YouTube Video: Fibonacci Numbers and the Mysterious Golden Ratio

This is a YouTube Video, based on my earlier post on Fibonacci Numbers and the Mysterious Golden Ratio!

Thanks for watching! Remember to speed up the video when necessary!

Featured Book:

The Fabulous Fibonacci Numbers

The most ubiquitous, and perhaps the most intriguing, number pattern in mathematics is the Fibonacci sequence. In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature – from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world.

With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples).

Intro Video made using Flixpress

This is an example of Intro Video made using Flixpress!

Pretty easy to make, just take a few minutes. I will be adding more videos to my YouTube Channel soon.

Featured Page:

Math YouTube Videos

Factorize a^3-b^3 (O Level Math Tuition Question)

https://www.youtube.com/watch?v=buhghuawde0

This is my first video on YouTube! 🙂

Please subscribe to my channel for more Math Videos coming in the future!

Featured Book:

Algebra Survival Guide Workbook: Thousands of Problems To Sharpen Skills and Enhance Understanding

Mathtuition88

$latex (a-b)^3=a^3-3a^2b+3ab^2-b^3$

So,
$latex
begin{array}{rcl}
a^3-b^3&=&(a-b)^3+3a^2b-3ab^2
&=&(a-b)(a-b)^2+3a^2b-3ab^2
&=&(a-b)(a^2-2ab+b^2)+(a-b)(3ab)
&=&(a-b)(a^2+ab+b^2)
end{array}
$

View original post

Giant VS Golem: Clash of Clans Math

My previous posts on Clash of Clans Math (on Mortar damage, and Gold mine) were fairly popular, so I have decided to write one more post! This shows that Math can be applied to almost everything, even games!

Giant VS Golem: Clash of Clans Math

Giant lvl7 Vs Golem5

Recently, players of COC will know that the Level 7 Giant has been released. For fans of the Giant (I am one of them), this is great news. The Giant is a cheap substitute for tanking vs the Golem, and can be used in many strategies for instance Giwipe (Golem, Wizard, Pekka), Garch (Giant archer), among many others.

In this post, I will use Math to concretely compare the Level 7 Giant and the Level 5 Golem. For fairness sake, we will compare 6 Giants with 1 Golem (since they take up 30 spaces). Sources are taken from http://clashofclans.wikia.com/.

Health

Level 5 Golem has 6300+2×1260=8820 HP (We have factored in the 2 golemites)
Six Level 7 Giants have 6×1100=6600 HP

Conclusion: Golem is around 30% better than Giants in term of HP.

Calculation: (8820-6600)/6600 x 100%=33.6%

For pure tanking, nothing beats a max level Golem.

Damage per second

Max Golem has 54 Damage per second + a 550 damage upon death. (We have ignored Golemites damage since it is really negligible)
6 Max Giants has 6×50=300 DPS

Conclusion: Giants are 450% better than Golems in terms of DPS!

This can be quite significant, for example, when using Giants in Giwipe, often one does not even need to use wallbreakers, since the giants can break through the walls on their own. This frees up more spaces for wizards/other troops.

NewGiantTroopInfoImage

Against Spring Traps

Spring Traps are the ultimate nemesis of Giants, since each Spring Trap can bounce 15 Housing spaces, or 3 Giants.

Golems are unaffected by Spring Traps. (1 Golemite can be bounced by each Spring trap though)
Each Spring Trap can bounce 3 Giants. Town hall 10 has 6 Spring Traps, potentially bouncing a whopping 18 Giants.

To avoid Spring Traps, place a few barbarians before sending out your giants. Hopefully the barbarians will activate (and waste) a few spring traps.

Conclusion: Golems are more resistant to Spring Traps.

Against Inferno Towers (Multi-mode)

A Level 3 Inferno Tower does just 42 DPS to a Golem
It does 42×6=252 DPS to 6 giants.

Conclusion: Superficially, it seems good that Golems take 80% less damage than giants from Multi-mode Infernos. However, a bit of thinking reveals that the inferno in multi-mode will be attacking your other troops (for example wizards) instead, together with the 1 Golem. Hence, in other words, Golems also tank 80% less damage than giants from Multi-mode Inferno towers.

Against Inferno Tower (Single Target)

This calculation gets a little complicated. The inferno (Level 3) has 36 DPS initially, then 140 DPS after 2 seconds, then a whopping 1400 DPS after 5 seconds.

