Author: mathtuition88

Math and Education Blog

How to prove square root of 2 is irrational?

A rational number is a number that can be expressed in a fraction with integers as numerators and denominators.

Some examples of rational numbers are 1/3, 0, -1/2, etc. Now, we know that \sqrt{2}\approx 1.41421\cdots.

Is the square root of 2 rational? Or is it irrational (the opposite of rational)? How do we prove it? It turns out we can prove that the square root of two is irrational using a technique called proof by contradiction. (One of the earlier posts on this blog also used proof by contradiction to show that there are infinitely many prime numbers.)

First, we suppose that \displaystyle\sqrt{2}=\frac{p}{q}, where \displaystyle\frac{p}{q} is a fraction in its lowest terms.

Next, we square both sides to get \displaystyle 2=\frac{p^2}{q^2}.

Hence, 2q^2=p^2. We can conclude that p^2 is even since it is a multiple of 2. Thus, p itself is also even. (the square of an odd number is odd).

Thus, we can write p=2k for some integer k. Substituting this back into 2q^2=p^2, we get 2q^2=4k^2, which can be simplified to q^2=2k^2.

Hence, q^2 is also even, and hence q is also even!

But if both p and q are even, then \displaystyle\frac{p}{q} is not in the lowest terms! (we could divide them by two). This contradicts our initial hypothesis!

Thus, the only possible conclusion is that the square root of two is not a rational number to begin with!

irrational

Featured book:

Math Jokes 4 Mathy Folks

Who says math can’t be funny? In Math Jokes 4 Mathy Folks, Patrick Vennebush dispels the myth of the humorless mathematician. His quick wit comes through in this incredible compilation of jokes and stories. Intended for all math types, Math Jokes 4 Mathy Folks provides a comprehensive collection of math humor, containing over 400 jokes.

– Highly rated on Amazon.com

 

What to do if fail Mid Year Exams?

Source: http://news.asiaone.com/News/Education/Story/A1Story20080601-68205.html

When the Mid Year Exams are over, students will receive their results nervously. What to do if one fails the Mid Year Exams?

In many schools, it is common to have a significant portion of the school actually failing the Mid Term exam. “40 per cent of his school cohort failed Social Studies and 30 per cent English.” in the school mentioned in the above article.

“Such significant failure rates have become common in schools here when mid-year or preliminary exams roll around, especially for those with a big national exam – PSLE, O or A levels – at the year-end.”

Here are 5 tips on what are the best actions to take for one who fails the Mid Year Exams, especially for Mathematics:

  1. Do not be discouraged! Try to maintain a positive attitude on Math. There is still time before the final exams. With proper time management, you will be able to set aside time for revision, which will definitely help.
  2. Analyse what went wrong. Are you studying Math the correct way? (i.e. practising with understanding) Are you studying Math just by reading the textbook? (not effective for studying Math as Math needs practice.) Is time management an issue? Or is the main issue careless mistakes?
  3. Work out a new study strategy and stick to it religiously. For better results, you need to change your study habits for the better. This may include better time management, or seeking help from Math tutors.
  4. O Level Exams are not about intelligence, it is more about good study techniques. The content for O Levels can definitely be mastered by any student given the right amount of time and effort. The key is to put in time and effort to the studies. Even an average student is capable of scoring an A1 in O Levels if he or she works hard. Whereas, a very intelligent but lazy student may not do well for the exams.
  5. It is possible to improve tremendously for Maths if you study enough and using the right method. This is a truth that many people can attest to. I have seen students going from fail to A1. Improving one or two grades is also very common.

There are usually two types of students, the ones who are more playful and laidback, and the very perfectionistic student but is prone to stress. For the more playful students, the tough Mid Year exams are actually meant as a wake up call to start studying before it is too late. “‘Papers must be a bit challenging so that they can shake one out of complacency and make one study harder,’ said Mr Lak Pati Singh, 56, principal of St Patrick’s School.”

For students who are too stressed up and already trying their best, the way to improve may be to study more efficiently using the right methods (especially for Maths, the right way to study is practice with understanding). A healthy lifestyle balance may also be very helpful. Again, seeking help from Math tutors may be a choice to be considered, which can alleviate stress from not understanding the subject material.

Read more at: http://news.asiaone.com/News/Education/Story/A1Story20080601-68205.html

 

 

Studies and Studying: How do top students study?

Source: http://www.quora.com/Studies-and-Studying/How-do-top-students-study/answer/Qiaochu-Yuan-1

Check out this post by MIT almost perfect-scorer, on how to study. His secret is to study the material in advance, before the lessons even start! This is really a useful strategy, if implemented correctly. Imagine being in Primary 3 and already knowing the Primary 4 syllabus! Primary 3 Math will be a breeze then. This is one of the reasons why China students are so good at Math – they have already studied it back in China, where the Math syllabus is more advanced!

Do try out this strategy if you are really motivated to improve in your studies. The prime time to do this is during the June and December holidays – take some time to read ahead what is going to be learnt during the next semester.

This is an excerpt of the thread:

I graduated from MIT with a GPA of 4.8 (out of 5.0) in mathematics. I had two non-As, both of which were non-math classes.

That doesn’t imply that I have good study methods, but anyway, here’s how I studied at MIT. My main study method as an undergraduate, for math classes, was knowing a sizable chunk of the material in advance.

This isn’t a method that will work for everybody. I did a lot of mathematics outside of the classroom both in high school and at MIT, and I often saw a substantial portion of the material in a given class before I took it. I can’t emphasize enough how much easier this makes a class, and not just for the reasons you might expect: one of the most valuable things you get out of knowing a lot of the material already is just not being intimidated by it. (And you can get this benefit even if you’ve only seen some of the material before and possibly forgotten some of it too.) You’re much more relaxed, and that makes it easier to process the part of the material that you don’t know.

What that translates to in terms of practical advice is this:

  • cultivate a sense of curiosity,
  • don’t restrict your learning to the classroom,
  • only take classes that actually seem really interesting to you, and
  • try to learn something related to those classes the semester before.

None of this is advice for studying for a class you’re taking now, but it’s advice for reducing the extent to which you will need to study for classes you’ll take in the future.

– Qiaochu Yuan

Math News: Math student from Nanyang Technological University detects OAuth, OpenID security vulnerability

Is it safe to log in through well known sites such as Facebook and Google? Think again, for Wang Jing, a PhD student in mathematics at the Nanyang Technological University in Singapore, has detected critical security vulnerabilities in the OAuth, OpenID security protocols. (Source: http://phys.org/news/2014-05-math-student-oauth-openid-vulnerability.html) [Second article in the list below]

Forward this information to your friends via the Tweet button below to warn them of the potential danger!

Unique Math Learning Center Opens in Lake Forest: Local After-School Program to Provide …
Chicago Tribune
Mathnasium – The Math Learning Center opened its doors in Lake Forest in March to students looking for math help and math enrichment. The new …
Math student detects OAuth, OpenID security vulnerability
Phys.Org
(Phys.org) —To get right to the point, a doctoral candidate in math has discovered two holes in OAuth and OpenID that could leak data and redirect …
A math lesson for city: Teachers’ contract likely to cost billions
SILive.com
Mayor Bill de Blasio, who visited Staten Island Wednesday evening to speak at an SIEDC cocktail reception at the Hilton Garden Inn, has cleared his …
Math error halts Bank of America’s stock buy back and dividend increase
UPI.com
WILMINGTON, Del., April 28 (UPI) — Bank of America has had to halt its proposed stock buy back and dividend increase because of a math error in its …
Philadelphia girl makes math a game – and excels
Philly.com
Josephine Nyugen, a sixth-grader at St. Cecelia, right, with her father, Joseph, left, plays the math game ‘Into the Vortex’ on the First in Math website.
Math for public works borrowing bill proves tough
St. Cloud Times
Lawmakers from the Minnesota House Capital Investment Committee look around the prison yard near the loading dock inside the Minnesota …
Houghton Mifflin Harcourt takes Go Math! Academy into the home market
Boston Globe
Houghton Mifflin Harcourt, a Boston-based education company, developed the program for students in kindergarten to sixth grade to learn basic math …
Steve Ballmer’s math on Apple innovation doesn’t add up
ZDNet
His math of Apple innovation appears lacking to this longtime Mac user. Let me add a few more of his “tricks” to the list: The Apple II platform. Ballmer …
Math class helps special needs student try to win a wheelchair van
KOB.com
There’s a lot more going on than just addition and subtraction in Mr. Green’s math class. “We just want to help out this family,” Said Cody Green.
Budget math takes a U-turn: Christie blames federal tax law that brought windfall last year
NorthJersey.com
The same federal tax policy that Governor Christie is now blaming for New Jersey’s $807 million budget shortfall helped save his budget last year …

