Jack Ma of the Alabama.com gives this Arithmetic question to the audience, only 1% get the answer right !
Jack has cash $50, which he uses to buy:
Clothing : $20 (Balance $50-20 = $30)
Shoes: $15 (Balance = $30-15 = $15)
Candy: $9 (Balance = $15- 9 = $6)
Food: $6 (Balance = $6 – 6=$0)
Question:
Add up the Balances = $ 30+15+6 = $51
Where does the extra $1 come from ?
French Concours was influenced by Chinese Imperial Exams (科举ko-gu in ancient Chinese, today in Hokkien dialect) from 7AD till 1910. The French Jesuits working in China during the 16th -18th centuries were the culprits to bring them to France, and Napoleon copied it for the newly established Grande École “École Polytechnique” (a.k.a. X).
The “Bachelier” (or Baccalauréat from Latin-Arabic origin) is the Xiucai (秀才), only with this qualification can a person teach school kids.
With Licencié (ju-ren 举人) a qualification to teach higher education.
Concours was admired in France as meritocratic and fair social system for poor peasants’ children to climb up the upper social strata -” Just study hard to be the top Concours students”! As the old Chinese saying: “十年寒窗无人问, 一举成名天下知” (Unknown poor student in 10 years, overnight fame in whole China once top in Concours).Today, even in France, the top Concours student in École Polytechnique…
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Here are some tips to organize your studying time!
How to Better Organize After School Studying?
The key to achieving success in every academic discipline is practice, practice and more practice. However, this is where many students struggle the most: finding the time and the right methods to study after school. If you want to help your child study better, here is a simple to-do list:
Find the best method for your kid
Children have their own individual studying patterns, some of them prefer to study by themselves, some kids learn more when they participate in study groups, while other children, especially students with learning difficulties, might require a help of a professional tutor. You have to first recognize your child’s needs, try different methods and evaluate the results. Remember that the key to successful studying is regularity: even the best tutor will not be able to help your child, if they meet sporadically. Schedule a time for after school studying every week and check if your child adheres to it.
Take regular breaks
It is good to have a strict studying schedule, but breaks are also important. Regular breaks help boost child’s creativity and approach the task at hand with more enthusiasm.
Intensify as the exam approaches
If the after school studying is meant as a preparation for the upcoming exam, remember to start studying early and intensify as the day of the exam approaches. For example, start from doing simple Singapore Math exercises a few weeks before the day of the exam and progress to more complex issues, while increasing the workload. Never let your child study overnight before the exam, it will only make him feel more tired and stressed out on the day of the exam, plus this kind of behavior supports bad studying habits and false convictions that everything can be mastered within a few hours and there is no need to learn on a day to day basis.
Resource: http://eastwestmath.com
Here is a helpsheet that I created on the topic of Domain and Range of Inverse Functions, a topic no longer in O Levels but still in IP Math.
Featured Book:
韓非子是战国法家, 荀子的高徒, 秦始皇宰相李斯的同学。他说”白马非马”, 即白马不是马, 可以用集合論(Set Theory) 证明:
Let 马 = H = {w, b, r, y …}
w : 白马
b : 黑马
r ：红马
y：黄马
Let 白马 = W = {w}
To prove:
H = W
We must prove:
H ⊂ W and H ⊃ W
From definition we know:
$latex w in H supset W $
$latex H nsubseteq W $
$latex implies H neq W $
白马≠马
白马非马
[QED]
其他例子:
木魚非鱼
Definition: $latex text{Sequence } (a_n) $
has limit a
$latex boxed{forall varepsilon >0, exists N, forall n geq N text { such that } |(a_n) -a| < varepsilon}$
$latex Updownarrow $
$latex displaystyle boxed{ lim_{ntoinfty} (a_n) = a }$
What if we reverse the order of the definition like this:
∃ N such that ∀ε > 0, ∀n ≥ N,
$latex |(a_n) -a| < varepsilon$
This means:
$latex boxed {forall n geq N, (a_n) = a }$
Example:
$latex displaystyle (a_n) = frac{3n^{2} + 2n +1}{n^{2}-n-3}$
$latex displaystyletext{Prove: } (a_n) text { convergent? If so, what is the limit ?}$
Proof:
$latex displaystyle (a_n) = 3 + frac{5n +10}{n^{2}-n-3}$
$latex n to infty, (a_n) to 3$
Let’s prove it.
$latex text {Let } varepsilon >0$
$latex text{Choose N such that } forall n geq N, $
$latex displaystyle |(a_n) -3| = Bigr|frac{5n +10}{n^{2}-n-3}Bigr| < varepsilon$
$latex text{Simplify: }…
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Cédric Villani (Médaille Fields 2010) “Théorème Vivant”:
“La fameuse ligne directe, quand vous recevez un coup de fil du dieu de la mathématique, et qu’une voix résonne dans votre tête. C’est très rare, il faut l’avouer!”
“The famous direct line, when you receive a ‘telephone call’ from the God of the Mathematic, and that a voice resonates in your head. It is very rare, one has to admit.”