To kill the initial Golem (6300 HP), the inferno tower needs to take around 9.1 seconds. The first two seconds will pump out 36×2=72 damage, next 3 seconds will pump out 140×3=420 damage, while the remaining 4.1 seconds will deal the bulk of 4.1×140=5740 damage.
To kill 1 single giant (1100 HP), the inferno tower needs around 5.5 seconds. (36×2+140×3+1400×0.5=1192) Hence to kill 6 giants, 5.5×6=33 seconds is needed.

Conclusion: Giants survive 260% longer than Golems under Inferno (Single Target) Fire!

Inferno3

Other last points to note are that everytime a giant dies, there is a switch of targets, potentially attacking weak but crucial units like wizards or witches. This is a downside of giants.

So, who do you think is better? Giants or Golems? Leave your comments below!

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Trisecting an Angle (Possible?) [Very Interesting Videos]

In O Level E Maths, we learn how to bisect an angle using compass and straightedge (ruler). However, is it possible to trisect an angle?

It turns out it is impossible! This took 2000 years to prove, and requires the use of a very difficult theory called Galois Theory.

Check out this interesting video on trisecting angles:

It turns out it is possible to trisect angles using Origami though:

Featured Book:

Galois’ Theory Of Algebraic Equations

Galois’ Theory of Algebraic Equations gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The main emphasis is placed on equations of at least the third degree, i.e. on the developments during the period from the sixteenth to the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as “group” and “field”. A brief discussion on the fundamental theorems of modern Galois theory is included. Complete proofs of the quoted results are provided, but the material has been organized in such a way that the most technical details can be skipped by readers who are interested primarily in a broad survey of the theory. This book will appeal to both undergraduate and graduate students in mathematics and the history of science, and also to teachers and mathematicians who wish to obtain a historical perspective of the field. The text has been designed to be self-contained, but some familiarity with basic mathematical structures and with some elementary notions of linear algebra is desirable for a good understanding of the technical discussions in the later chapters.

Liu Hong (Ancient Chinese Mathematician)

Source: Baidu Encyclopedia (Liu Hong)

刘洪(约公元130～210)，字元卓，东汉泰山郡蒙阴县（今山东省临沂市蒙阴县）人，东汉鲁王刘兴后裔，我国古代杰出的天文学家和数学家，珠算发明者，被后世尊为“算圣”。

Liu Hong (Year 130~210) was an ancient Chinese Mathematician who studied astronomy and mathematics. He was the inventor of the art of abacus arithmetic, and hence was given the title of “Sage of Arithmetic”.

Recently, I was fortunate to visit a statue of Liu Hong at his birthplace (modern day Linyi).

(Me beside statue of Liu Hong at Linyi People’s Square, Shandong)

Featured Book:

How To Use A Chinese Abacus: A step-by-step guide to addition, subtraction, multiplication, division, roots and more.

This book will teach you step-by-step how to perform addition, subtraction, division, multiplication, square roots and cube roots on a Chinese abacus. It also explains the ancient ‘extra bead’ method and the ‘suspended bead’ method. Great for both children and adults. Clearly explained with text and pictures throughout every stage of your calculation.

Discriminant of Quadratic Polynomial Olympiad Question

The discriminant of a quadratic polynomial ( $b^2-4ac$ ) is a source of confusion for many students taking O Level A Maths. After explaining, students usually will understand the concept, but it remains really tricky. It is a really useful concept, and can be used here in this Math Olympiad Question:

Question:

Solution: http://www.fen.bilkent.edu.tr/~cvmath/Problem/1411a.pdf

One of the above people who answered correctly, Toshihiro Shimizu, is an IMO Gold Medalist from Japan.

Featured Book:

Mathematical Olympiad Challenges

Highly Rated on Amazon!

Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory

Historical insights and asides are presented to stimulate further inquiry

Emphasis is on creative solutions to open-ended problems

Domain and Range of Inverse Helpsheet

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.

View this document on Scribd

Featured Book:

Motivational Books for Students and Teenagers

What are the Main Careers in Automobile Industry?

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.

AuthorBio

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.

Fourier Series Videos

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.

Should I take H1 or H2 Maths?

