Matter : Bruce Lipton

Math Online Tom Circle

Key Points:

1. The Foundation of Science has changed since Newtonian Era, except Biology / Medicine and Psychology which don’t keep up:

Math => Fractal Math

Newton Physics (Matter)=> Quantum Physics (Energy)

(Organic) Chemistry => Electro-Chemistry

Energy = Field = 气 Chi / Qi

3. Environment -> Mind -> Perception -> Genetic Control

4. Consciousness (5%), Subconscious-ness (95%)

Examples:

Driving car: inexperienced driver (consciousness), experienced driver (subconscious).
Dating (conscious behavior)

Note: The successful DeeplearningAI is using the concept of Perception called “Perceptrons” by analysing the Environmental (BIG DATA) pattern with the help of Mathematics (Calculus : Gradient Descent, Statistics : Bayesian Probability, Algebraic Topology, etc).

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“Deep Learning” Online Book

Math Online Tom Circle

Most popular AI Deeplearning Book by MIT :

[English]

http://www.deeplearningbook.org/

[中文版]

https://exacity.github.io/deeplearningbook-chinese/

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NS Overseas Notification SMS Number (NOT 36767)

The new number to SMS is no longer 36767.

SMS to 82411633 instead.

The format is still the same (separated by space):

MNC NRIC DestinationCountry DepartureDate (DD/MM/YYYY) ReturnDate YourHPNumber

Notification for NSmen Overseas Trip is only needed if you travel for more than 14 days.

Source: ns.sg

Disclaimer: The above is correct at the time of posting. Please double confirm with the official sources in case there are any updates.

Update 2019: NSmen no longer need to notify Govt of overseas travel under 6 months. Read more at: https://www.todayonline.com/singapore/nsmen-no-longer-need-notify-govt-overseas-travel-under-6-months

Creator of ‘Grand Unified Theory of Mathematics’ Wins Prestigious Math Prize

Professor Langlands is very famous in the field of Number Theory. Congratulations to Prof. Langlands for winning the very prestigious Abel Prize.

Source: LiveScience

A mathematician who developed what some consider the “grand unified theory of mathematics” has won one of the most prestigious prizes in mathematics.

Robert Langlands, an emeritus professor at the Institute for Advanced Study at Princeton University, has won the Abel Prize, a prestigious mathematics prize that honors a lifetime of groundbreaking work, organizers of the prize announced yesterday (March 20).

Langlands, 81, won the prize for work in which he found deep connections between two seemingly disparate areas of mathematics: number theory and harmonic analysis, according to a statement from the organizers of the prize.

How to help gifted children deal with hyper-sensitivity

This should be useful for parents of gifted kids.

Linear Algebra Online Calculator (Matrix Calculator)

Just came across this online tool (http://matrix.reshish.com/). Probably one of the nicest online matrix calculators that can do most stuff like calculating determinant, inverse, rank, Gauss-Jordan Elimination, etc.

Very intuitive and easy to use. Recommended to bookmark it for further use!

Cannot Login to SP Services

The SP Services website (https://services.spservices.sg/#/login) seems to be down as of 21 March 2018.

The error message received is:

Error: We’re currently facing issues communicating your request, please try again in a few minutes.

SP Services Utilities for Resale Flat

By the way, something I learnt from calling the hotline is that there is now no need for the old owner to cancel or to transfer the account. The new owner can simply proceed to open a new utilities account, and the old one will be cancelled automatically one day before the new account is opened. There will be no disruption to the water/electricity supply.

This is an improvement over the old method where the SP account has to be cancelled before opening a new SP services account.

Choosing a Programming Language

Math Online Tom Circle

…
https://dev.to/drminnaar/choosing-a-programming-language-493h

…

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Programmers need Advanced Math ?

Math Online Tom Circle

As software becomes more complicated for high-speed trains, driverless cars, missile weapons. .. and AI deeplearning algorithm, we can’t depend our life safety on the programmers who don’t understand the advanced maths behind these algorithms.