屈原 QuYuan (343–278 BCE) Symmetry:
http://en.wikipedia.org/wiki/Qu_Yuan
离騷《天问》
1. “九天之际, 安放安属,
隅隈多有, 谁知其数 ?”
=> 天 (Sky) 和 地 (Earth) must be 2 symmetric spheres.
If 地 (Earth) were flat, then there would be (隅隈) edges and angles at the 天 (Sky) & 地 (Earth) boundary (九天之际).
2. “东西南北, 其修孰多,
南北顺橢, 其衍几何。”
=> 南北顺橢 = The Earth is ellipse (橢), with north-south (南北) slightly flatten.
几何 = Geometry
3. How did QuYuan know this advanced astronomy & geometry in ~ 300 BCE?
屈原
Mozi
墨子 Mozi (468 BCE~ 376 BCE), 2000 years earlier than Newton
“墨子” : “力, 行之所以奋也。”
行: Moving
奋: Acceleration
力: Force is due to acceleration by the moving object.
F ∝ a
F = m.a
Difference Between Good & Bad Mathematicians
S.S. Chern (陈省身): “The former gives many concrete examples, the latter has only abstract theories.”
Triangle
1. Not always true!
Sum of 3 internal angles = Π =180 degrees
depends on which geometry:
Euclidean / non-Euclidean / Riemann
2. True always!
Sum of 3 exterior angles = 2 Π = 360 degrees
Kurt Gödel‘s Mathematical Proof of God’s Existence
Axiom 1: (Dichotomy) A property is positive if and only if its negation is negative.
Axiom 2: (Closure) A property is positive if it necessarily contains a positive property.
Theorem 1. A positive is logically consistent (i.e., possibly it has some instance).
Definition. Something is God-like if and only if it possesses all positive properties.
Axiom 3. Being God-like is a positive property.
Axiom 4. Being a positive property is (logical, hence) necessary.
Definition. A Property P is the essence of x if and and only if x has P and is necessarily minimal.
Theorem 2. If x is God-like, then being God-like is the essence of x.
Definition. NE(x): x necessarily exists if it has an essential property.
Axiom 5. Being NE is God-like.
Theorem 3. Necessarily there is…
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Pascal Wager:
1. We can choose to believe God exists, or we can choose not to so believe.
2. If we reject God and act accordingly, we risk everlasting agony and torment if He does exist (Type I error in Statistics lingo) but enjoy fleeting earthly delights if He doesn’t exist.
3. If we accept God and act accordingly, we risk little if He doesn’t exist (Type II error) but enjoy endless heavenly bliss if He does exist.
4. It’s in our self-interest to accept God’s existence.
5. Therefore God exists!
Mathematical Proof:
Pascal assumed
Probability of God exists = p
Probability God doesn’t exist = 1-p
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This is an article describing careers in the automobile industry. Hope it is useful for students interested in this area of work! 🙂
What are the Main Careers in Automobile Industry?
The automobile industry contributes greatly to the employment of many citizens in the country. It is one industry, which supports just any other industry you might think of. Many people feel its influence – the people commuting to work, the drivers who deliver goods to customers, the emergency services engineers, technicians, and mechanics. As one way of promoting the growth of the automobile industry, the Ideal Auto USA provides direct and indirect employment through selling some of the eco-friendly cars in the industry.
Careers in the automobile industry
There are many kinds of employment opportunities in this industry often employing some of the brightest minds like the engineers. Because there is a wide array of jobs, one would have to find a suitable choice based on his or her interest and qualifications. If you have the right training, you can easily advance higher in the positions. The technicians are responsible for things like replacing air filters, changing oils, and balancing wheels. These technicians handle many other maintenance tasks such as doing tune ups and changing the brake pads.
Apart from the technicians, there are the mechanics that repair cars. These workers are categorized one or two levels up the employment ladder from the technicians. At times, people confuse the mechanics with technicians, but the reality is that mechanics are more advanced than automobile technicians are.Besides performing many of the tasks done by technicians, they have knowledge on how to repair cars and work on engines.
While mechanics may work for companies or other people, when they have the business skill and the required capital, they can set up their own business. A repair shop is certainly one rewarding business, which can help mechanics further their career.
The automakers and car dealers employ many workers from the cleaners, service team, the mechanics, engineers, sales persons, drivers, and managers. All these people and their families get support from the industry. There are also indirect jobs, which come with this industry such as the workers employed in steel plants, glass making plants, or computer chip makers, which make the materials for manufacturing cars.
Salary range for automobile careers
According to Bureau of Labor Statistics, the automotive service technicians as well as the mechanics earned an average wage of about $38,560 as in May 2011 while the average salary for the mechanical engineers who work in the automobile manufacturing was at averagely $95,080. These figures show that the workers especially those with some skill in the automobile sector command quite a substantial pay.
If you want to make a living when working in the automobile industry, you might want to get some education be it in sales and marketing, engineering, motor vehicle mechanics, or even a driver. With Ideal Auto USA, it offers the best cars in the industry, which is a way of expanding the career market as more workers get employment as drivers and mechanics.