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

What Maths do Engineers Learn: Singapore Engineering Maths (University) Tuition

Some of the Maths topics that Engineering Students need to learn are:

Fourier Series
Laplace Transform
Total and Partial Differentiation
Line Integral

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.

Second-derivative Test For Extrema Of Functions Of Two Variables

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)

Movie Math Quiz

Source: Spiked Math

$Spiked Math Comic - Movie Math Quiz 5$

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!

Undergrad Math Tuition: Maxima and Minima (Multivariable Calculus)

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!

View this document on Scribd

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. 🙂

H2 Maths Tuition: Integration by Parts

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.

View this document on Scribd

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. 🙂

Matchstick Problem

Translation: How do we move only 1 matchstick to make the equation valid?

(“Not Equals” sign $\neq$ is not allowed)

This is a really tricky question… Hint: Need to think in Chinese, this is a Chinese joke 😛

Featured Post:

Motivational Books for Students (Educational)

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. 🙂

The Math that won World War II: Free Online Course

Cryptography Online Course

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.

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

Source: http://en.wikipedia.org/wiki/Mathematical_coincidence

If you have a calculator, check out the value of $e^\pi-\pi$ . It is 19.99909998…

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 $e^\pi-\pi\approx 20$ may well mean something.

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.

System of Equations Solver App / Widget

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.

Integration by Substitution (H2 Maths Tuition)

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. 🙂

View this document on Scribd

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.

List of Schools Taught

Permalink: https://mathtuition88.com/list-of-schools/

List of Schools of students taught by Mr Wu (Maths Tuition)

Here is a list of schools of some of the students that I taught over the years:

Anglo-Chinese School (Independent) (ACS(I))
Barnard College, (Columbia University, USA)
Cedar Girls’ Secondary School
Clementi Town Secondary School
Henry Park Primary School
Hwa Chong Institution (HCI)
Jurong Junior College (JJC)
Kuo Chuan Presbyterian Secondary School
Mayflower Secondary School
Methodist Girls’ School (MGS)
Millennia Institute (MI)
Nanyang Girls’ High School (NYGH)
Pei Hwa Presbyterian Primary
Pioneer JC (PJC)
Singapore Management University (SMU)
St Andrew’s Secondary School
Yishun Junior College (YJC)
Private Candidate (Candidates retaking exams)

Featured post:

List of Motivational Books for Students

Why We Use “X” as the Unknown in Math

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

25 High-Paying Jobs For People Who Hate Math

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:

2. Law Teacher, Postsecondary

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

Love Math Graphs!

How to remember graphs?

Many students have a hard time remembering how graphs look like.

Here is a humorous cartoon (suitable for Valentine’s Day) on how some graphs look like!

Remember, Maths is not just about exams, homework, or getting A1/A2. Maths, above all, is about the LOVE of learning and thinking.

$math graphs$

Featured book:

Love and Math: The Heart of Hidden Reality

A New York Times Science Bestseller

What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren’t even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry.

In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we’ve never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.

Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before.

At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

Learning Pyramid (How to Learn Maths)

learning_pyramid

The best way to learn maths is actually to teach others. The second best way to learn maths is to practice doing it!

Featured book:

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

From a well-known actress, math genius and popular contestant on “Dancing With The Stars”—a groundbreaking guide to mathematics for middle school girls, their parents, and educators

As the math education crisis in this country continues to make headlines, research continues to prove that it is in middle school when math scores begin to drop—especially for girls—in large part due to the relentless social conditioning that tells girls they “can’t do” math, and that math is “uncool.” Young girls today need strong female role models to embrace the idea that it’s okay to be smart—in fact, it’s sexy to be smart!

It’s Danica McKellar’s mission to be this role model, and demonstrate on a large scale that math doesn’t suck. In this fun and accessible guide, McKellar—dubbed a “math superstar” by The New York Times—gives girls and their parents the tools they need to master the math concepts that confuse middle-schoolers most, including fractions, percentages, pre-algebra, and more. The book features hip, real-world examples, step-by-step instruction, and engaging stories of Danica’s own childhood struggles in math (and stardom). In addition, borrowing from the style of today’s teen magazines, it even includes a Math Horoscope section, Math Personality Quizzes, and Real-Life Testimonials—ultimately revealing why math is easier and cooler than readers think.