The Advanced Math is the Category Theory – the most advanced math foundation above “Set Theory” since WW2. Functional Programming is based on Category Theory with mathematical functions – always output correctly with no “side-effects”.

https://www.extremetech.com/computing/259977-software-increasingly-complex-thats-dangerous

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Which Countries Produce Best Programmers

Math Online Tom Circle

https://blog.hackerrank.com/which-country-would-win-in-the-programming-olympics/

The result is surprising … China, Russia, Poland are the top 3 countries based on the tests, not the usual expected countries such as USA, India, UK.

Reason: Mathematics ! China, Russia and Poland are strong in Advanced Math education in university. Functional Programming requires the Advanced Math eg. Category Theory.

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Prime Number Theorems Conjectures Explained

Math Online Tom Circle

1. Twin Primes Conjecture : there are infinitely many pairs of Twin Primes among the infinitely many prime numbers.

Note: 2013 Zhang YiTang proved the gap between the twin primes is no more than 70,000,000 [Terence Tao’s Polymath Project using Zhang’s method to further narrow the gap to 246 ]

2. Goldbach’s Conjecture

Chen’s “1+2” Theorem

3. Palindromic Primes (eg.11, 101, 16561)

4. Riemann Hypothesis

https://www.sciencealert.com/prime-number-theorems-conjectures-explained

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Trigonometric Identities and Differential Equations

Trigonometric Identities
$\begin{aligned} \sin(A\pm B)&=\sin A\cos B\pm\cos A\sin B\\ \cos(A\pm B)&=\cos A\cos B\mp\sin A\sin B\\ \tan(A\pm B)&=\frac{\tan A\pm \tan B}{1\mp \tan A\tan B} \end{aligned}$
$\begin{aligned} \sin A+\sin B&=2\sin\frac{1}{2}(A+B)\cos\frac{1}{2}(A-B)\\ \sin A-\sin B&=2\cos\frac{1}{2}(A+B)\sin\frac{1}{2}(A-B)\\ \cos A+\cos B&=2\cos\frac{1}{2}(A+B)\cos\frac{1}{2}(A-B)\\ \cos A-\cos B&=-2\sin\frac{1}{2}(A+B)\sin\frac{1}{2}(A-B) \end{aligned}$

Reduction to Separable Form
Equations of the form
$y'=g(\frac{y}{x}).$
Set $\frac{y}{x}=v$ . Then $y=vx$ and $y'=v+xv'$ . Thus the original equation becomes $v+xv'=g(v)$ which is separable.

Linear Change of Variable
$y'=f(ax+by+c)$ can be solved by setting $u=ax+by+c$ .

Newton’s Law of Cooling
Rate of change of temperature of an object ( $\frac{dT}{dt}$ ) is proportional to the difference between its own temperature ( $T$ ) and the ambient temperature ( $T_\text{env}$ ). That is, $\frac{dT}{dt}=-k(T-T_\text{env})$ .

Funniest Math Video

This is probably one of the funniest Math video I have watched:

Another one that is very humorous is: Mr Bean Calculus and Trigonometry Math Exam.

Best “Do-nothing” Saving Accounts in Singapore (Better than Fixed Deposit)

Albert Einstein once said that “Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.”

In E Maths, students will learn that the formula for Compound Interest is $\text{Total amount}=P(1+r/100)^n$ . The exponential “to the power of n” explains the powerful effect of compound interest.

Choosing the right savings account can earn you hundreds of dollars or more per year (depending on how much savings you have).

There are many savings accounts that require a lot of “action” on your part, notably you need to credit your salary (with SAL code) to the bank, use their card, buy their investment/insurance/loan products, etc. These accounts include DBS Multiplier, OCBC 360, BOC Smart Saver, etc.

However, many people may not meet their criteria (or may not want to use so much of their products). For instance, self-employed people may not have SAL code salary.

Currently, I think the 2 best “Do-nothing” saving accounts in Singapore are:

Citi MaxiGain

From Citibank, the interest rate of MaxiGain is tied to the SIBOR rate. Starting interest will be 80% of SIBOR, stepping up 0.1% for 12 counters. Final rate is around 2% or more. This is frankly better than many fixed deposits. The only downside is that if you withdraw from the account, the counter will drop to 0 (or to 6 once you reach the checkpoint of 6 counters). But even with the counter dropping to zero, the interest is around 0.8% or more which is pretty decent.