Tim Bryson is a practising automobile mechanic and has been working in this industry for more than 8 years. For the best eco-friendly cars that will drive the automobile industry, you can visit Ideal Auto USA.
These are some Fourier Series (learnt in University Maths courses) videos from YouTube. Very interesting and enlightening!
The gist of the theory of Fourier Series is that a function (periodic) can be expressed as an infinite sum of sine and/or cosine functions.
Featured Book:
Fourier Analysis: An Introduction (Princeton Lectures in Analysis)
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences–that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.
I like this analogy:
“Programming without Mathematics is like Sex without Love.”
Google Search is powerful because of Linear Algebra theory in finding core “EIGENVALUES” in order to manipulate the billion rows X billion columns matrices comprised of PageRanks (another formula invented by 2 Stanford Applied Math Masters degree students who co-founded Google.)
Facebook’s two Harvard undergrads Mark Zuckerberg and roommate Eduardo Savarin (now migrated to Singapore) created the prototype of Campus Facebook to rank Harvard girls with the Elo Formula (applied Normal Distribution Theory, used as standard in Chess and Sport rating).
Other examples:
RSA Encryption using Prime number factorization with a public and a private key.
Black-Sholes Formula (won 1997 Nobel Prize in Economics) for Derivatives trading software used by stock traders worldwide. The abuse of this formula was the main culprit of the 2010 Sub-prime global financial crisis.
Black-Scholes Equation (1997 Nobel Economics)
Use: Pricing Derivatives (Options): calculate the value of an option before it matures.
1/2 (σS)².∂²V/∂S² + rS.∂V/∂S + (∂V/∂T – rV) =…
Without last 2 terms=> heat equation !
Time T
Price S of the commodity
Price V of the derivative
Risk free interest r (govt bond)
Volatility = σ of the stock = standard deviation
Assumptions: (Arbitrage Pricing Theory)
No transaction costs
No limit on short-selling
Possible to borrow/lend at risk-free rate
Market prices behave like Brownian motion: constant in rate of drift and market volatility
Put option: right to sell at a specific time for an agreed price if you wish.
Call option: right to buy at a specific time for an agreed price if you wish.
One Black-Sholes formula each for Put and Call respectively.
Derivative was invented in 1900 by Mr. Bachelier, a French PhD student of Poincaré, the Mathematics…
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Students studying Mathematics at university will sooner or later hear of the famous eccentric Mathematician Paul Erdos, and the concept of Erdos Number. People who have written a paper with Erdos have a Erdos number of 1. People who have cowritten with the above people (with Erdos number 1), have Erdos number 2. Unfortunately, it is now impossible to get Erdos number 1, as Paul Erdos has passed away.
But what is an Imaginary Erdos Number?
This YouTube channel Numberphile has really succeeded in making Maths interesting! I watch almost every new episode that comes out, and will feature it on my website.
Featured Book:
MY BRAIN IS OPEN: The Mathematical Journeys of Paul Erdos
Paul Erdõs, one of the greatest mathematicians of the twentieth century, and certainly the most eccentric, was internationally recognized as a prodigy by age seventeen. Hungarian-born Erdõs believed that the meaning of life was to prove and conjecture. His work in the United States and all over the world has earned him the titles of the century’s leading number theorist and the most prolific mathematician who ever lived. Erdõs’s important work has proved pivotal to the development of computer science, and his unique personality makes him an unforgettable character in the world of mathematics. Incapable of the smallest of household tasks and having no permanent home or job, he was sustained by the generosity of colleagues and by his own belief in the beauty of numbers.
Witty and filled with the sort of mathematical puzzles that intrigued Erdõs and continue to fascinate mathematicians today, My Brain Is Open is the story of this strange genius and a journey in his footsteps through the world of mathematics, where universal truths await discovery like hidden treasures and where brilliant proofs are poetry.
There are pros and cons of taking H1 or H2 Maths:
H1 Maths is an easier version, and will definitely take less time to study. This time can be used for studying other subjects. Also, it covers statistics which can come in handy for majors like Psychology, Social Science, or Business. Students who take A Maths in O Level will find that the Pure Math part of H1 Maths is basically the same, if not even easier than O level A Maths.
H2 Maths is the harder version, more difficult than even the O Level A Maths. New and interesting topics like Complex Numbers and Vectors will lay a good foundation for University majors like Engineering and Physics. Try not to forget what you have learnt in O Level A Maths, it will come in handy.
Students who wish to enter SMU & take H1 Maths in JC may want to note that SMU has a introductory module on calculus which is pretty much compulsory, even for majors like social science. I have taught a student from SMU, and would say that the content is heavier than even H2 Math Calculus; there is multivariable calculus in the SMU Course.
Featured Book:
Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks
To all Singaporean readers and parents,
We are proud to recommend some excellent Graphic Design and Fashion Degree Programmes, by First Media Design School. The degree is being conferred by the University of the West of England, Bristol.
For those who are interested to enroll in this school, please contact me (Mr Wu) at mathtuition88@gmail.com. I have some extra information booklets about the course provided by the company, and will be pleased to guide you in the registration process.
Once again, if you are interested to enroll, please contact me as soon as possible. Thanks!