Education News Update

The Straits Times holds its first Education Forum on Sunday
Straits Times
The Straits Times’ first Education Forum on May 4, 2014, held at the Singapore Management University’s Mochtar Riady Auditorium. — ST PHOTO: …
All 300 places at The Straits Times’ first education forum this Sunday taken up
Straits Times
Mr David Hoe, an undergraduate at the National University of Singapore (NUS), is one of the speakers at the inaugural The Straits Times Education …
Many turn up at E Plus International Education fair
The Hindu
The aspirants evinced keen interest in countries like Holland, Singapore, New … Official boards of all the countries presented seminars on education …
Tuition and divorce
The Independent Singapore News
In September 2013, The Independent Singapore reported on Senior Minister of State for Education Ms Indranee Rajah’s observation on the perceived …
NS committee may propose changes to IPPT management
TODAYonline
SINGAPORE — Suggestions to improve the management of the Individual … Veterans’ League, which was founded to promote National Education.
Should India Embrace Socialism, Singapore Style?
Businessinsider India
This is because the Singapore government only borrows to develop a … What offers a ray of hope to Indian educators is that Singapore’s education …
How does one of the top-performing countries in the world think about technology?
The Hechinger Report
SINGAPORE—Forty students in bright yellow shirts hunched over their … Investments in education technology have been a key part of Singapore’s …
Why Indonesian education is in crisis
Jakarta Post
Does anyone seriously believe “education” in Indonesia is on par with the west, or even Asian countries like Japan, Korea or Singapore? Ask the …
Are you getting a little crazy in your classroom?
T.H.E. Journal
We have asked Dr. Zachary Walker, an assistant professor at the National Institute of Education, Singapore, an American who is traveling the world …
GEMS Education eyes expansion in the region
Business Times (subscription)
GEMS Education, the world’s largest operator of private schools, aims to … from kindergarten to pre-university, will open in Singapore later this year.

Riemann Hypothesis Proof

Latest News: Riemann Hypothesis Proved?

Source: http://arxiv.org/abs/1402.5952

Recently, I saw on Arxiv (an online Math journal) that a professor from South-China Normal University, Mingchun Xu, has proved the notoriously difficult Riemann Hypothesis.

Quote: “By using a theorem of Hurwitz for the analytic functions and a theorem due to T.J.Stieltjes and I. Schur, the Riemann Hypothesis has been proved considering the alternating Riemann zeta function. “

His paper can be downloaded here: http://arxiv.org/pdf/1402.5952v2

More verification is needed to check if it is indeed a proof.

What is the Riemann Hypothesis about? Watch this Youtube Video:

Featured book:

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

In 1859, Bernhard Riemann, a little-known thirty-two year old mathematician, made a hypothesis while presenting a paper to the Berlin Academy titled  “On the Number of Prime Numbers Less Than a Given Quantity.”  Today, after 150 years of careful research and exhaustive study, the Riemann Hyphothesis remains unsolved, with a one-million-dollar prize earmarked for the first person to conquer it.

Rated: 4.5 stars on Amazon

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

5 Ways to get Pi on Calculator without pressing the Pi button:

1) 22/7

22/7 is not an exact value for Pi, but it is a pretty good approximation. 22/7=3.142857143… has just a percentage error of 0.04% compared to the actual value of Pi!

Percentage error is calculated by: \displaystyle\frac{22/7-\pi}{\pi}\times 100\%=0.04\%

2) 355/113

355/113 is an even better approximation for Pi. 355/113=3.14159292… has merely a percentage error of 0.000008%! This is incredibly accurate for a “relatively” simple fraction like 355/113. 355/113 has a cool Chinese name called “Milü” 密率, given by the ancient Chinese Mathematician astronomer Zǔ Chōngzhī (祖沖之) who discovered it.

3) 3.14

Using the simple and straightforward 3.14 (0.05% error) may be sufficient for everyday purposes. 🙂

4) 2\sin^{-1}(1) or 2 arcsin(1) (Radian Mode)

This relies on the fact that \sin^{-1}(1)=\pi /2.

5) \lim_{n\to\infty}{n\sin(180^\circ/n)}

We can let n=180 for convenience, and get {180\sin(1^\circ)\approx 3.14143}. This is a pretty decent approximation for \pi, with just 0.005% error. The approximation gets better as n gets larger.

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.

 

 

Recommended Tuition Agency: Startutor

startutor

If you are wondering which tuition agency is the best, look no further. The best tuition agency in Singapore is without a doubt Startutor.

Startutor is highly recommended by our tutor Mr Wu, and he himself is listed there.

For other subjects besides Mathematics, request for a tutor at Startutor! Startutor is Singapore’s most popular online agency, providing tutors to your home. There are no extra costs for making a request. Tutors’ certificates are carefully vetted by Startutor. (Website: http://startutor.sg/request,wwcsmt)

Startutor is suitable for English Tuition, Social Studies Tuition, Geography Tuition, Physics Tuition, Chemistry Tuition, Biology Tuition, Chinese Tuition, Economics Tuition, GP Tuition, Piano Lessons and more!

Startutor: http://startutor.sg/request,wwcsmt

(Please use the link above directly, thanks!)

How to become better at Math?

 

Source: http://math.stackexchange.com/questions/766657/becoming-better-at-math?newsletter=1&nlcode=97485%7cd140

How can I become excellent at math? It really interests me but when I fail I become demotivated and begin to give up.

EDIT: Could anyone suggest books for someone with a math education that just barely touches on high-school Algebra (got into parabolas, rationalizing, some graphing and functions). This is what I am currently doing: attending high school as a Junior.

Read the answers given by experts at Math Stackexchange!

Some gems of wisdom:

Researchers have shown it takes about ten years to develop expertise in any of a wide variety of areas, including chess playing, music composition, telegraph operation, painting, piano playing, swimming, tennis, and research in neuropsychology and topology.

The key is deliberative practice: not just doing it again and again, but challenging yourself with a task that is just beyond your current ability, trying it, analyzing your performance while and after doing it, and correcting any mistakes. Then repeat. And repeat again.

All the best in your math studies!

Featured book:

Men of Mathematics (Touchstone Book)

Here is the classic, much-read introduction to the craft and history of mathematics by E.T. Bell, a leading figure in mathematics in America for half a century. Men of Mathematics accessibly explains the major mathematics, from the geometry of the Greeks through Newton’s calculus and on to the laws of probability, symbolic logic, and the fourth dimension. In addition, the book goes beyond pure mathematics to present a series of engrossing biographies of the great mathematicians — an extraordinary number of whom lived bizarre or unusual lives. Finally, Men of Mathematics is also a history of ideas, tracing the majestic development of mathematical thought from ancient times to the twentieth century. This enduring work’s clear, often humorous way of dealing with complex ideas makes it an ideal book for the non-mathematician.

Best Singapore Math Books

Just to reblog this earlier post on Recommended Singapore Math Books. Ideal for parents living outside Singapore who wish to teach their child the Singapore Math curriculum!

mathtuition88's avatarMathtuition88

We have compiled a list of Top 5 Best selling and Top rated Singapore Math Books on Amazon. This list is more targeted towards parents and students living outside Singapore, like in the United States. Students in Singapore are already breathing and living Singapore Math!

Hope this list will help you in finding the Best Singapore Math Books for your child. The reviews are from actual customers on Amazon.
1)

Singapore Math Practice, Level 1A, Grade 2

This math practice book contains wonderful teaching strategies from the Singapore math program including number bonds and counting on. This would be a good book for homeschooling. We use it as an enrichment tool when we have a little extra time during vacations or on weekends.
I would recommend it to parents who would like to teach their struggling kids math, because it tells you how to teach these concepts.

2)

Why Before How: Singapore Math Computation…

View original post 271 more words

Maclaurin Series Informal Proof

Most students will encounter the Maclaurin Series (also known as the Taylor’s Series centered at zero) when they are studying JC H2 or College Maths. The formula looks pretty intimidating at the start:

\displaystyle \boxed{f(x)=f(0)+xf'(0)+\frac{x^2}{2!}f''(0)+\cdots+\frac{x^n}{n!}f^{(n)}(0)+\cdots}

How on earth does one come up with that formula?

However, it turns out it is not that hard to prove the Maclaurin Series informally, or at least to derive the above formula. (The hard part is related to rigorous proof of convergence, etc.)

The idea is to approximate a function by a power series (a kind of infinite polynomial) and then find out what are the coefficients.

So, we assume we can write the function as such:

\boxed{f(x)=f_0+xf_1+x^2f_2+x^3f_3+\cdots+x^nf_n+\cdots\;(\dagger)}, where f_i are the coefficients of the polynomial (to be determined).

We also assume that the above equation holds for all x.

Then, letting x=0, we get f(0)=f_0. We have just found the first coefficient!

Next, we differentiate the equation (\dagger) to get:

f'(x)=f_1+2xf_2+3x^2f_3+\cdots+nx^{n-1}f_n+\cdots

Letting x=0 again, we get: f'(0)=f_1.

Now, differentiating the above equation one more time gives us:

f''(x)=2f_2+6xf_3+\cdots+n(n-1)x^{n-2}f_n+\cdots

Letting x=0 gives \displaystyle f_2=\frac{f''(0)}{2}.