Citibank is a very reliable bank from America, with bigger market capital than DBS. Tip: According to online sources, your account may be temporarily “frozen” for inactivity if you don’t have any transaction for too long a period. Hence, it is recommended to set up an automatic credit of $1 monthly to your Citibank Maxigain account.

CIMB FastSaver Account

Most people would not have heard of CIMB bank. It is a Malaysian bank. Not to worry though, they are listed under Singapore Deposit Insurance, that means you are insured up to $50,000 even if something bad happens to the bank. CIMB FastSaver is quite amazing in that it gives 1% interest, with no minimum balance or penalty for withdrawing. That means you can withdraw as and when you like. Their account is entirely online, you don’t have to step into their branch even for creating your account. It is a simple and effective savings account.

Happy Anniversary with WordPress.com! You registered on WordPress.com 5 years ago.

Just received this nice message from WordPress. 🙂

Happy Anniversary with WordPress.com!

You registered on WordPress.com 5 years ago.

Thanks for flying with us. Keep up the good blogging.

When religion (Pope Francis) met science (Stephen Hawking)

Also interesting is that the founder of the “Big Bang” theory was a Catholic priest!

A Catholic priest, Fr. Georges Lemaître, is “Father of the Big Bang Theory”

Source: https://aleteia.org/2016/12/03/when-religion-pope-francis-met-science-stephen-hawking/

The meeting was cordial, in spite of their diametrically opposed views regarding the existence of God.

[A surprising encounter took place between the pope, who holds that God’s mercy is infinite, and a scientist who rejects the existence of God due to the infinity of the Universe. On December 2, Stephen Hawking participated in a conference in Rome on the Big Bang, today considered the most widely accepted theory for the origin of the universe—a theory proposed by the Catholic priest Georges Lemaître (1894-1966) in 1927. ]

Pope Francis and Stephen Hawking: Faith and reason reach out to each other

British scientist Stephen Hawking and Pope Francis met face to face on November 28 in the Vatican, just days after that renowned astrophysicist had confidently declared that asking “what was before the Big Bang” is meaningless, since it “is like asking what lies south of the South Pole.”

The meeting between these two charismatic figures, world-renowned representatives of the Catholic Faith (Francis) and of reason based on scientific knowledge (Hawking), was rare but cordial, although they have completely opposite stances regarding the idea of God.

Pope Francis considers God to be an infinitely merciful Father, greater than the Universe He created — the same Universe that Hawking has been studying for decades and which he believes arose from nothing, without divine intervention.

Hawking stated that “the discovery of the expansion of the Universe” — the “big bang” theory — has been one of the “most important intellectual discoveries” of recent times. However, “With James Hartle from the University of California, I worked out what physical conditions the early universe must have, if space-time had no boundaries in the past. Our model became known as the ‘No-Boundary Proposal,’” said Hawking, during the Science and Sustainability conference organized by the Pontifical Academy of Sciences at the Casina Pio IV in the Vatican.

Although the Big Bang is a well-accepted theory among experts, and it is fundamental for the formation of galaxies and planets, there is still no convincing answer to what happened before the explosion, what caused it, and consequently the reason for existence. Nevertheless, the theory fits into a logical explanation of the universe. “The message of science is that we are the children of logic and not of chaos,” explained Italian nuclear physicist Antonino Zichichi, a colleague of Hawking, in an interview with Vatican Radio.

Happy Pi Day!

Happy Pi Day to all readers of Mathtuition88.com!

Check out our previous posts on Pi:

Did you know, Pi day is also Einstein’s Birthday?

How to get Pi on Calculator – Without pressing the Pi Button

The Mystery of e^Pi-Pi (Very Mysterious Number)

Euler’s proof of Pi^2/6 (Basel Problem)

Category Theory: How to Make Pi

Pi hiding in prime regularities

Also, check out our cooking blog for the following Pie recipes!