It is confusing for students regarding the two forms of the Fermat’s Little Theorem (which is the generalization of the ancient Chinese Remainder Theorem):
General: For any number a
$latex boxed { a^p equiv a mod p, forall a}$
We get,
$latex a^{p} – a equiv 0 mod p$
$latex a. (a^{(p-1)} -1) equiv 0 mod p$
$latex p mid a.(a^{(p-1)} -1)$
If (a, p) co-prime, or g.c.d.(a, p)=1,
then p cannot divide a,
thus
$latex p mid (a^{(p-1)} -1)$
$latex a^{(p-1)} -1 equiv 0 mod p$
Special: g.c.d. (a, p)=1
$latex boxed {a^{(p-1)} equiv 1 mod p, forall a text { co-prime p}}$
Some of the Maths topics that Engineering Students need to learn are:
All the above topics are rather challenging and deep. Fortunately, for most engineering students, application of the theorems would suffice, the deep proofs are not really necessary. It would be good to know them though.
Featured Book:
Schaum’s Outline of Advanced Mathematics for Engineers and Scientists (Schaum’s Outline Series)
This is the book you are looking for, if you are looking for a book to help ace Engineering Maths.
Just to summarize the 10 Surprising Facts:
Read more at: http://www.takepart.com/photos/ten-surprising-facts-finlands-education-system-americans-should-not-ignore/more-languages
Featured book:
This book is highly recommended for those who are interested in the 4 Temperaments and related research (Introvert, Extrovert, Sanguine, Choleric, Melancholic, Phlegmatic, etc.)
Prove : For any positive integers p, k,
$latex (p^k)! text { is divisible by p }$
Proof:
Apply Factorial Formula:
$latex boxed {n!=n.(n-1)! } $
$latex (p^k)! = (p^k). (p^k -1)!
= p.(p^{k-1}).(p^k -1)!
$
hence divisible by p. [QED]
Source: http://www.math.illinois.edu/~verahur/18.024/notesSD.pdf
Excerpt:
Proof of the second-derivative test. Our goal is to derive the second-derivative test, which determines the nature of a critical point of a function of two variables, that is, whether a critical point is a local minimum, a local maximum, or a saddle point, or none of these. In general for a function of n variables, it is determined by the algebraic sign of a certain quadratic form, which in turn is determined by eigenvalues of the Hessian matrix [Apo, Section 9.11]. This approach however relies on results on eigenvalues, and it may take several lectures to fully develop. Here we focus on the simpler setting when n = 2 and derive a test using the algebraic sign of the second derivative of the function.
The full proof can be found in the featured book below: T. Apostol, Calculus, vol. II, Second edition, Wiley, 1967
Featured book:
Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability (Volume 2)
Sounds bizarre, but it is true! Something “uniquely Singapore” as 92 marks is usually the top echelon for most other countries.
Students need not be disappointed, as 88 to 92 marks is already a very respectable score. Most important is to understand the subject well, and try to improve.
Source: http://news.asiaone.com/news/education/tuition-no-enough
Despite scoring between 88 and 92 marks for his subjects, he was placed in the third quartile of his cohort.
“Which means he was not among the top 50 per cent,” says his mum, Mrs Jaclyn Chew, 41.
Her son, who attends an all-boys school in north-eastern Singapore, was crestfallen after he asked his parents how he fared.
“I had to tell him the truth about where he stood compared to his peers,” Mrs Chew says.
“It’s just bizarre that with his grades and the tuition, he’s still in the lower half of the grade spectrum.”
– See more…
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Source: Spiked Math
Can you guess what are the names of the movies above (phrased in terms of Math).
Some hints:
are some of them.
You may discuss in the comments below!
At the undergraduate level, sometimes functions are of two variables (x,y). How do we find the maximum or minimum points of such a function?
Read the following PDF to find out!
Recommended Book:
Multivariable Calculus, 7th Edition
This is a highly practical book on Multivariable Calculus. It is also suitable for Engineers / Physics Majors. I learnt Multivariable Calculus from this book. 🙂
Here is a Integration by Parts helpsheet I created and uploaded on Scribd. Integration by Parts is a really useful technique, in fact it is one of the two key integration techniques in H2 Maths. The other technique is Integration by Substitution.
Featured book:
The Humongous Book of Calculus Problems
This book is really “humongous”. If you need to source for practice problems for Calculus, this is a good place to start. 🙂
Translation: How do we move only 1 matchstick to make the equation valid?
(“Not Equals” sign 
This is a really tricky question… Hint: Need to think in Chinese, this is a Chinese joke 😛
Featured Post:
The Motivational Books recommended in the above post seems to be very popular with readers on this site. Many readers (presumably parents) have bought the books! Buy a Christmas present for yourself this Xmas. 🙂
“It is more blessed to give than to receive.” – Acts 20:35
Source: http://www.bbshare.sg/
Join the Boys’ Brigade in spreading the Christmas cheer to needy families in Singapore.
To most of us, items like rice and biscuits are ordinary and common, but to the needy and elderly in Singapore, they are necessities and much needed items.