A Mind For Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)

Featured book:

A Mind For Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)

Whether you are a student struggling to fulfill a math or science requirement, or you are embarking on a career change that requires a higher level of math competency, A Mind for Numbers offers the tools you need to get a better grasp of that intimidating but inescapable field. Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life.

In A Mind for Numbers, Dr. Oakley lets us in on the secrets to effectively learning math and science—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn math. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. A Mind for Numbers shows us that we all have what it takes to excel in math, and learning it is not as painful as some might think!

The Scientific (Mathematical) Way to Cut a Cake

Ever wondered if there is an alternative way to cutting cake so that it can stay fresh and softer in the refrigerator?

This is how!

Featured book:

The Calculus Lifesaver: All the Tools You Need to Excel at Calculus (Princeton Lifesaver Study Guide)

For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it.

All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner’s popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A’s but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an “inner monologue”–the train of thought students should be following in order to solve the problem–providing the necessary reasoning as well as the solution. The book’s emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory.

The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus.

Serves as a companion to any single-variable calculus textbook
Informal, entertaining, and not intimidating
Informative videos that follow the book–a full forty-eight hours of Banner’s Princeton calculus-review course–is available at Adrian Banner lectures
More than 475 examples (ranging from easy to hard) provide step-by-step reasoning
Theorems and methods justified and connections made to actual practice
Difficult topics such as improper integrals and infinite series covered in detail
Tried and tested by students taking freshman calculus

World Cup Math

World Cup Math: Birthday Paradox

Source: http://www.bbc.com/news/magazine-27835311

It’s puzzling but true that in any group of 23 people there is a 50% chance that two share a birthday. At the World Cup in Brazil there are 32 squads, each of 23 people… so do they demonstrate the truth of this mathematical axiom?

Imagine the scene at the Brazilian football team’s hotel. Hulk and Paulinho are relaxing after another stylish win. Talk turns from tactics to post World Cup plans.

“It’ll be one party after another,” says Hulk, confidently assuming Brazilian victory on home soil. “First the World Cup, then my birthday a couple of weeks later.”

“Your birthday’s in July?” replies Paulinho. “Me too – 25 July, when’s yours?

“No way, exactly the same day!” exclaims Hulk incredulously. “What are the chances of that?”

With 365 days in a regular year, most people’s intuitive answer would probably be: “Pretty small.”

But in this case our intuition is wrong – and the proof of that is known as the birthday paradox.

Hulk and Paulinho

Also read our earlier post on Understanding the Birthday Paradox!

Featured book:

The Math of Sports: Integrating Math in the Real World (Integrating Math in the Real World Series)

Dyscalculia — A Parent’s Guide

Dyscalculia specialist Ronit Bird talks about the difficulties some children have in developing number sense and learning basic arithmetic. She explains some of the common symptoms and indicators for dyscalculia and offers suggstions for how parents can help their children at home. For more information on Dyscalculia please visit http://www.ronitbird.com/

Featured book:

The Dyscalculia Toolkit: Supporting Learning Difficulties in Maths

‘The new dyscalculia toolkit has a great introduction that is broken down into manageable chunks, brilliant explanations and interesting reading. The new tables explain what each game entails at the start of the book, making planning and using the toolkit much easier and effective especially if short on time! Very enjoyable to read, and highly recommended’
-Karen Jones, Chartered Educational Psychologist, The Educational Guidance Service

With over 200 activities and 40 games this book is designed to support learners aged 6 to 14 years, who have difficulty with maths and numbers. Ronit Bird provides a clear explanation of dyscalculia, and presents the resources in a straightforward fashion.

The Monty Hall Problem

This is the clearest and most interesting explanation of the Monty Hall Problem I have ever seen:

What is the Monty Hall Problem? It is basically a game show with 3 doors. Behind one of the doors is a car, while behind the other two doors are two goats. Most people will want to get the car of course.

The player gets a chance to choose one of the doors. Then, the host will open a door which contains a goat. Now, the player is allowed two choices: either stick to his original choice, or switch to the other unopened door. Which choice is better?

Watch the video to find out!