Keep on differentiating, and we will see that \displaystyle f_n=\frac{f^{(n)}(0)}{n!}.

This is how we get the Maclaurin Series: 🙂

\displaystyle \boxed{f(x)=f(0)+xf'(0)+\frac{x^2}{2!}f''(0)+\cdots+\frac{x^n}{n!}f^{(n)}(0)+\cdots}

Excellent Video by Khan Academy


Calculus

Interested to learn more about Calculus? After reading this thick book about Calculus, you will probably know more Calculus than Isaac Newton himself!

 

A Math Formulas Not in the Formula Sheet

Are you looking for a list of A Maths (O Level Additional Maths) Formulae that is not found in the formula list?

Check it out at https://mathtuition88.com/math-notes-worksheets-sale/

The PDF file above contains A Maths Formulae on Algebra, Geometry & Trigonometry, and Calculus (Differentiation and Integration).

We also conduct A Maths Tuition class at Bishan.

If you find this Formula List helpful, feel free to Tweet or share this page on Facebook using the buttons below. 🙂

keep-calm-and-all-the-best-in-your-exams

SG Education News: Even Saudis are learning Singapore way of Teaching

Saudis learning the Singapore way of teaching
Straits Times
Since last October, the National Institute of Education (NIE) has taken leadership trainers from the kingdom under its wing, training them in curriculum …
All 300 places at The Straits Times’ first education forum this Sunday taken up
Straits Times
Mr David Hoe, an undergraduate at the National University of Singapore (NUS), is one of the speakers at the inaugural The Straits Times Education …
Singapore Plows Ahead of US With Tech in Schools
NBCNews.com
In the late 1990s, the Singapore Ministry of Education unveiled its master plan for technology. The first phase was spent building up infrastructure and …
Govt mulls more recognition for NSmen in housing, health, education
Channel News Asia
SINGAPORE: More recognition could be given to National Servicemen (NSmen) in areas such as housing, healthcare and education. Defence …
Singapore to beef up nuclear technology expertise
Channel News Asia
Singapore is beefing up its nuclear technology expertise with a newly-announced programme. The 10-year Nuclear Safety Research and Education …
Many turn up at E Plus International Education fair
The Hindu
The aspirants evinced keen interest in countries like Holland, Singapore, New … Official boards of all the countries presented seminars on education …
AWARE’s pushback on more benefits for NSmen ignites debate
TODAYonline
SINGAPORE — The Government’s plan to enhance housing, healthcare and education benefits for operationally ready national servicemen has …

Introduction to Ricci Flow & Poincare Conjecture

This is an interesting introduction to some extremely advanced Math: Ricci Flow & Poincare Conjecture!

Ricci Flow was used to finally crack the Poincaré Conjecture. It was devised by Richard Hamilton but famously employed by Grigori Perelman in his acclaimed proof. It is named after mathematician Gregorio Ricci-Curbastro.

In this video it is discussed by James Isenberg from the University of Oregon (filmed here at MSRI).

The famed Poincaré Conjecture – the only Millennium Problem cracked thus far.

Grigori Perelman’s paper: http://bit.ly/perelmanpaper

Math News April 28

Can Monkeys do advanced Math?

Read the below news for the answer and more!

Math wiz monkeys providing researchers with insights into human brain activity
Fox News
Monkeys trained to solve math problems are providing researchers with new insights into understanding a human learning disability in which children …
Math and Science Pay, But High Schoolers Care Less
Wall Street Journal (blog)
Math and science are the peas and carrots of the jobs market: great for a career future, but resolutely unpopular with the young. Even amid a relatively …
Math wrath in Pincher Creek?
Pincher Creek Echo
Protesters gather during a rally to support a petition calling for math curriculum reform at the Alberta Legislature Building in Edmonton, Alta., …
Monkey Math and Other Number-Crunching Critters
Discovery News
Rhesus monkeys are able to perform math at an advanced level, reports a study this week from Harvard Medical Medical school. The monkeys were …
Math department wins national award for exemplary program
The Williams record
According to Susan Loepp, professor of mathematics, the College’s department is unique in several regards. “Everyone likes math even if they don’t …
From math failure to savant: How a mugging made a numbers whiz
CTV News
Padgett describes the brutal bar attack and his subsequent transformation into a math savant in his new book, Struck by Genius: How a Brain Injury …

E Maths List of Formulae to Memorize (Not in Formula List)

Here is a compilation of the Formulas needed in GCSE O Levels E Maths Exam.

Includes Formulae on Algebra and Numbers, Geometry and Measurement, Statistics and more!

Check it out at https://mathtuition88.com/math-notes-worksheets-sale/

Students in my Maths Tuition class will be taught how to memorize the formulae with understanding, and how to apply them correctly!

Keep calm, and all the best for your mid-year exams.

Fibonacci Numbers and the Mysterious Golden Ratio

What are Fibonacci Numbers?

Fibonacci Numbers, named after Leonardo Fibonacci, is a sequence of numbers:

F_0=0, F_1=1, F_2=1, F_3=2, F_4=3, F_5=5,

with a recurrence relation F_n=F_{n-1}+F_{n-2}.

Fibonacci.jpg
Fibonacci

Relation to Golden Ratio

Fibonacci Numbers are linked to the mysterious Golden Ratio, \displaystyle \phi=\frac{1+\sqrt{5}}{2}\approx 1.61803

In fact, the ratio of successive Fibonacci numbers converges to the Golden Ratio! The first person to observe this is Johannes Kepler.

How do we prove it?

Recall the recurrence relation: F_n=F_{n-1}+F_{n-2}

Dividing throughout by F_{n-1}, we get \displaystyle \frac{F_n}{F_{n-1}}=1+\frac{F_{n-2}}{F_{n-1}}

(We will first assume \displaystyle\lim_{n\to\infty}\frac{F_n}{F_{n-1}} exists for the time being, and prove it later)

Taking limits, we get \displaystyle\lim_{n\to\infty}\frac{F_n}{F_{n-1}}=1+\lim_{n\to\infty}\frac{F_{n-2}}{F_{n-1}}.

Denoting \displaystyle\lim_{n\to\infty}\frac{F_n}{F_{n-1}} as \phi, we get:

\displaystyle \phi=1+\frac{1}{\phi}

Multiplying by \phi, we get \phi^2=\phi +1

\phi^2-\phi-1=0

This is a quadratic equation, solving using the quadratic equation, we get:

\displaystyle \phi=\frac{1\pm\sqrt{1^2-4(1)(-1)}}{2}=\frac{1\pm\sqrt{5}}{2}

Since \phi is clearly positive, we have \displaystyle \phi=\frac{1+\sqrt{5}}{2} which is the Golden Ratio!

For a complete proof, actually we will need to prove that \displaystyle\frac{F_n}{F_{n-1}} converges. This is a bit tricky and requires some algebra.

Interested readers can refer to the excellent website at: http://pages.pacificcoast.net/~cazelais/222/fib-limit.pdf

for more details.

Interesting video on Fibonacci numbers!

Fibonacci numbers and the Golden Ratio can also be used for trading stocks.

 

 

Finding E Maths or A Maths Difficult?

Are you finding Elementary Maths (E Maths) or Additional Maths (A Maths) Difficult?

Do not be discouraged if you find E Maths or A Maths difficult. The main reason why you are finding it to be difficult is that it is new. You have not gotten enough exposure to the type of questions asked. It is like learning to ride a bicycle, at the start it is difficult and you may even fall down. But after you have mastered riding the bicycle, you will be able to ride as fast as you wish. You need to get over the initial difficulty of learning in order to master the art of riding the bicycle.

At our Group Tuition at Bishan, we constantly practice actual exam questions, be it on Trigonometry, Differentiation or Integration (A Maths), or Vectors, Matrices and Probability (E Maths). We learn different methods to check and do the questions. You will find out, at last, that once you master the art of solving O Level questions, all the O Level questions are just repackaging the same questions in different forms. Once you know how to do one question, you will know how to do all similar questions. Expanding your repertoire of questions you know will enable you to get that coveted “A”. Constant practice, as opposed to cramming one month before the O Levels, is absolutely necessary to avoid panic and to consolidate our Mathematical memory.

Some Math formulas like the quotient rule, \displaystyle\frac{d}{dx}(\frac{u}{v})=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}, you will automatically memorize it once you have done enough practice.

In the end, you may even find that E Maths or A Maths is easy!

Motivational Story to motivate you

(Source: http://www.indianchild.com/inspiring_stories.htm)

THE OBSTACLE IN OUR PATH
In ancient times, a king had a boulder placed on a roadway. Then he hid himself and watched to see if anyone would remove the huge rock. Some of the king’s wealthiest merchants and courtiers came by and simply walked around it.