There are 3 ways to help:
Wishing all our readers a Merry Christmas!
Featured Book:
For any parent who has ever been told, “your child isn’t performing up to his or her potential,” this book has the answer. Renowned clinical psychologist Michael Whitley, Ph.D. offers a proven ten-step program to motivate underachieving children. This easy-to follow book identifies the six types of underachievers from the procrastinator to the hidden perfectionist to the con artist, and it…
View original post 13 more words
https://mathtuition88.com/2014/11/20/what-is-vixra/
“arXiv” opposite is “viXra”.
The former “arXiv” is administered by Cornell University for Math paper publishing online. The traditional math journals would take 2 years to review and publish.
The Russian Mathematician G. Perelman was fed up of the long and bureaucratic review process, sent his proof of the 100-year-old unsolved “Poincaré Conjecture” to arXiv site. Later it was recognized to be correct but Perelman refused to accept the Fields Medal and $1 million Clay Prize.
See http://tomcircle.wordpress.com/2013/03/31/grigory-perelman-arxiv/
The new site “viXra” is open to anybody in the world while “arXiv” is still restricted to academics.
This young Singapore mathematician William Wu proved his new found Math Theorem on “viXra” site:
Prove that: if p is prime, for any number k,
$latex boxed {(p – 1)^{p^k} equiv -1 mod {p^k}}$
[By using the Binomial Theorem and Legendre’s Theorem.]
Example: p = 3, k=2, 3^2=9
2^9 = 512…
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Just to share a career guide, for those students about to graduate. Hope it helps!
Launch Your Career with Salesforce Award-Winning Recruitment Programs for College Students
It is never too early to start building your career, especially if you have certain goals you intend to achieve by certain landmark years. It is therefore important to look for a place where you can feel challenged to grow in your career and as an individual in a stimulating and supportive environment. Well, the good news is that Salesforce has not only one but also two programs that you can plug into to get your career moving.
Award-winning recruitment
These are not your ordinary, run-of-the-mill types of college recruitment programs. Both programs have won the Best Places to Work for Recent Grads awards three times (2011, 2012 and 2014) and the Indiana Intern.net Employer of the Year award twice (2011 and 2012). However, what are these programs that I’m harping about here?
First, you have the Catapult Rotational Program. This is a summer internship for undergraduate and graduate students. How does it work?
You choose a track that you would like to receive training in; whether in Business, Technology or Consulting (your college degree should give you a hint here).
Then you rotate among three teams for three months each where you will develop your main professional skill along with obtaining valuable experience in related departments.
At the end of the nine months, you will be absorbed into a full-time, permanent position in your specific department, where you will enjoy all the benefits of being a full-time employee of the ExactTarget Marketing Cloud (there’s dental too)
The other program is the Slingshot Internship program,which also runs during the summer for graduates and undergraduates who are in their sophomore, junior or senior year in college. This offers a real-world feel of what you can expect in your field of expertise.
You will have the opportunity for some hands-on work like working on the Salesforce metadata api and you will be required to complete two projects worthy of being included in your resume within the stipulated time of internship. You get the opportunity to network with the executive team and shadow an individual in your preferred career.
It’s not all work though. There are social events and philanthropic outings plus you receive a house stipend and competitive pay for all your hard work.
Not a dull moment
Regardless of the program that you choose, you have a guarantee that no two days will be the same. These programs expose you to the reality of life in your chosen career and get you more than ready for what is to come. It is very high octane and you are going to love it!
How do I get in?
Application for the programs begin in August and as you can imagine they fill in quite quickly so it is advisable to keep tabs on when the application process opens so that you can get yours in as fast as you can.
As expected, there are also certain qualifications that you have to meet and you can take a look at them on their website or through their college recruitment program FutureForce which has accounts on Twitter and Instagram.
It is an overall excellent opportunity that you should certainly look into.
Author Bio
Brennan Booth is a careers blogger in the field of technology. She is trained as a software engineer with lots of experience in the industry. To read more about Salesforce metadata api click the link.
Do you want to be a tutor, but find tuition agencies’ 50% commission too high?
Wonder if there is a better way to find tuition job without paying any commision?
Apply for a free listing at Tuition Database now: http://tuitiondatabase88.wordpress.com/apply-to-be-tutors/
The site is currently new, which means that early birds will be listed at the top on a first-come-first-served basis. The earlier you apply, the higher your listing will be.
Verified Tutor / Ordinary Tutor package is 100% free of charge.
We are not a Tuition Agency, we are a free Tuition Database, providing services to tutors and parents.
We will be promoting the website proactively, to ensure that our tutors will get many visits and enquiries.
Apply at: http://tuitiondatabase88.wordpress.com/apply-to-be-tutors/
Good news for you who are interested in Cryptography, which is at the intersection of mathematics and computer science. Highly useful both in everyday life and also in top secret projects, like the cracking of the Enigma machine during World War II.
URL: https://www.coursera.org/course/crypto
The course is starting next year Jan 5, so bookmark the page if you are interested!
I will be joining the course too.