Beef Pie

Strawberry Cheesecake Pie

Lemon Pie

Easy Banana Pie

Fudgy Fudge Pie

Zuji Promo Codes

Zuji is a famous flight and hotel booking service. By using the below Promo Codes, you can save some money from their cheap and good bookings.

(Please use the links provided below to enter the official Zuji website!)

Product: Flights
Period: 19 March 2018 – 1 April 2018
Coupon Code: ZUJI15DFLT
Coupon Value: S$15
Minimum Spend: S$500
Travel by: 30 September 2018

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Coupon Code: ZUJI33DHTL
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Product: Packages
Period: 19 March 2018 – 1 April 2018
Coupon Code: ZUJI22DPKG
Coupon Value: S$22
Minimum Spend: Nil
Travel by: 30 September 2018

Stephen Hawking dies aged 76

RIP Stephen Hawking.

Source: http://www.bbc.com/news/uk-43396008

The British physicist was known for his work with black holes and relativity, and wrote several popular science books including A Brief History of Time.

“We are deeply saddened that our beloved father passed away today,” a family statement said.

At the age of 22 Stephen Hawking was given only a few years to live after being diagnosed with a rare form of motor neurone disease.

Researchers studying the Flynn effect have found that scores on IQ tests have actually improved over time.

This is an interesting read for parents and students. Basically, IQ is a complex notion that is dependent on various factors, including environment and educational factors.

Source: ThoughtCo

You’ve probably heard someone lament the state of “kids today”: that current generations aren’t as smart as the ones that came before them. However, psychologists who study intelligence have found that there isn’t much support for this idea; instead, the opposite may actually be true. Researchers studying the Flynn effect have found that scores on IQ tests have actually improved over time. Below, we’ll review what the Flynn effect is, some possible explanations for it, and what it tells us about human intelligence.

What Is the Flynn effect?

The Flynn effect, first described in the 1980s by researcher James Flynn, refers to the finding that scores on IQ tests have increased in the past century. Researchers studying this effect have found wide support for this phenomenon. One research paper, published by psychologist Lisa Trahan and her colleagues, combined the results of other published studies (which included a total of over 14,000 participants) and found that IQ scores have indeed increased since the 1950s. Although researchers have documented some exceptions, IQ scores have generally increased over time. Trahan and her colleagues observed, “The existence of the Flynn effect is rarely disputed.”

Why Does the Flynn Effect Happen?

Researchers have put forward several theories to explain the Flynn effect. One explanation has to do with improvements in health and nutrition. For example, the past century has seen a decrease in smoking and alcohol use in pregnancy, discontinuation of the use of harmful lead paint, improvements in the prevention and treatment of infectious diseases, and improvements in nutrition.

As Scott Barry Kaufman writes for Psychology Today, “The Flynn effect serves as a reminder that when we give people more opportunities to prosper, more people do prosper.”

In other words, the Flynn effect could be partially due to the fact that, over the twentieth century, we’ve started addressing many of the public health issues that prevented people in earlier generations from reaching their full potential.

Another explanation for the Flynn effect has to do with societal changes that have occurred in the past century as a result of the Industrial Revolution. In a TED talk, Flynn explains that the world today is “a world where we’ve had to develop new mental habits, new habits of mind.” Flynn has found that IQ scores have increased the most rapidly on questions that ask us to find similaritiesbetween different things, and more abstract types of problem solving — both of which are things that we need to do more of in the modern world.

Several ideas have been put forward to explain why modern society might lead to higher scores on IQ tests. For example, today, many more of us have demanding, intellectually rigorous jobs. Schoolshave also changed: whereas a test at school in the early 1900s might have been more focused on memorization, a recent test might be more likely to focus on explaining the reasons for something. Additionally, more people today are likely to finish high school and go on to college. Family sizes tend to be smaller, and it has been suggested that this may allow children to pick up on new vocabulary words while interacting with their parents. It’s even been suggested that the entertainment we consume is more complex today.