Many loudly blamed the king for not keeping the roads clear, but none did anything about getting the big stone out of the way. Then a peasant came along carrying a load of vegetables. On approaching the boulder, the peasant laid down his burden and tried to move the stone to the side of the road. After much pushing and straining, he finally succeeded. As the peasant picked up his load of vegetables, he noticed a purse lying in the road where the boulder had been. The purse contained many gold coins and a note from the king indicating that the gold was for the person who removed the boulder from the roadway. The peasant learned what many others never understand.

Every obstacle presents an opportunity to improve one’s condition.

Chinese Version

石头的故事

从前有一个国王，他故意派人搬来一块大石头放在道路中间。然后这个国王躲在旁边静静地观察，想知道是否会有人过来把这块大石头搬走。有几个富有的商人经过这块石头，只是直接绕过它。之后又来了几个人，他们只是埋怨国王居然没有找人来清理道路，然后仍然是绕过这块巨石走掉了。又过了一会，一个农夫经过这里，他身上背着沉甸甸的蔬菜。走到巨石的前面，把身上背的蔬菜放下，然后试着去把这块巨大的石头移到道路的旁边。农夫竭尽全力去推那块巨石，终于成功得把石头推到道路的一侧。农夫背起蔬菜准备继续赶路，却发现石头原来所在的地方下面有一个袋子。农夫好奇得打开袋子，里面有许多金币还有一个纸条。纸条是国王留下的，原来金币是用来奖励移走石头的人。
这个小故事讲述了一个简单的道理：困境也有可能是机会。遇到困难的时候，有些人会像商人那样，直接选择放弃。有些人会像那几个埋怨者，只会抱怨却不想着付出行动来改变现状。很少人会像故事中的农夫那样选择迎难而上。然而，最终收获最多的往往就是这部分迎难而上的人。
平常生活中和工作中也是这样，遇到问题，首先要不抛弃不放弃，积极寻求解决方法。无休止的抱怨只会白白错失机会，抱怨多了，好运气也会绕道而行。在困境中寻找机会方法，在挫折中吸取经验教训，那么就会很容易走出困境了，说不定还会有意外的收获哦！

Math Teachers at Play (MTaP) Blog Carnival: Top Math Blog Posts!

This is the 73rd Edition of the Math Teachers at Play (MTaP) blog carnival!

Some interesting facts about 73 from Wikipedia!:

  • Seventy-three is the 21st prime number. The previous is seventy-one, with which it comprises the 8th twin prime. It is also a permutable prime with thirty-seven. 73 is a star number.
  • 73 is the largest minimal Primitive root in the first 100000 primes. In other words, if p is one of the first 100000 primes, then at least one of the primes 3, 5, 7, 11, 13, 17, …, 73 is a primitive root modulo p.
  • 73 is the smallest prime congruent to 1 modulo 24.
  • 73 is an emirp, meaning that the reverse of 73, that is, 37, is also a prime number. Interestingly, 73 is also the 21st prime number while 37 is the 12th prime number.
  • Want to find 73 in other bases? Check out the Base Converter: Convert any number into any base!
  • Which animal is year 1973 in the Chinese Zodiac? Check out this post on the Mathematics of Chinese Zodiac!

Check out the following awesome blogs!

  • Math Strategies
    There is such an emphasis on learning math facts that our children do not spend enough time learning strategies that will help them solve math problems. Read about two types of strategies for solving math problems—working left to right and regrouping into what you know.
    – Crystal Wagner
  • Nim Games
    This is a game that is generally used to show how math can be involved in game play. I explain the rules of the game as well as the mathematical strategy involved. There is also a script where users can compete against the computer
    – Aftermath
  • Show That Questions
    This is a post around the questions that crop up in maths exams where students have to show something. I wrote it after I was surprised to hear some students hate it!
    The Straight Lines Debate
    This is a post exploring the benefits of the different methods of calculating straight lines.
    – Stephen Cavadino
  • Day 85 – Related Rates
    Two separate trucks carrying a very long wind turbine blade need to turn the corner. Describe how their speeds vary throughout the turn. The blog is dedicated to these types of discussion starters, at all levels.
    – Curmudgeon
  • The missing $1 puzzle and more
    You can read about that at the actual page it points to, http://www.homeschoolmath.net/online/favorite_challenging_puzzles.php
    : )
    – Maria
  • Eggs in the Basket Review Game
    This review game can be adapted to almost any level and any topic, yet it consistently provides a really effective way to review Algebra content.  It is a great way to review a lot of problems and have students work collaboratively while having fun – I just love hearing them explain their thought process to teammates when playing the game 🙂  With Easter almost here I thought it would be a good post to submit!
    – Mary Williams
  • Decimals in a One Frame
    Inspired by Chris Hunter’s blog post about decimals on a ten frame, I thought it would be a great opening number talk for my decimal unit to see where my students were before starting our decimal journey.
    – Kristin @MathMinds
  • Counting Basics
    – Bhaskar Lakshman
  • Circle Grid Designs
    This post is part of a series of geometrical design activities in which shapes and patterns were found in grids constructed based on circles.
    – Julie
  • Ten Sticks to Make, Count With, and Play a Game With
    Ten sticks created from common items can be just as much fun to make as well as to be used for counting by ones and tens  AND to play a game with.
    – Margo Gentile
  • Why I Always Lead with the Punchline
    I wrote this after reading another blog about how listing objectives for the day takes the punchline out of the math class.  This blog just about my thoughts on sharing the learning objectives for the entire unit with students on the first day.
    – Brooke Powers
  • My Nemesis Maths
    This post is about my journey as a teacher, trying to make maths relevant and enjoyable to all students when I myself had issues with enjoying maths as a student.
    – Danielle Myburgh
  • Quotable: Focus on Being Silent
    The best way for children to build mathematical fluency is through conversation, especially one-on-one conversation with interested adults. Check out these ideas to encourage discussion-based math.
    – Denise Gaskins
  • 2048 Free Strategy Guide
    Stuck at playing the popular and addictive Math game 2048? Do not worry, for after reading this Strategy Guide, your chance of winning will increase tremendously!

Math Teachers at Play is a traveling blog carnival. It moves around from month to month but its home base is http://letsplaymath.net/mtap/. From there you can visit the archives, submit your blog post for inclusion in a future edition, and volunteer to host the site. You can also check out the Carnival of Mathematics.  Thanks for visiting!

Subscribe to our free newsletter, for updates on Math, Education and other General Knowledge topics!

Enter your email address to subscribe to this blog and receive notifications of new posts by email.

Meaningful learning VS rote learning (Featured Post)

This is a featured post by Epigami (a tuition agency).

Source: http://www.epigami.sg/blog/dont-just-learn-understand/

In the last decade, the Singapore educational system has become a global leader in the education field, helping exemplary pupils to be accepted in the worlds best universities. But with the increasing competitiveness of those top tier universities, students are faced with mounting pressure to excel in every aspect which might have an impact on their exams. This has led to the mass implementation of ‘rote learning’ in Asia, where students focus more on memorising knowledge than the full comprehension of the concepts behind it.

What is ‘rote learning’ and what’s wrong with it?

From the earliest days of schooling, rote learning is an essential tool to efficiently memorize educational fundamentals.  It is a knowledge acquisition process based on repetition. Simply put, make a child say the alphabet every day for 6 months, and they will remember it ‘forever’. This is of course the most obvious way of learning and no other method could be better suited for the developing mind of an infant, as the concepts taught are simple in nature, and do not require a broader knowledge base.

Though, as one progresses through the ranks and gets shifted through the numerous streams put into place by the MOE, new knowledge starts to build upon old concepts, some aspects converging, others diverging, and all of if defining a complex web of knowledge which requires the student to delve into a deeper state understanding if he is to find any further use to it.

How many of us wonder at one point or another: Why am I learning this?

Read more at: http://www.epigami.sg/blog/dont-just-learn-understand/

In the last decade, the Singapore educational system has become a global leader in the education field...[read more]

Email Correspondence with Epigami Team:

Dear Mr Wu, 

Epigami has recently written an article on meaningful learning as compared to rote learning. Once again, we believe that such an article would be useful and beneficial for your students in Singapore, especially in the subject of Mathematics. You can read more about our article at: http://www.epigami.sg/blog/dont-just-learn-understand/ and we hope that you can share it with your readers on your blog. 

Thank you and have a great week ahead! 😀

Best regards, 

Sandra @ the Epigami Team

 

Best Fibonacci Number Videos on Youtube

Math is logical, functional and just … awesome. Mathemagician Arthur Benjamin explores hidden properties of that weird and wonderful set of numbers, the Fibonacci series. (And reminds you that mathematics can be inspiring, too!)

Dr James Grime on the Pisano Period – a seemingly strange property of the Fibonacci Sequence.