Featured book:
The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography
In his first book since the bestselling Fermat’s Enigma, Simon Singh offers the first sweeping history of encryption, tracing its evolution and revealing the dramatic effects codes have had on wars, nations, and individual lives. From Mary, Queen of Scots, trapped by her own code, to the Navajo Code Talkers who helped the Allies win World War II, to the incredible (and incredibly simple) logisitical breakthrough that made Internet commerce secure, The Code Book tells the story of the most powerful intellectual weapon ever known: secrecy.
Throughout the text are clear technical and mathematical explanations, and portraits of the remarkable personalities who wrote and broke the world’s most difficult codes. Accessible, compelling, and remarkably far-reaching, this book will forever alter your view of history and what drives it. It will also make yo wonder how private that e-mail you just sent really is.
Source: http://en.wikipedia.org/wiki/Mathematical_coincidence
If you have a calculator, check out the value of 
Why is it so close to the integer 20? Is it a coincidence (few things in Math are coincidence), or is it a sign of something deeper? e and Pi are two very fundamental numbers in Math, and the very fact that 
This was observed by a few mathematicians (Conway, Sloane, Plouffe, 1988) many years ago, but till this day there is no answer.
Do give it a thought!
Featured book:
Pi: A Biography of the World’s Most Mysterious Number
We all learned that the ratio of the circumference of a circle to its diameter is called pi and that the value of this algebraic symbol is roughly 3.14. What we weren’t told, though, is that behind this seemingly mundane fact is a world of mystery, which has fascinated mathematicians from ancient times to the present. Simply put, pi is weird. Mathematicians call it a “transcendental number” because its value cannot be calculated by any combination of addition, subtraction, multiplication, division, and square root extraction.
In this delightful layperson’s introduction to one of math’s most interesting phenomena, Drs. Posamentier and Lehmann review pi’s history from prebiblical times to the 21st century, the many amusing and mind-boggling ways of estimating pi over the centuries, quirky examples of obsessing about pi (including an attempt to legislate its exact value), and useful applications of pi in everyday life, including statistics.
This enlightening and stimulating approach to mathematics will entertain lay readers while improving their mathematical literacy.
Also check out: Recommended Books for GEP
PSLE Results will be out tomorrow!
Wishing all students and parents all the best. 🙂
Currently, the PSLE Top Scorer is not released in mainstream media unlike in the past. It is perhaps a good thing too, to make PSLE less stressful.
PSLE is a stepping stone for students, it is important to remember that there is still a long way ahead. Many students who didn’t do well in PSLE end up excelling in O Levels. Education is really about lifelong learning.
1The results of the 2014 Primary School Leaving Examination (PSLE) will be released on Friday, 21 November 2014. Students may obtain their result slips from their respective primary schools from 11.00 am on 21 November 2014.
Read more at: http://www.moe.gov.sg/media/press/2014/11/release-of-2014-psle-results-and-2014-secondary-one-posting.php
Featured book:
Math Doesn’t Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail
Recently I have started accepting some sponsored posts and family-friendly advertisements on my blog: https://www.fiverr.com/mathtuition88/put-permanent-link-on-my-pagerank-4-site?funnel=2014112008100627112079920
Education related guest posts are welcome.
Need to be family-friendly sites. 🙂
Link will be put on my website: http://mathtuition88.com with PageRank 4, and over 500 unique views per day.
Do check out the widely acclaimed portal Fiverr: https://www.fiverr.com/mathtuition88/put-permanent-link-on-my-pagerank-4-site?funnel=2014112008100627112079920 for more details.
Due to the educational nature of this blog, I will only accept family-friendly and kid-friendly advertisements. 🙂
Advertisements related to education will almost certainly be approved as it fits the theme of our blog.
WordPress.com accepts Sponsored Posts: http://en.support.wordpress.com/sponsored-posts/ and it is one of the ways to fund the hosting of websites. Do give it a try if you have a blog to0. 🙂
Just to test out this amazing System of Equations Widget by Wolfram Alpha:
It works! 🙂
Featured book:
Linear Algebra For Dummies
An easy-to-follow guide to practical, real-world applications of linear algebra Linear algebra is a branch of mathematics that uses matrices to solve systems of linear equations; it has applications in many disciplines, from sociology and game theory to computer programming, engineering, and business.
Here is a guide for preparing for interviews, for students about to graduate. Also useful for those applying for scholarship interviews. 🙂
Guide for Preparing for Interviews
Preparation is a vital aspect of any successful interview. After receiving an invite to attend an interview, you need be prepared in order for you to make the right kind of impression on the interviewer. This will make it possible for you to express how you will be a worthwhile addition to the company. You need to do a number of things before the interview. One of the most crucial steps towards a successful interview is research and implementing the tips on validatejob.com.
Carry out Research
Carry out enough research regarding the role you have applied for as well as what the organization does. Find out the terms of the position in regards to aspect such as whether it will be an hourly job or part time job. During this process, you will be able to establish whether you have the right set of skills and experience for the job or not. You need to find out exactly what the employer needs from you and on how you can fulfill this need through your expertise in a particular field.