Featured book:

The Monty Hall Problem: The Remarkable Story of Math’s Most Contentious Brain Teaser

Mathematicians call it the Monty Hall Problem, and it is one of the most interesting mathematical brain teasers of recent times. Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host–call him Monty Hall–opens a different door, always choosing one he knows to be empty. Left with two doors, will you do better by sticking with your first choice, or by switching to the other remaining door? In this light-hearted yet ultimately serious book, Jason Rosenhouse explores the history of this fascinating puzzle. Using a minimum of mathematics (and none at all for much of the book), he shows how the problem has fascinated philosophers, psychologists, and many others, and examines the many variations that have appeared over the years. As Rosenhouse demonstrates, the Monty Hall Problem illuminates fundamental mathematical issues and has abiding philosophical implications. Perhaps most important, he writes, the problem opens a window on our cognitive difficulties in reasoning about uncertainty.

Singapore Education News

PSLE tweaks will come but as part of broader changes to education system: Heng
Straits Times
SINGAPORE – Changes being made to the Primary School Leaving … be done in the light of the broader changes to Singapore’s education system, …

SMU to broaden learning for freshmen
Straits Times
Freshmen entering the Singapore Management University (SMU) in August next year will go through a revamped syllabus, in the university’s bid to …

MOE to focus on tertiary, secondary education before turning to PSLE
Channel News Asia
SINGAPORE: With the Character and Citizenship Education syllabus being rolled out in all schools, the Ministry of Education (MOE) will tilt its focus …

How many Pentagons and Hexagons are there on a Soccer Ball?

Watch the above video to prove that there has to be 12 Pentagons and 20 Hexagons on a Soccer Ball!

The video also teaches us about the beautiful Euler Formula, $\boxed{V-E+F=2}$ .

Featured Book:

Euler: The Master of Us All (Dolciani Mathematical Expositions, No 22)

An ideal book for enlivening undergraduate mathematics…he (Dunham) has Euler dazzling us with cleverness, page after page. — Choice

Mathematician William Dunham has written a superb book about the life and amazing achievements of one of the greatest mathematicians of all time. Unlike earlier writings about Euler, Professor Dunham gives crystal clear accounts of how Euler ingeniously proved his most significant results, and how later experts have stood on Euler’s broad shoulders. Such a book has long been overdue. It will not need to be done again for a long long time. — Martin Gardner

William Dunham has done it again! In “Euler: the Master of Us All”, he has produced a masterful portrait of one of the most fertile mathematicians of all time. With Dunham’s beautiful clarity and wit, we can follow with amazement Euler’s strokes of genius which laid the groundwork for most of the mathematics we have today. — Ron Graham, Chief Scientist, AT&T

William Dunham has written a superb book about the life and amazing achievements of one of the greatest mathematicians of all time. Unlike earlier writings about Euler, Dunham gives crystal clear accounts of how Euler ingeniously proved his most significant results, and how later experts have stood on Euler’s broad shoulders. Such a book has long been overdue. It will not need to be done again for a long, long time.Martin Gardner

Dunham has done it again! In “Euler: The Master of Us All,” he has produced a masterful portrait of one of the most fertile mathematicians of all time. With Dunham’s beautiful clarity and wit, we can follow with amazement Euler’s strokes of genius which laid the groundwork for most of the mathematics we have today. — Ronald Graham, Chief Scientist, AT&T

Math Handheld Computer Game

Featured Item:

Educational Insights Math Whiz

Is your child disinterested in Math? Looking for some fun and educational Math games?

Math Whiz plays like a video game and teaches like electronic flash cards. This portable ELA quizzes kids on addition, subtraction, multiplication and division, AND works as a full-function calculator at the press of a button. Problems are displayed on the LCD screen. Features eight skill levels, as well as lights and sounds for instant feedback. Two AAA batteries required (not included).

NUS Math Ranked among Top in Asia

In the latest Quacquarelli Symonds (QS) World University Rankings by Subject (2014), NUS Math is ranked among the best mathematics departments in Asia.

nus ranking

Featured book:

Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning Series)

Chinese students typically outperform U.S. students on international comparisons of mathematics competency. Paradoxically, Chinese teachers receive far less education than U.S. teachers–11 to 12 years of schooling versus 16 to 18 years of schooling.

Studies of U.S. teacher knowledge often document insufficient subject matter knowledge in mathematics. But, they give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education.

This book describes the nature and development of the “profound understanding of fundamental mathematics” that elementary teachers need to become accomplished mathematics teachers, and suggests why such teaching knowledge is much more common in China than the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts.

The Boy With The Incredible Brain – Autism Math Documentary

This is the breathtaking story of Daniel Tammet. A twenty-something with extraordinary mental abilities, Daniel is one of the world’s few savants. He can do calculations to 100 decimal places in his head, and learn a language in a week.