Fibonacci Fun: Fascinating Activities With Intriguing Numbers
From “Raising Rabbits” to “Prickly Pinecones”, 24 easy-to-use, reproducible activities and projects introduce students to Fibonacci numbers and the golden ratio. Grades 4-8

Singapore Education Top News (20 April)

MOE officers recognised for providing holistic education experience
Channel News Asia
SINGAPORE: A total of 7,103 Ministry of Education (MOE) officers were promoted this year, with some recognised for their contributions at a promotion …
Parents should start saving up early for kids’ education
Channel News Asia
Nearly all Singaporean parents want their children to get a university education — that is what a recent survey “The Value of Education: Springboard …
Education in Singapore: When Number 1 is not enough
Asian Correspondent
Singapore students pass PISA tests with flying colors, but critics say ‘so what?’, writes Zach Isaiah Chia. “Who says Singaporean’s are rote learners?
Singapore to train 3000 Saudi school principals
Arab News
Singapore’s National Institute of Education (NIE) will train 3,000 Saudi school principals over the next few years, Singapore’s Ambassador Lawrence …
CET campuses in full operation by second half of 2014
Channel News Asia
SINGAPORE: The two national Continuing Education and Training (CET) campuses will be fully operational by the second half of this year, where they …
New school-to-work transition programme to help special needs students
Channel News Asia
This was announced by Education Minister Heng Swee Keat at the official … Students attend a class at a special education school in Singapore.
Lee Kuan Yew Fund for Bilingualism supports 5 more projects
Channel News Asia
The Ministry of Education (MOE) said the fund is sponsoring another five … Brainchild Pictures, YMCA of Singapore, and Saintly Education Centre.
Boy who exposed- and fought- the education monster
The Independent Singapore News
He is Singapore’s role model. He is the boy who fought his way from Normal (Technical) Stream to a place at the National University of Singapore …
GBSN & INSEAD organize Edu Technology Summit in Singapore
MBAUniverse.com
Eminent leaders in business education and industry participated at INSEAD’s Asia campus in Singapore on April 6, 2014 to participate in a summit on …
A lesson learnt from Singapore
The Australian (blog)
Education authorities should be encouraged that the national executive of the Australian Primary Principals Association was impressed after a briefing …

http://www.pastyearpaper.com

Just to share a website on Tuition Agency and Past Year Papers.

Website:  http://www.pastyearpaper.com

Past Year Paper is an established Singapore Home Tuition Agency that brings to you quality private tutors and free exam papers for primary, secondary school to junior college level students.

Amazing Math Magic Video

http://www.ted.com In a lively show, mathemagician Arthur Benjamin races a team of calculators to figure out 3-digit squares, solves another massive mental equation and guesses a few birthdays. How does he do it? He’ll tell you.

TEDTalks is a daily video podcast of the best talks and performances from the TED Conference, where the world’s leading thinkers and doers are invited to give the talk of their lives in 18 minutes — including speakers such as Jill Bolte Taylor, Sir Ken Robinson, Hans Rosling, Al Gore and Arthur Benjamin. TED stands for Technology, Entertainment, and Design, and TEDTalks cover these topics as well as science, business, politics and the arts. Watch the Top 10 TEDTalks on TED.com, at
http://www.ted.com/index.php/talks/top10

Interested to learn more tricks? Check out these two books:

Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks

Mathemagics: How to Look Like a Genius Without Really Trying

Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks

These simple math secrets and tricks will forever change how you look at the world of numbers.
Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun.

Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.

Best Jobs in the World mostly related to Maths?

Students in school are advised to practice their Math! It turns out many of the best jobs in the 21st Century are related to Maths. Even if you are not thinking of becoming a Mathematician, it is good to know your Quadratic Equations well. Math may prove useful when you need it in your job!

Source: http://www.cbsnews.com/news/when-it-comes-to-jobs-mathematicians-are-no-1/

Want one of the best jobs in the nation? Then do the math — and do a lot of it. According to a new report, mathematicians, statisticians and actuaries are now three of the four best jobs to be had.

The CareerCast.com report ranks 200 jobs each year based on a number of criteria, including income, outlook, environmental factors, stress and physical demands. Mathematician, this year’s No. 1 job, and statistician, No. 3, both jumped up 17 places from last year’s ranking. Actuary, last year’s winner, fell to No. 4, while tenured university professor took second place on the new list.

Mathematicians came in first because demand for people who can do statistical analysis is growing in all business sectors. That need is expected to lead to a 23 percent increase in demand by 2022. As you might expect, the pay isn’t too bad. Last year, mathematicians earned a median annual salary of $101,360.

“In today’s data-driven economy, math skills unlock a world of career opportunities,” Tony Lee, CareerCast’s publisher said in a statement. “In fact, the outlook for all STEM careers is very positive, as evidenced by many of this year’s best jobs — mathematician, statistician, actuary, software engineer and computer systems analyst.”

Source: https://www.math.ucdavis.edu/~kouba/MathJobs.html

Why Choose a Mathematics-Related Profession ?

Mathematics teaches patience, discipline, and step-by-step problem-solving skills. For those with a substantial background in mathematics, an unlimited number of career opportunuities are available. According to Jobs Rated Almanac , a 1990 publication of World Almanac Books of New York, NY, careers that require a very strong background in mathematics were listed as the five “best” jobs. They were :

  • software engineer
  • actuary
  • computer systems analyst
  • computer programmer
  • mathematician

Source: http://blogs.wsj.com/atwork/2014/04/15/best-jobs-of-2014-congratulations-mathematicians/

Another day, another reason to get better at math.

It’s no secret that quantitative skills are in high demand on the job market—one analytics recruiter recently told The Journal that workers who can’t crunch numbers may ultimately face a “permanent pink slip.”

Now, a new ranking from the job-search website CareerCast.com names mathematician as the best occupation of 2014. “Math skills unlock a world of career opportunities,” publisher Tony Lee said. (Cue the Square One theme, and tune in Mathnet.)

Data whizzes of all stripes fared well in the annual list: Statisticians (No. 3), actuaries (No. 4) and computer systems analysts (No. 8) all landed near the top.

Mathematicians pull in a midlevel income of $101,360, according to CareerCast.com, and the field is expected to grow 23% in the next eight years. Other high earners include actuaries and software engineers, who can expect to earn about a midlevel income of $93,000 per year.

Speaking of math, the list is tallied by scoring 200 types of jobs according to four categories: environment, which rates things like competitiveness; income at low, middle, and high career positions; the outlook for income and employment growth; and stress factors such as travel and deadlines.

Really hate math? Want to change your mindset about Math? Read this award-winning and Top Selling Math Book:


Math Doesn’t Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail

Free Online Math Game for Very Young Kids

http://edu-games.atspace.com/

Help the Gorilla find bananas by adding the numbers correctly!

Suitable for ages 5 and above.
More games:
Math Memo – click on cards to match the correct pairs
Star alphabet – press letters on the keyboard to hear their names
Star numbers – press digits

How to Find Asymptotes of Graphs

This post is all about finding  Vertical and Horizontal asymptotes of graphs.

Vertical Asymptotes

Usually, vertical asymptotes come about when there is a rational function with a numerator and a denominator, for instance, \displaystyle y=\frac{2}{x-3}. When the denominator is 0, the function is undefined, and hence there is a vertical asymptote there.

Hence, to find the asymptote, let the denominator be 0. E.g. x-3=0, so x=3.

graph1
\displaystyle y=\frac{2}{x-3}

Another way vertical asymptotes can come about is via logarithmic graphs, e.g. y=\ln (x+2).

\ln 0 is undefined, so when x+2=0 or x=-2, there will be a vertical asymptote at x=-2.

graph2
y=\ln (x+2)

 

Horizontal Asymptote

Horizontal asymptotes usually come about when one of the terms approaches zero as x approaches infinity.

To find the Horizontal Asymptote, find the value of y when x approaches infinity (i.e. when x becomes a very big number).

For example, \displaystyle y=\frac{1}{x}+1. When x is a very big number, say x=10000, y will be close to 1 since 1/10000 is almost zero. Hence, the horizontal asymptote is y=1.

graph3
\displaystyle y=\frac{1}{x}+1

Another time where Horizontal Asymptotes appear is for Exponential Graphs. For instance, y=e^{-x}+1. When x is very large, e^{-x} will be very small, and hence y approaches 1. This means that the Horizontal Asymptote will be y=1.

exponential
y=e^{-x}+1

Note: The graphs above were drawn using the software Geogebra. 🙂

Model-Centered Learning: Pathways to Mathematical Understanding Using GeoGebra

Good Friday Math

Is it possible for Good Friday to fall on the 13th?

Source: http://mathforum.org/library/drmath/view/52364.html
From: Susan Melanson
Subject: Good Friday on the Thirteenth

How many times has Good Friday fallen on the 13th? I have looked at
your formulas and don’t seem to find one that fits this question,
since Good Friday doesn’t fall on the same date each year. I’ve looked
at some other sources as well, to no avail.

Thanks for your help on this,
Susan Melanson

Check out the above website for the answer! It turns out that Good Friday will fall on the 13th approximately once in 29 years.

Wishing all Christians a blessed Good Friday.