Before the interview, it is a good idea to anticipate what kind of questions you should expect and practice how you will answer them. Make an effort to find out what kind of interview it will be in terms of where and how the employer will conduct it. Proper planning will ensure that you arrive at the interview earlier than expected. Give yourself enough time to get to the location of the interview and have a moment to relax before the interview starts.
Dress Appropriately and Arrive on Time
Be fully aware of what you will wear to the interview and make sure that your choice is appropriate for the day. Wear the right kind of clothes and shoes to ensure that you look professional without compromising on comfort. It is advisable for you to get enough rest before the day of the interview. You are more likely to perform well if you have enough hours of sleep.
Making a positive impression during the interview will depend on factors such as how early you arrive as well as your level of organization. You will stand out from the rest of the candidates if you arrive on time or earlier than scheduled. You will also make a long lasting impression if you show how organized you are by ensuring that you carry all relevant documentation with you.
Pay Attention and Communicate Effectively
When the interviewer asks questions, pay attention and listen keenly. This will make sure that you give the right answers and address the concerns of the interviewer. Your answers should be informative but not too long or too short. Maximize on the opportunity by ensuring that the employer knows what your best qualities are as well as their relevance to the role that you are aspiring for.
Both verbal and non-verbal communication will have an effect on the interviewer. Speak confidently and make eye contact while maintaining good posture. Your actions should mirror your words because interviewers are generally observant in regards to body language. It is normal for people to be nervous before and during interviews. However, you need to find a way to overcome your nervousness in order for you to excel at the interview. Ample preparation and practice will help to ease your nerves and calm you down.
Featured post:
Website: Research Driving Simulator
Just to introduce this website featuring Research Driving Simulator, an amazing new technology that produces training simulators for driver training.
A lot of mathematics must have been involved in creating the state of the art simulators, which are really useful. One of the reasons why science and math are so interesting nowadays.
Read more at: https://www.rijschool-simulator.nl/research_simulator.html
This is a 1 page article prepared by me for students to learn how to do Integration by Substitution, a very useful technique that can integrate many functions.
This is especially useful for students taking H2 Maths, as it is one of the two tools for integration. The other is Integration by Parts. SMU First Year Students also have to take a calculus course which includes Integration by Substitution too.
This is also my first time trying out embedding Scribd into WordPress, so that users can view the document on the website itself without downloading anything. 🙂
Print version: Integration by Substitution
Featured book:
Calculus: An Intuitive and Physical Approach (Second Edition) (Dover Books on Mathematics)
Application-oriented introduction relates the subject as closely as possible to science. In-depth explorations of the derivative, the differentiation and integration of the powers of x, and theorems on differentiation and antidifferentiation lead to a definition of the chain rule and examinations of trigonometric functions, logarithmic and exponential functions, techniques of integration, polar coordinates, much more. Clear-cut explanations, numerous drills, illustrative examples. 1967 edition. Solution guide available upon request.
Permalink: https://mathtuition88.com/list-of-schools/
Here is a list of schools of some of the students that I taught over the years:
Featured post:
Why do we use “x” in algebra? Why not “a”, “b” or even “z”?
Find out the answer here: http://gizmodo.com/why-we-use-x-as-the-unknown-in-math-1657254357
Excerpt:
For hundreds of years, x has been the go-to symbol for the unknown quantity in mathematical equations. So who started this practice?
Algebra was born in the Middle East, during the Golden Age of medieval Islamic civilization (750 to 1258 AD), and its early form can be seen in the work of Muhammad Al-Khwarizmi and his 9th century book, Kitab al-jabr wal-muqabala (al-jabr later morphing into algebra in English). During this heyday, Muslim rule and culture had expanded onto the Iberian Peninsula, where the Moors encouraged scholarship in the sciences and math.
So what does this have to do with the letter “x” in math? In a recent TED talk, the director of The Radius Foundation, Terry Moore, posited that the the use of “x” in this way began with the inability of Spanish scholars to translate certain Arabic sounds, including the letter sheen (or shin). According to Moore, the word for “unknown thing” in Arabic is al-shalan, and it appeared many times in early mathematical works. (For example, you might see “three unknown things equals 15,” with the “unknown thing” then being 5.)
But since Spanish scholars had no corresponding sound for “sh,” they went with the “ck” sound, which in classical Greek is written with the chi symbol, X. Moore theorizes, as many others before him have done, that when this was later translated into Latin, the chi (X) was replaced with the more common Latin x. This is similar to how Xmas, meaning Christmas, came about from the common practice of religious scholars using the Greek letter chi (X) as a shorthand for “Christ.”
Featured book:
Algebra Survival Guide: A Conversational Guide for the Thoroughly Befuddled
Although this is a math site, we just want to show that there is still much hope for those who really dislike math!
The catch is this: even though the jobs below do not require math skills, to enter the university courses listed below typically require good grades, inclusive of math! For example, to enter NUS or SMU Law School in Singapore, straight As are typically a prerequisite, inclusive of the highly challenging H2 Mathematics! Hence, this is a incentive for those who really dislike math to persevere through and study math well for JC! Hopefully, along the way you will find it interesting too.