Trying to understand and anticipate plot points in a favorite book or TV drama may actually be making us smarter.

Singapore’s Only Live Turtle And Tortoise Museum Is Closing This March & Here’s How You Can Help

I have visited the Turtle Museum around 2015/2016. It was a very impressive collection of turtles and tortoises, right in the middle of the Chinese Gardens. Even includes rare species like the Alligator Snapping Turtle.

Quite sad to hear that they are closing down. Land price / rental in Singapore is notoriously expensive, so I can understand that having a space to house all those turtles is very hard in land-scarce Singapore. I would estimate that their rental would easily be at least S$10,000 a month for such a large space. They have kept the ticket prices low at just $5 for each person.

Do help by donating (https://gogetfunding.com/turtles-need-a-home/), or even just sharing this news will help. Every share leads to more views and potentially more donors.

Link: http://thesmartlocal.com/read/turtle-museum

Singapore’s Chinese Garden is known for its imperial styled pagodas and arch building, but within all that beauty lies another: Singapore’s very own Live Turtle & Tortoise Museum.

A Guiness World Record Holder, the museum holds over 500 turtles and tortoises from 40 different species, ranging from the most dangerous alligator snapping turtle to the world’s 2nd largest tortoise species, the Giant Aldabra. All this is run by Connie Tan and a handful of workers, as part of her family’s legacy.

Unfortunately, this marvel may soon no longer be – the museum is scheduled to be evicted from Chinese Gardens by 31st March. We headed down to understand what drives Connie to keep this museum alive against all odds.

Poll Results: Which JC is the Best?

62 people have voted for the best JC in Singapore. (Poll is at: Which JC is the best in Singapore?

At top place is Nanyang Junior College 12.9% (8 votes), tied with Raffles Institution 12.9% (8 votes).

Visit the poll to see the full results! Some other interesting options voted are as follows:

Other Answer	Votes
DKJC	1
Definitely not SR	1

Also see: Which Secondary school is the best in Singapore.

Stolen A-Level scripts: 75 of 238 affected students will re-sit Chemistry Paper 3

Sincerely wishing good luck to those retaking their exams. It is certainly not easy, especially for boys who by that time will be in National Service. Also, for a fact-intensive course like Chemistry, with each passing month it gets harder since one’s memory would not be as fresh.

SINGAPORE: Of the 238 students whose A-Level Chemistry scripts were stolen in the United Kingdom last year, 75 have opted to be re-examined for the affected paper, the Singapore Examinations and Assessment Board (SEAB) told Channel NewsAsia on Monday (Mar 12).

The students, who received their A-Level results on Feb 23, are from Anderson JC, Anglo-Chinese JC (ACJC), Hwa Chong Institution (HCI) and Nanyang JC (NYJC). The stolen scripts were for Paper 3, which consists of free-response questions and carries a weightage of 35 per cent of the entire H2 Chemistry examination.

The final A-Level grades of the affected students were derived through a projection. But given the “unique circumstances”, the affected students were given the option to re-sit the H2 Chemistry Paper 3 in April or November, and have the better of their two grades recorded in their A-Level result slip and certificate.

Those who wished to register for the re-examination had to do so by Friday (Mar 9).

SEAB said that of the 75, there were 28 students each from AJC and ACJC, seven from HCI and 12 from NYJC.

Out of the total, 57 of the candidates registered for the re-examination in April, while 18 registered for the re-examination in November

The magic (and math) of skating on thin ice without falling in

Very interesting video. Do try to imagine the sound of the ice and check out the video to confirm your guess. Very surprising sound! It is a pity that not many countries have such ice to skate in.

The main mathematical principle is Archimedes’ Principle:

Congelation ice, while a solid form of water, does bend slightly and acts like an elastic plate buoyed by the water below. To Anje, it’s Archimedes buoyancy principle in action.

“A body partially immersed in water is buoyed by a force equal to the weight of the water displaced by the body,” he said.