Also check out this Wikipedia page on how to calculate the date of Easter (http://en.wikipedia.org/wiki/Date_of_Easter)

The calculation of the date of Easter is called Computus. It turns out calculating the date of Easter is quite complicated. Even the great Mathematician Gauss made a mistake (see http://en.wikipedia.org/wiki/Date_of_Easter#Gauss_algorithm).

In 1800, the mathematician Carl Friedrich Gauss presented this algorithm for calculating the date of the Julian or Gregorian Easter[38][39] and made corrections to one of the steps in 1816.[40] In 1800 he incorrectly stated p = floor (k/3). In 1807 he replaced the condition (11M + 11) mod 30 < 19 with the simpler a > 10. In 1811 he limited his algorithm to the 18th and 19th centuries only, and stated that 26 April is always replaced with 19 April and 25 April by 18 April. In 1816 he thanked his student Peter Paul Tittel for pointing out that p was wrong in 1800.[41]

Amazon Kindle for Reading Math Books

Looking for an alternative to the Ipad? Why not try out the Amazon Kindle?

Are your books taking up too much space and collecting dust? Want to switch to Ebooks in this Electronic Age?


Kindle Fire HDX 7″, HDX Display, Wi-Fi, 32 GB – Includes Special Offers

There are many free or affordable Kindle Math Books online for download/purchase. Other than Math books, the Kindle can also be used for reading other books, and also for playing games and using apps. It is a decent alternative to the Ipad, if you are not a fan of Apple.


Kindle Paperwhite, 6″ High Resolution Display with Next-Gen Built-in Light, Wi-Fi – Includes Special Offers

Unlike tablets, Kindle Paperwhite is designed to deliver the best reading experience
  • No screen glare in bright sunlight
  • Read with one hand—over 30% lighter than iPad mini
  • Battery lasts weeks, not hours
  • Next-gen built-in light—read without eyestrain

Here are some very afforadable Kindle Math Books/Apps:

1)

Math BINGO – Kindle Fire (Kindle Tablet Edition)

Price: $0.99

Math BINGO Kindle Fire Edition!

The object of Math BINGO is to practice math facts while playing BINGO!

Features:
-Choose from 5 games: Addition, Subtraction, Multiplication, Division and Mixed
-Choose from 3 different levels of difficulty: Easy, Medium and Hard
-Create up to 5 player profiles
-Choose from 8 different fun cartoon avatars
-Keep track of number of games played by player profile
-The Scoreboard keeps track of scores for each game and level
-Collect and play with BINGO Bugs when you earn a high score!
-Fun bonus game: BINGO Bug Bungee

2)

Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks

3)

Preschool and Kindergarten Learning Games Free

FREE Learning Games for Young Children!

Check out this post on Why the Kindle Fire HDX is a far better tablet than the iPad, if you are not convinced.

“I used to think that the iPad was the king of the tablets, but not any more. It’s time to whip the crown away from Apple and give it to its rightful holder – Amazon’s Kindle Fire HDX.”

 

Check out our Top Posts at Mathtuition88.com

Top Posts for all days ending 2014-04-16 (Summarized)

All Time

Title Views
Maths Tuition Free Exam Papers (Primary, Secondary, O Levels, A Levels) Links More stats 34,478
Maths Strategy Tuition More stats 14,095
Home page / Archives More stats 11,788
Fees & Schedule More stats 5,623
Free Exam Papers (Primary, Secondary, O Levels, A Levels) Download More stats 5,541
About Tutor More stats 4,821
JC Cut Off Points More stats 4,310
Group Tuition at Bishan More stats 3,330
Maths Tuition O Level: Formula List / Formula Sheet for E Maths and A Maths More stats 2,601
How to avoid Careless Mistakes for O-Level / A-Level Maths? More stats 2,207
H2 Maths Tuition: Foot of Perpendicular (from point to line) (Part I) More stats 1,783
Maths Resources for Sale More stats 1,715
Recommended Books More stats 1,526
Sec 3 Hwa Chong Institution Maths Test Papers and Resources More stats 1,331
Academic grading in Singapore: How many marks to get A in Maths for PSLE, O Levels, A Levels More stats 1,303
Contact Us More stats 1,262
H2 Maths Tuition: Foot of Perpendicular (from point to plane) (Part II) More stats 1,211
Math Problem of the Month More stats 1,141
Math equation could help find missing MH370 plane More stats 1,122
Free Exam Papers (Primary) (Java samples) More stats 1,110
O Level Logarithm Question (Challenging) More stats 1,039
Free Exam Papers (Secondary) (Siglap) More stats 991
Ten Year Series: How many questions or papers to practice for Maths O Levels / A Levels? More stats 847
PSLE Cut Off Point More stats 816
Sec 2 IP (HCI) Revision 1: Expansion and Factorisation More stats 793

Free Math Movies

Want to watch movies about Mathematics? There is a nice website with Free Movies involving Math. It is not the full movie, but the portion of the movie that involves math.

The site is: http://www.math.harvard.edu/~knill/mathmovies/

This is a collection of movie clips in which Mathematics appears. The site is now in HTML5 video and should be accessible by all devices. If not, chose the direct video links. To include a clip into a presentation, chose the quicktime version.

Some interesting examples include: A Blackboard in linear algebra lecture at MIT on Parseval’s identity in Fourier theory. (http://www.math.harvard.edu/~knill/mathmovies/swf/goodwillhunting.html)

Another example: Young Spock learns Math. He memorizes the formula (4pi/3) r3 for the volume of the sphere, the square root of 2396324 and the definition of dimensionality log(n)/log(d). (http://www.math.harvard.edu/~knill/mathmovies/swf/startrek_spock.html)

If you are really interested in Math in the Movies, check out this book:

Math Goes to the Movies

Mel Gibson teaching Euclidean geometry, Meg Ryan and Tim Robbins acting out Zeno’s paradox, Michael Jackson proving in three different ways that 7 x 13 = 28. These are just a few of the intriguing mathematical snippets that occur in hundreds of movies. Burkard Polster and Marty Ross pored through the cinematic calculus to create this thorough and entertaining survey of the quirky, fun, and beautiful mathematics to be found on the big screen.

Math Goes to the Movies is based on the authors’ own collection of more than 700 mathematical movies and their many years using movie clips to inject moments of fun into their courses. With more than 200 illustrations, many of them screenshots from the movies themselves, this book provides an inviting way to explore math, featuring such movies as:

• Good Will Hunting• A Beautiful Mind• Stand and Deliver• Pi• Die Hard• The Mirror Has Two Faces

The authors use these iconic movies to introduce and explain important and famous mathematical ideas: higher dimensions, the golden ratio, infinity, and much more. Not all math in movies makes sense, however, and Polster and Ross talk about Hollywood’s most absurd blunders and outrageous mathematical scenes. Interviews with mathematical consultants to movies round out this engaging journey into the realm of cinematic mathematics.

This fascinating behind-the-scenes look at movie math shows how fun and illuminating equations can be.

Looking for a Math Board Game / Fun Math Game?

Look no further! In this post I will recommend the Top 5 Math Games for kids, on Amazon.com. Amazon is one of the biggest companies in the world, and is a highly trusted and respected online retailer. Sometimes, it is hard to find Math Games in the local area, the internet provides a convenient and hassle-free way to buy Fun Math Games.

Without further ado, these are the Top 5 Math Games for children:

1)

Learning Resources Sum Swamp Game

Math becomes an adventure

  • Takes kids on a journey through the Sum Swamp
  • Endless loop of adding and subtracting
  • Make your way over the crocodile shortcut
  • For 2-4 players

222 people rated it 4.8 out of 5 stars. #301 selling item in Amazon (Office Products section)

2)

Learning Resources Penguins On Ice Math Activity Set

Bars hold 10 penguins each and connect 2 ways

  • Reinforces math concepts – numbers, counting, patterning, sorting, operations, hundreds and base ten
  • Includes 10 plastic ice bars (12 x 1 Inches), 100 plastic penguins in 10 colors and Activity Guide

Rated 4.6 out of 5 stars.

3)

Learning Resources Hands-On Standards Photo-Illustrated Lessons for Teaching with Math Manipulatives-Grades 5-6

Teaches fractions, problem solving, multiplication, division, algebraic thinking and more

  • Offers problems designed to resemble questions on standardized math tests
  • Aligned with NCTM standards and expectations
  • For children between 10 to 11 years

4)

Equate: The Equation Thinking Game

Have fun creating equations crossword-style.

  • Includes a laminated playing board, 190 tiles, and 4 racks behind which players hide their tiles.
  • Ages 8 through adult. 2 to 4 players.
  • Great for the family or classroom
  • Easy to learn

5)

Carson Dellosa Math File Folder Game (140306)

Perfect for use in centers or for individual practice.

  • Challenging games include What’s Scoop, Royal Patterns, Under the Sea, Facts in Flight and more!
  • Explores concepts in place value, time, shapes, skip counting, addition and subtraction and more.
  • Includes 16 full color game boards with 21 sheets of cards, and 24 page resource guide.