Source: http://www.businessinsider.sg/high-paying-jobs-for-people-who-hate-math-2014-11/#.VGmyUPmUd8E
Did you dread math class as a kid? If so, that feeling probably didn’t go away, and you’re likely not too keen on the idea of doing math as a career.
Luckily, there are plenty of high-paying jobs for those who can’t stand the thought of crunching numbers and sifting through data all day.
We combed through the Occupational Information Network (O*NET), a US Department of Labor database that compiles detailed information on hundreds of occupations, to find positions with a median annual salary of over $65,000 that don’t require heavy math skills.
O*NET ranks how important “using mathematics to solve problems” is in any job, assigning each a “math importance level” between 1 and 100. Math-centric positions, such as mathematicians and statisticians, rank between 90 and 100 on the spectrum, while jobs such as massage therapists and actors are under 10.
Here are the highest-paying positions with a math importance level of 31 or less.
Some excerpts:
Median salary:$105,080
Math importance level: 25
Law professors teach courses in law at a university or graduate level. This title includes both those primarily engaged in teaching and those who do a combination of teaching and research.
Read the full list at: http://www.businessinsider.sg/high-paying-jobs-for-people-who-hate-math-2014-11/#.VGmyUPmUd8E
Featured book:
Teaching STEM in the Early Years: Activities for Integrating Science, Technology, Engineering, and Mathematics
Check out this very interesting video on how Pixar makes 3D Movies using Math. If you are a fan of Pixar cartoons, you must watch this! Eigenanalysis, a branch of Math mentioned in the video, seems to be related to the subject Linear Algebra, which is taught in undergraduate Math courses.
This is one of Pixar’s earlier short films, titled Geri’s game, which is also mentioned in the first video.
Featured book:
Geometric Modeling
Completely updated to include the most recent developments in the field, the third edition like the two previous editions, emphasizes clarity and thoroughness in the mathematical development of its subjects. It is written in a style that is free of jargon of special applications, while integrating the three important functions of geometric modeling: to represent elementary forms (curves, surfaces, and solids), to shape and assemble these into complex forms, and to determine geometric properties and relationships. With hundreds of illustrations, this unique book appeals to the readers visual and intuitive skills in a way that makes it easier to understand its more abstract concepts. Upper-division and graduate students, teachers, and professionals studying, teaching or practicing geometric modeling, 3D modeling, computational geometry, computer graphics applications, animation, CAD/CAM, and related subjects will find this to be a very valuable reference.
Christmas is almost here, and what could be a better Christmas present than a motivational book? Books, although viewed as old-fashioned in the current world of iPhones and iPads, are still very important learning tools that can change a person’s life.
Sometimes, bright or even gifted children don’t do well in school, because of motivational issues. Many academically weak students are actually bright students, but not focused on studies due to lack of motivation. They may feel that school is boring, or see school as a chore. Teenage years are often a difficult period of time. If successfully motivated, these children can often make a wondrous turnaround to get back on track academically.
Let me share some books that are actually purchased by viewers from my website through Amazon.com:
2)
Drive: 9 Ways to Motivate Your Kids to Achieve
3)
Empowering Underachievers: New Strategies to Guide Kids (8-18) to Personal Excellence
4)
Have a New Kid by Friday: How to Change Your Child’s Attitude, Behavior & Character in 5 Days
5)
Making Children Mind without Losing Yours
7)
Smart Parenting for Smart Kids: Nurturing Your Child’s True Potential
8)
The Motivation Breakthrough: 6 Secrets to Turning On the Tuned-Out Child
Inspirational Video by Nick Vujicic – DVD Clip from No Arms, No Legs, No Worries – Jr. High Talk
Life Without Limits: Inspiration for a Ridiculously Good Life
Latest Math News: Chinese maths teachers show way. Seems like Asia (especially China) is really going to be a world power in the next century, in terms of both education and economy. Students really need to improve their Chinese and Math skills in order to take advantage of this future trend!
See also:
Source: http://www.nottinghampost.com/Chinese-maths-teachers-way/story-24165050-detail/story.html
CHINESE maths teachers have been sharing their tips on teaching the subject to teachers in Hucknall.
The teachers, from Shanghai, were part of a pioneering exchange programme to improve lessons in the subject.
On Monday, Hillside Primary School welcomed 29 teachers, the first group to come to England as part of the exchange between the Department for Education and the Shanghai Municipal Education Commission.
Two of the visitors will spend three weeks at the school.
In September, 71 top maths teachers from England travelled to Shanghai.
One was Tom Isherwood, a maths teacher at Hillside Primary and Nursery School.
He said: “The visit to Shanghai had a profound effect on the way I approach teaching mathematics.
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Featured book:
Carson Dellosa Singapore Math Bundle Gr 1-2
Get a complete math curriculum in one with this specially bundled package of Singapore Math learning. Singapore Math is one of the leading math programs in the world! Each grade-appropriate set includes level A and B of the Singapore Math Practice series, 70 Must-Know Word Problems, Mental Math, and Step-by-Step Problem Solving. So, jump start your math learning today!
Mathtuition88 