He also meets the world’s most famous savant, the man who inspired Dustin Hoffman’s character in the Oscar winning film ‘Rain Man’.

This documentary follows Daniel as he travels to America to meet the scientists who are convinced he may hold the key to unlocking similar abilities in everyone.

Featured books by Daniel Tammet:

Born On A Blue Day: Inside the Extraordinary Mind of an Autistic Savant

Bestselling author Daniel Tammet (Thinking in Numbers) is virtually unique among people who have severe autistic disorders in that he is capable of living a fully independent life and able to explain what is happening inside his head.

He sees numbers as shapes, colors, and textures, and he can perform extraordinary calculations in his head. He can learn to speak new languages fluently, from scratch, in a week. In 2004, he memorized and recited more than 22,000 digits of pi, setting a record. He has savant syndrome, an extremely rare condition that gives him the most unimaginable mental powers, much like those portrayed by Dustin Hoffman in the film Rain Man.

Thinking In Numbers: On Life, Love, Meaning, and Math

The irresistibly engaging book that “enlarges one’s wonder at Tammet’s mind and his all-embracing vision of the world as grounded in numbers.” –Oliver Sacks, MD
THINKING IN NUMBERS is the book that Daniel Tammet, mathematical savant and bestselling author, was born to write. In Tammet’s world, numbers are beautiful and mathematics illuminates our lives and minds. Using anecdotes, everyday examples, and ruminations on history, literature, and more, Tammet allows us to share his unique insights and delight in the way numbers, fractions, and equations underpin all our lives.

Notes on Coordinate Geometry by Hwa Chong Institution

Coordinate Geometry Notes

Source: http://mathace2012.wiki.hci.edu.sg/

Check out these Formulas for:

Distance between 2 points
Midpoint between 2 points
Gradient Formulas
and more

at http://mathace2012.wiki.hci.edu.sg/

Featured book: The Ultimate book of Formulas (2000+ Formulas!)

Schaum’s Outline of Mathematical Handbook of Formulas and Tables, 4th Edition: 2,400 Formulas + Tables (Schaum’s Outline Series)

This Schaum’s Outline gives you

More than 2,400 formulas and tables
Covers elementary to advanced math topics
Arranged by topics for easy reference

Chinese Lucky Numbers – Numberphile

8 and 6 are lucky but 4 is unlucky… if you’re Chinese!

Featuring Xiaohui Yuan from the University of Nottingham.

Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile

Videos by Brady Haran

Brady John Haran is an Australian independent film-maker and video journalist who is known for his educational videos and documentary films produced for BBC News and for his YouTube channels. (http://en.wikipedia.org/wiki/Brady_Haran)

Highly recommended to subscribe to Numberphile on Youtube for fun and interesting Math videos!

Featured book:

Number: The Language of Science

Number is an eloquent, accessible tour de force that reveals how the concept of number evolved from prehistoric times through the twentieth century. Tobias Dantzig shows that the development of math—from the invention of counting to the discovery of infinity—is a profoundly human story that progressed by “trying and erring, by groping and stumbling.” He shows how commerce, war, and religion led to advances in math, and he recounts the stories of individuals whose breakthroughs expanded the concept of number and created the mathematics that we know today.

– Rated 4.5/5 on Amazon

News: Math, reading performance is stagnant among US 12th-graders, assessment finds

Math, reading performance is stagnant among US 12th-graders, assessment finds
Washington Post
The nation’s high school seniors have shown no improvement in math and reading performance since 2009, and large racial achievement gaps …

Math, reading performance stagnates among US 12th-graders, assessment finds
Business Mirror
WASHINGTON—The United States’s high-school seniors have shown no improvement in math and reading performance since 2009, and large racial …

Social Math: Why Learning Math Involves More Than Writing Numbers
Huffington Post
My lifelong passion for creating better ways to learn math got its start in a school not unlike the Israeli one I visited — and at the very same age.