If you are interested in buying Singapore Math books, please check out our post on Singapore Math books.

2048 Math Game Free Strategy Guide / Walkthrough

2048 Strategy

2048 is a highly popular Math/Puzzle game that can be played on the computer or on mobile devices. The game is about adding two tiles together until you get the number 2048.

The link for the desktop version is: http://gabrielecirulli.github.io/2048/. Alternatively, 2048 can also be enjoyed on your mobile device (or desktop), here.

Like most fun games, the concept of 2048 is deceptively simple, even a 5 year old kid could play it. However, it is hard to master it, and getting the coveted “2048” could prove quite tricky. Do not despair, for after reading this strategy guide, you have a much higher chance of winning the game!

2048
Finally…!!! This is a screenshot of my personal game

 Strategy Guide / Walkthrough / FAQ

The 3 Top Priorities for 2048 game:

1) Keep your highest tile in the top left corner of the grid. This is your top priority.

2) Do not let low tiles, especially 2’s or 4’s, clog up the upper two rows. This is your second priority.

3) Keep your top row in the following order, from left to right, 2^{n+3}, 2^{n+2}, 2^{n+1}, 2^{n}. An example would be, 512, 256, 128, 64.

The reason for Priority 1 is that this immensely increases your chances of successful merges of two higher numbers into 1. It synergises with Priority 3 to create a chain-effect. For example, imagine you have 512, 256, 128, 64 on the top row. After merging another 64 with the 64 on the top row, you will have 512, 256, 128, 128. The two 128’s can merge together, making 512, 256, 256. The two 256’s can merge together, making 512, 512. And then, we have a 1024!

The reason for Priority 2 is that letting 2 or 4’s clog up the top rows is very bad. It greatly reduces your mobility (the top 2 rows clogged up with even a single ‘2’ is hard to move). The 2 or 4’s up there have little to no chance to get merged since most of the numbers at the top are high numbers.

Top 3 Guidelines for 2048 game:

1) Press up and left arrows only. Only press right when the upper row is full. Press down only when you have utterly no other choice.

2) Keep the top row filled up, as far as possible.

3) Your general aim is to target the lowest tile on the upper row, to set up the chain effect described above.

Reason for Guideline 1: Pressing right when the upper row is not full has the chance of introducing a new tile on the upper left corner, so now your highest tile is no longer on the upper left corner. This is not good. (Violates Priority 1)

Reason for Guideline 2: Keeping the top row filled up enables you to press “right” without fear of introducing a new tile on the upper left corner.

Reason for Guideline 3: After reaching the late game, we need to think a few steps in advance, and think of which is the best move in accordance to the Top 3 Priorities, and also can target the lowest tile on the upper row to set up a chain effect.

Top 3 Time Saving Quick and Fast Tips for 2048 game

1) The first few steps do not require thinking. Just spam up and left until you get a moderately high number like 128 or 256. There is no harm done about this as the board is uncluttered and there is little chance of losing. You only need to start thinking deeper during the later part of the game, when your highest tile is 512 or more.

2) If Priority 1 is violated, i.e. your highest tile is no longer in the top left corner of the grid, try a few steps to see if you can salvage the situation and get it back to the top left corner. If no, it is better to quit and start a new game to save time. Same for Priority 2, if there is a 2 or 4 clogging the upper row, try a few more steps to see if you can salvage the situation, by merging to make a higher number. If no, we can restart to save time. Priority 3 is less crucial, if the numbers in the top row do not form 2^{n+3}, 2^{n+2}, 2^{n+1}, 2^{n}, no need to restart. But keep it in mind and keep trying your best to achieve the ideal order.

3) When there is only one possible move, make that move without thinking to save time. (No other choice anyway)

This is the best video on youtube about 2048 Strategy. (Note: They put the highest tile on the bottom right instead. Should be no difference due to the symmetry of the board)

Note: Even the expert maker of this video only has a 30% winning rate! 2048 has some element of luck (the tiles arrive randomly). Personally, I took quite some time to beat the game too.

Good luck! 🙂

Featured from Amazon:

Kindle Paperwhite, 6″ High Resolution Display with Next-Gen Built-in Light, Wi-Fi – Includes Special Offers

Unlike tablets, Kindle Paperwhite is designed to deliver the best reading experience
  • No screen glare in bright sunlight
  • Read with one hand—over 30% lighter than iPad mini
  • Battery lasts weeks, not hours
  • Next-gen built-in light—read without eyestrain

Math Weekly News

This is the list of Top Weekly Math News around the world. To view more Math News, you can scroll down to the bottom of this website, and there will be more Free Math News for your viewing.

Math, reading scores tick up; low proficiency levels persist
Milwaukee Journal Sentinel
Results from the final administration of an annual standardized reading and math exam show student achievement has ticked upward very slightly in …
Math homework gives some parents trouble
Sturgis Journal
Some educators say more and more parents are having trouble helping their young children with basic math. They say Common Core State Standards …
Math Minions are market masters: Oak Grove sixth-graders’ stock picks beat teams at top US …
WDAY
FARGO –- Oak Grove Lutheran School has some sixth-grade minions worth investing in. Math teacher Dave Carlson’s “Math Minions” posted 21.6 …
Math Field Day draws almost 700 junior, senior high school students
Southeast Missourian
Students from 28 area schools compete during the Southeast Missouri State University Department of Mathematics’ 37th annual Math Field Day …
New math app shortcuts jet-lag recovery
Financial Express
SummaryA new smartphone app uses math to help travellers alter their internal body clocks to new time zones more quickly in order to overcome jet …
Math team from UNO finishes in top 10 percent
Omaha World-Herald
Some math students at the University of Nebraska at Omaha are celebrating their finish in the top 10 percent in the annual William Lowell Putnam …
Math Academy expands program in county
Shelby Star
The summer program that serves Cleveland County Schools students to enhance their math skills is planning to have a permanent location in Kings …
Math-O-Vision Calls for Video Contest Entries
DigitalJournal.com
Here’s some math for you: High school students could win $4,000 simply by entering Math-O-Vision’s video contest to show how they see and …
Doing the math on Red Sox’ poor start
Boston Globe
NEW YORK — The Red Sox took two of three games from Baltimore to open the season and it appeared the defending World Series champions were …
STEM Heroines: Math role models for girls
Christian Science Monitor
The number of women in science, technology, engineering, and math fields is growing, but women are still a minority overall in STEM career paths.

Singapore Education News April 2014

Singapore education minister shares 4 principles on ICT use in education
FutureGov Magazine
The Ministry of Education in Singapore is now preparing for the fourth Education Master Plan. According to Heng Swee Keat, Minister for Education, …
Despite criticisms, education system delivers, says PM Lee
TODAYonline
SINGAPORE — Although the education system here has often been criticised, it is essentially a good system that has delivered good results, said …
Oman, Singapore sign MoU for cooperation in education
Times of Oman
The Ministry of Education hopes through this MoU to cooperate in the future with the National Institute of Education in Singapore for teacher training, …
Teachers urged to innovate to bring out the best in students
Channel News Asia
SINGAPORE: Education Minister Heng Swee Keat has said that whether innovation in education is successful depends on whether a child is able to …
S’pore will raise quality of all schools: PM Lee
Channel News Asia
Be it special needs or neighbourhood schools, tertiary institutions or those for special talents — Singapore will raise the quality of every educational …
Huge response for UniSIM degrees in arts, sports and music education
TODAYonline
SINGAPORE — More than 250 applications have been received for SIM … music and sports education, surpassing the number of places available.
Masagos Zulkifli meets Omani ministers in Muscat
Channel News Asia
A statement from Singapore’s Ministry of Foreign Affairs (MFA) said they … collaboration in education on teacher training and assessment systems.
Bridge students’ digital interests to school learning: Heng Swee Keat
Channel News Asia
Minister for Education Heng Swee Keat made this point on Wednesday as he … by the Ministry of Education and Academy of Principals, Singapore.
Universities need to offer ideas with ‘great impact’
TODAYonline
SINGAPORE — Senior Minister of State (Education and Law) Indranee Rajah yesterday threw down the gauntlet to Singapore universities to come up …
Jurong library sets up children’s corner to encourage early reading
TODAYonline
Minister of State, Ministry of Communications and Information and Ministry of Education, Ms Sim Ann with her youngest child, at the Early Literacy …

HCI Confession Page Math Joke

Source: https://www.facebook.com/HwaChongConfessions

“Today I asked the girl I like on FB to help me do math prob
9x-7i>3(3x-7u)
9x-7i>9x-21u
-7i>-3(7u)
-i>-3u
=
i<3u

but she go put the ans as 3u>i ruining my whole plan T.T”
-HCJC Student (M)

hwa chong


Math Girls

Math isn’t hard. Love is.
Currently in its eighteenth printing in Japan, this best-selling novel is available in English at last. Combining mathematical rigor with light romance, Math Girls is a unique introduction to advanced mathematics, delivered through the eyes of three students as they learn to deal with problems seldom found in textbooks. Math Girls has something for everyone, from advanced high school students to math majors and educators.