Source: https://www.pbs.org/newshour/science/the-magic-and-math-of-skating-on-thin-ice-without-falling-in

Stepping onto an inch-and-a-half thick piece of lake ice — much less doing laps on it — is a no-go for most people. But for experienced Swedish skaters Henrik Trygg and Mårten Anje, few things top skating on thin ice.

In December, still photographer Trygg filmed Anje skating on 1.8 inches of fresh ice on a lake outside Stockholm. The resulting mini-documentary— filled with the eerie, laser-like sounds of bending ice — went viral in February.

One shot shows the ice, commonly called “black ice,” visibly bending under the skater’s weight. Which raised the question: Why doesn’t this thin frozen surface break?

For the answer, we turned to Anje, a 35-year veteran of nordic skating whose day job is calculating risk. He is a mathematician and actuary at a consulting firm.

Brand’s Essence of Chicken Effectiveness

Students studying hard for exams may often feel mentally tired, though technically they are sitting on the chair most of the time. This is because the brain actually uses around 20% of the body’s energy despite the brain only being 2% of total body weight.

Not to mention if the child is in a sports CCA, in addition to being mentally exhausted, he/she is also physically tired after all the training. Having energy after school has ended is very important, as 90% of the important revision takes place at home after school has ended.

Is Essence of Chicken Effective

There is quite a lot of scientific research on the effectiveness of chicken essence:

Effectiveness of Essence of Chicken in Improving Cognitive Function in Young People Under Work-Related Stress

Effects of chicken essence on recovery from mental fatigue in healthy males

Chicken essence is basically condensed chicken soup, which contains a lot of vitamins and amino acids in easily absorbed form. This may be even better than eating vitamin pills which may not be absorbed well by the body.

Brandsworld E-Store is the official online store of Brand’s, where you can buy Brand’s Chicken Essence online for your children, or even yourself. Other than Chicken Essence, Brand’s also sells other health products such as Birds Nest, and Collagen.

Brandsworld E-Store

Free Entry into Science Centre (In Conversation with … John Edmark)

Students interested in the fusion of math, science and art may be interested to attend this wonderful event. Note: Pre-registration is needed for your free entry into the Science centre.

URL: http://www.science.edu.sg/events/Pages/EventDetail.aspx?ID=1251@event?ID=1251

24 March 2018 10:30 – 12:00

Location: Maxwell Auditorium

The Tinkering Studio @ Science Centre Singapore cordially invites you to interact with John Edmark, inventor, designer and artist who teaches design at Stanford University in Palo Alto, California. His most recent work is a series of animated sculptures called Blooms which endlessly unfolds and animates as it spins beneath a strobe light.

Come join us for this talk where John will share his work with logarithmic spiral structures, Fibonacci numbers, and the Golden Ratio (Ф), and how it all led to his inventing Blooms. His masterful illusions are the results of a marriage between art and mathematics.

RSVP: to Ms Jenny Leong by 18 March 2018.

Pre-registration is required for your complimentary entry into the Science Centre.

Wakin Chau 周华健 was a Math Major at University

Something interesting that not many people know?

Also see Famous Nonmathematicians who studied Mathematics.

Wakin Chau was born in a rice store owned by his family in Sai Ying Pun, Hong Kong. Growing up as the fourth son in his seven-member family, Wakin learned to play the guitar when he was about 13 years old. In 1979, he left for Taipei to major in mathematics at National Taiwan University. During his college years, he sang and played folk songs in local coffee shops. This activity was a tradition among NTU students, and it is how Wakin learned to sing in Mandarin, which would be key to his future as a music-maker in Taiwan.

Source: Wikipedia

Probably one of his most famous songs is “Friends”, 朋友.

Latest SG Education News

Policies In Brief: Tuition fee subsidies

The Straits Times

Income eligibility criteria for the Mendaki Tertiary Tuition Fee Subsidy scheme will be revised upwards from August. … Students previously unable to take part in Outward Bound Singapore adventure training or overseas volunteer programmes organised by Youth Corps Singapore may get opportunities …

More Malay students from low-income families to benefit from revision of Tertiary Tuition Fee …

Channel NewsAsia

SINGAPORE: The Government will revise the income eligibility criteria for the Tertiary Tuition Fee Subsidy (TTFS) scheme to benefit more Malay students from low-income families. The TTFS scheme, introduced in 1991, covers tuition fees at tertiary institutions and benefits 11,000 students currently.