Math games aim to keep kids sharp over summer
Scranton Times-Tribune
JAKE DANNA STEVENS / STAFF PHOTOGRAPHER Kaylynn Howe, 8, left, and her sister, Destine Howey, play a math game at Bancroft Elementary …

Common Core math gains are worth the pain
New York Daily News
As more than a million New York students in grades 3-8 took the state math exams last week, a small but vocal cadre of parents railed at the new …

Lindblom Math and Science principal among Golden Apple winners
Chicago Tribune
The organization quickly realized that Mather, principal of Lindblom Math and Science Academy In Chicago’s West Englewood neighborhood was the …

Math Learning – A Universal Language?
Huffington Post
Fifth-grade students at Woodward Elementary School had an interesting math assignment this fall: watching college football games. Though …

US students’ reading, math show no progress
TheChronicleHerald.ca
WASHINGTON — In an abysmal showing, only about one-quarter of U.S. high school seniors performed solidly in math in a major assessment known …

Using math in the fight against cancer
WNYT
But a local college professor says many people don’t like math because they don’t see a connection to it. In this Friday’s STEM 13 report, learn how the …

Math Day at Molly Stark honors memory of Gail Harwood
Bennington Banner
BENNINGTON — The Molly Stark School honored a longtime teacher on Monday with “Gail Harwood Math Day.” Harwood passed away in January …

News: Singapore Education Ranked Third in World

Singapore takes third spot in global education rankings
Straits Times
Teacher Anthony Tan conducting an English lesson with a class of Primary 6 pupils at Woodlands Primary School. Singapore’s education system has …

Singapore offers Saudi Arabia help in education
Arab News
PROPOSAL: Singapore Senior Minister of State Lee Yi Shyan with Mazen Batterjee, vice chairman of the JCCI, on Wednesday. (AN photo by Irfan …

In Singapore, Training Teachers for the ‘Classroom of the Future’
Education Week News
Welcome to the Classroom of the Future—a mock-up housed by Singapore’s National Institute of Education (NIE) to demonstrate what learning might …

Singapore Polytechnic Assists CDIO Implementation At Malaysia’s Polytechnic
Bernama
PUTRAJAYA, May 6 (Bernama) — Singapore Polytechnic is assisting Malaysia on the implemention of innovative engineering education framework …

Lift education standards: Linfox boss
The Australian
“Most of our graduates are now coming out of Thailand, Vietnam, Singapore and China because they are just so well educated,” he said. “I can get …

In search of education
The News International
Unless we start investing massively in education, science, technology and innovation, as was done by Singapore, Korea, Malaysia, China and others, …

Sultanate, Singapore and the Indian Ocean
Oman Daily Observer
These are thoughtful words from your education minister (Heng Swee Keat), … a pragmatism which incidentally I believe we share with Singapore.

Direct School Admission not meant to lower academic standards
TODAYonline
In Singapore, there is no compromising a good education. Having a talent does not give a student the licence not to pursue academic excellence.

NAFA inspires
The Hindu
The safe and comfortable cosmopolitan environment Nanyang Academy of Fine Arts, Singapore makes it the perfect destination for education abroad.

Japan’s Education Minister visits SMU
Perspectives@SMU
Singapore Management University (SMU) received a special guest on its campus on 3 May 2014 – Japan’s Minister of Education, Culture, Sports, …

Monster Group

Check out this Youtube video on the Monster Group (related to Group Theory, a branch in Mathematics)

In the mathematical field of group theory, the monster group M or F₁ (also known as the Fischer–Griess monster, or the Friendly Giant) is a group of finite order. (See Wikipedia: http://en.wikipedia.org/wiki/Monster_group)

Featured book:

The Symmetries of Things

This book is written by John Conway, one of the mathematicians who worked on the Monster Group. Rated highly on Amazon.

Start with a single shape. Repeat it in some way—translation, reflection over a line, rotation around a point—and you have created symmetry.

Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments.

This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.

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:

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.
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?
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.
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.
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.

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)
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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.

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.

Giant VS Golem: Clash of Clans Math

Health

Damage per second

Against Spring Traps

Against Inferno Towers (Multi-mode)

Against Inferno Tower (Single Target)

So, who do you think is better? Giants or Golems? Leave your comments below!

Cryptography Online Course

List of Schools of students taught by Mr Wu (Maths Tuition)

2. Law Teacher, Postsecondary

World Cup Math: Birthday Paradox

Coordinate Geometry Notes

Latest News: Riemann Hypothesis Proved?

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

1) 22/7

2) 355/113

3) 3.14

4) or 2 arcsin(1) (Radian Mode)

5)

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

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