Praise for Math Girls!

“…the type of book that might inspire teens to realize how much interesting mathematics there is in the world—not just the material that is forced upon them for some standardized test.” “Recommended”
—CHOICE: Current Reviews for Academic Libraries

“Imagine the improbable: high-school students getting together on their own — not in a Math Club or Math Circle, not in preparation for any Math Olympiad or “regular” test, not on the advice of any of their teachers, not as part of any organized program — to talk about pure math, math more interesting than the math found in their textbooks. The three students in this book do that for the sheer love of it. That to me is the beauty and fascination of this novel for young people, mostly young people interested in math.”
—Marion Cohen, Arcadia University, MAA Reviews

“Sometimes the math goes over your head—or at least my head. But that hardly matters. The focus here is the joy of learning, which the book conveys with aplomb.”
—Daniel Pink, NYT and WSJ best-selling author of Drive and A Whole New Mind

“if you have a…teenager who’s really into math, this is a really interesting choice”
—Carol Zall, Public Radio International, The World

“Math Girls provides a fun and engaging way to learn and review mathematical concepts…the characters’ joy as they explore and discover new and old ideas is infectious.” —review, “Experiments in Manga” blog

Reviews from amazon.co.jp

“As a physics major, math has always been a painful tool to use and nothing more. But Math Girls changed the way I look at mathematics. Now I actually find it interesting!”
— “Au”

“Math Girls is a fun read, but I was surprised to find that it’s also a serious math book chock full of careful explanations. I hope that people who think they don’t like math will read it. Even when the formulas go over your head, just following the story gives you a great feel for how fun math can be.”
— “Nyanta”

“I got hooked on this book during summer vacation, and had a great time reading it by the pool. It was so good that I read it twice, the second time while working out the problems on the hotel stationary.”
— “Kei0210”

“Advanced math, explained in a playful way. But it’s not just a textbook, with dry solutions to problems. It’s a bittersweet story, with mathematics telling part of the tale. A brilliant comparison between the uncertainties of youth and the absolute proofs of symbols and numbers.”
— Shiori Oguchi

 

Paul Erdos’ Proof that there are Infinite Primes

 Paul Erdos’ Proof that there are Infinite Primes (with Examples)

Every integer can be uniquely written as rs^2, where r is square-free (not divisible by any square numbers). For instance, 6 is square-free but 18 is not, since 18 can be divided by 3^2.

We can do this by letting s^2 to be the largest square number that divides n, and then let r=n/s^2. For instance, if n=108, 6^2 is the largest square number that divides 108, so we let r=108/6^2 = 3.

Now, suppose to the contrary that a finite number k of prime numbers exists. We fix a positive integer N, and try to over-estimate the number of integers between 1 and N. Using our previous argument, each of these numbers can be written as rs^2, where r is square-free and r and s^2 are both less than N.

By the fundamental theorem of arithmetic, there are only 2^k square free numbers. (The number of subsets of a set with k elements is 2k) Since s^2<N, we have s<\sqrt{N}.

Hence, the number of integers less than N is at most 2^k \sqrt{N}. (2^k choices for r and \sqrt{N} choices for s)

i.e. \boxed{ 2^k \sqrt{N} \geq N}, for all N.

This inequality does not hold for N sufficiently large. For instance, we can let N=2^{4k}, then 2^k \sqrt{2^{4k}}=2^{3k} < 2^{4k}.

Hence, this is a contradiction, and there are infinitely many primes!

An example of how the above argument works: Suppose the only prime numbers are 2, 3, 5. (k=3)

Then, there are only 2^3=8 square-free numbers, namely, 1, 2, 3, 5, 2×3=6, 2×5=10, 3×5=15, 2x3x5=30.

For example, if we fix N=2^{12}, s< \sqrt{2^{12}}=2^6.

2^k \sqrt{2^{12}} = 2^3 \cdot 2^6 = 2^9 < N, which is a contradiction.


The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth

References:

http://en.wikipedia.org/wiki/Euclid’s_theorem#Erd.C5.91s.27s_proof

An elegant proof from Erdős

PAUL ERDOS – N IS A NUMBER

E Maths Tuition Centre

https://mathtuition88.com/group-tuition/

Singapore Math Tuition

E Maths Challenging Question

Sometimes, E Maths can seem more difficult than A Maths!

Nevertheless, exposure and practising E Maths questions will make it easier as the student gets used to the problem solving techniques required to solve “tricky” E Maths questions.

Can you solve the following E Maths Problem? 🙂

It takes 8 workers to complete a certain job. The job can be completed 2 days earlier if 8 more workers are added. How many workers are needed if the house has to be completed 3 days earlier?

E Maths Group Tuition at Bishan:
https://mathtuition88.com/group-tuition/

Singapore Math Tuition

Best Singapore Math Books

This page has moved to:

https://mathtuition88.com/buy-singapore-math-books/

The story of Euclid and the infinitude of primes

Once upon a time, there lived a Mathematician named Euclid.

Euclid came up with an ingenious method of proving that there are infinitely many prime numbers. Prime numbers are whole numbers that only have two factors, one and itself. For instance, 7 is a prime number while 6=2×3 is not.

The proof is by contradiction. Suppose that there are only a finite number of prime numbers, p_1, p_2, \cdots, p_n.

Now, we consider the number P=p_1 \cdot p_2 \cdots p_n+1.

P is either a prime number, or it is a composite number.

If P is a prime number, then we have just contradicted the assumption that there are only a finite number of prime numbers p_1, p_2, \cdots, p_n!

If P is a composite number, then, it has a factor (smaller than P). However, none of p_1, p_2, \cdots, p_n can be a factor since P divided by those primes will leave a remainder of 1! Hence, P has another factor that is not in the original list, contradicting the initial assumption once again.

(Strictly speaking, Euclid’s proof is not by contradiction, instead he used a similar argument to show that given any finite list of primes, there is at least one other prime.)

As of now, the largest known prime to mankind is 257,885,161 − 1, a number with 17,425,170 digits! (http://en.wikipedia.org/wiki/Largest_known_prime_number)


Euclid’s Elements

Tuition for All Subjects

If you are looking for tuition for other subjects, be it English Tuition, Social Studies Tuition, Geography Tuition, Physics Tuition, Chemistry Tuition, Biology Tuition, Chinese Tuition, Economics Tuition, GP Tuition or Piano/Violin Lessons …

Check out our page on Other Subjects Tuition!

We have a recommendation of a top tuition agency listed on that page, as well as top tutors in Singapore.

If you are looking for O Level E Maths and A Maths Tuition, …

Check out our page on O Level Group Tuition at Bishan!

67a2c-math1

 

Math Joke from China

Translation：

After class, Xiaogang asks Xiaodong what is the Math homework for today. Xiaodong replied, “The integer solutions of

\displaystyle \frac{x-2}{2}+3\geq x+1

1-3(x-1)<8-x

are the question numbers of the Math Homework that are due.”

A Netizen posted: “If I had such a classmate, I would say, “Sorry I don’t know you, bye””
chinese math joke

（10 分）放学时，小刚问小东今天数学作业是哪儿题，小东回答说：“不等式组

\displaystyle \frac{x-2}{2}+3\geq x+1

1-3(x-1)<8-x

的整数解就是今天数学作业的题号”，聪明的你知道今天的数学作业是哪几题吗？

E Maths Group Tuition and Why E Maths is actually more difficult than A Maths

https://mathtuition88.com/group-tuition/

Come for E Maths Tuition at Bishan! Conveniently located at Block 230 Bishan Street 23 #B1-35 S(570230), near Catholic High School.

Schedule:

  • Monday 7pm-9pm (E Maths)

(Perfect for students who have CCA in the afternoon, or students who want to keep their weekends free.)

Do not underestimate E Maths!

Those who truly understand the Maths Syllabus at Secondary Level will know that E Maths is in some ways, more difficult than A Maths. Not to mention the infamous E Maths Bell Curve, which is definitely well above 75 marks to get a chance of A1. (Some sources say the Bell Curve for E Maths is 90 marks. See http://forums.sgclub.com/singapore/questions_about_o_378705.html )

“Amaths is good, like ditzy said, I tell you, if you practise amaths everyday and do past years papers, you can see amaths quite okay one. During my secondary school years i felt that emaths more difficult than amaths.”

Source: http://sgforums.com/forums/2297/topics/401226

“You can ask many people out there, which one is more tedious and require thinking more, they’ll say emaths.
Reason simple very simple:
Emaths:
They throw an entire paragraph at you which hidden clues here and there, slight errors is almost unavoidable.
Amaths:
Short and simple, they throw question at you. Just solve. End of story.”

Source: http://forums.sgclub.com/singapore/additional_maths_hard_336484.html

“My year some speculated that E Maths A1 was as high as 90?”

Source: http://forums.sgclub.com/singapore/questions_about_o_378705.html