Subsidies for master’s courses to be removed or reduced for foreign, PR students: Ong Ye Kung

TODAYonline

SINGAPORE — From next year, foreign students will no longer receive subsidies for most of the vocation-based master’s degrees and post-graduate … For example, according to the tuition fee schedule for students admitted in the Nanyang Technological University last year, international students pay …

NUS to offer three new degrees in 2018, including a first in veterinary medicine

TODAYonline

After that, the students will spend another three years in Melbourne to complete their studies. While they will pay prevailing NUS and University of Melbourne tuition fees during their time in Singapore and Australia, Singaporean students can expect to pay about 15 per cent less in tuition fees for the DVM …

RGS student who had learning disability pays it forward

The New Paper

But her business was unsustainable as her students couldn’t pay tuition fees. I believe in … She then founded HER Planet Earth (HPE) last year to raise funds for underprivileged women affected by climate change and organisations such as Zero Waste SG and World Wide Fund Singapore. Today, the …

Polytechnic courses to be cut by 20%, more Normal (Academic) students to enter poly via through …

TODAYonline

If there isn’t any PFP, some students who have the potential to succeed in polytechnic cannot enter the school only because they didn’t do well in their O-Level exams,” said Mr Yap, who has an offer to study information systems at the Singapore Management University (SMU). “Imagine if there’s only a …

Wanton Noodles

Cooking For Fun

As a Chinese born and grew up in northern part of China, I’m very familiar with noodles. Yet, its very difficult for me to cook southern pattern noodles well, like rice noodle, Hokkien mee. I tried wanton noodles before and it didn’t turn out well. I guess the main reason is that I didn’t pay much attention to the difference between southern noodles and northern noodles. Northern noodles are more hard and thicker. They need more time to be cooked. That is completely different from southern ones.

I corrected my way of cooking wanton noodle this time.

Noodle was bought from supermarket and so was the wanton wrap.

1. Prepare the wanton filling:

Minced pork (100g), some shrimps ( around 10), 1 stalk spring onion, 1 small slice ginger, 3-4 water chestnut. Chop them together and let them be sticky to each other.

Put chopped pork and shrimp in a…

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The Best Job: Mathematician

Math Online Tom Circle

The above survey was 2009 USA Job Market.
By 2018, Number 1 Job is AI / Data Scientist in USA / China / Europe high-tech market, which still needs Mathematics. eg.

Linear Algebra (Matrix)
Calculus (eg. Gradient descent, …)
Bayesian Statistics (Probability),
Algebraic Topology (eg. Homological Algebra, etc),
Abstract Algebra (eg. Category Theory, etc…)
etc.

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Speak Mandarin Campaign Activities

Just to share, for those who are interested. Two theatrical works, Four Horses Road, and Legend of the Monkey King, are happening this month/next month.

French Math “Coniques” : ellipses, paraboles, hyperboles.

Math Online Tom Circle

French Math is unique in treating these 3 conic curves: (ellipse, parabola, hyperbola), always starts from the first principle – a la the Cartesian Spirit “I think therefore I am” (我思故我在).

“Catersian” Analytical Geometry was co-invented by two 17CE French mathematicians René Déscarte and Pierre de Fermat.

Note: The “elliptic curve” is a powerful geometry tool used in Number Theory (proved the 350-year-old Fermat’s Last Theorem in 1994 by Andrew Wiles), also in the most advanced Encryption algorithm.

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Second Order Linear D.E. Summary

Sample Tikz code for drawing the above figure (polygon angles)

Why are many gifted children challenging and exhausting?

SP Services Utilities for Resale Flat

Citi MaxiGain

CIMB FastSaver Account

The meeting was cordial, in spite of their diametrically opposed views regarding the existence of God.

What Is the Flynn effect?

Why Does the Flynn Effect Happen?

Is Essence of Chicken Effective