The Mystery of the Sine of Nines, and a Math Olympiad question whose answer is 2015

Here are some of the latest updates back on

These two are highly recommended to view: The Mystery of the Sine of Nines, and a Math Olympiad question whose answer is 2015.

By the way, if you are looking for a good iPhone 6 case, do consider the iPhone 6 Case, Spigen Slim Armor Case for iPhone 6 (4.7-Inch) – Metal Slate (SGP11169). I just purchased it from Amazon, and it is working well. Looks quite good quality too. By the way, buying from Amazon is much faster than buying from the Spigen Singapore website. (see the reviews of the Spigen SG Website at Hardwarezone) Amazon delivery is always fast and reliable, even when shipping from a faraway place like the US.

iPhone 6 Case, Spigen Slim Armor Case for iPhone 6 (4.7-Inch) – Metal Slate (SGP11169)


Building a strong career in Internet Marketing

Hope this post is useful for students considering studying marketing in the future!

Building a strong career in Internet Marketing

If you want to break into the internet marketing field, there’s no time like the present. According to research, the amounts dedicated to digital marketing in enterprises of all sizes will steadily increase over the course of the next few years.

The internet marketing field is rather wide, and you’ll have to choose one or two areas you’re most comfortable with, but for all of these fields, the requirements for you in order to build a strong career and hence prove your worth to prospective clients and employers will mostly be the same.

The following is a list of five things you can do to distinguish yourself as an Internet marketing consultant, given by key players in the industry:

  • Marketing experience

A diploma or degree in a marketing related field will only go so far in honing your skill as a marketer; the more valuable education is the more experience you’ll gain working different cases out in the field. Most clients and employers look for candidates who have noteworthy marketing experience, so start building your expertise as soon as possible.

While in college, take up jobs and internships that will allow you to apply your classroom education and be involved hands-on in any marketing campaigns that come around you, no matter how small. Search for internships to occupy your holiday times while you are in school, so that you create for yourself an advantage over other recent graduates once you’re churned out into the job market.

  • Understand the field

Read everything you can in the field of Internet marketing that interests you: trends and statistics, new technologies, news, terminologies, metrics etc. You should also have a good working knowledge of all the metrics and analytical tools that are applied to the measurement of the efficacy of your campaign.

There are many methods of measuring effectiveness, so you should know as many as you can, and where each can be applied in order to add value to your client’s projects and campaigns.

  • Have an online presence

Create for yourself a vibrant online presence because all your clients will look into that before taking you on. Employers are also likely to choose the candidate with the stronger online presence when they have matching qualifications. Build your personal online brand as this may also be effective if you want to launch out and begin your own Internet marketing gig.

  • Jack of all trades, master in one

It’s good to know a little something about every field of internet marketing, but it’s better to have one or two fields that you know inside out. Distinguish yourself in areas of greatest interest, but know where and how you can find assistance in any other field if the need for it arises in the course of handling your employer’s or client’s businesses.

Begin by dipping your foot into the practical and basic aspects of everything, and then narrow down to the one you’re performing the best at.

  • Peer reviews and networks

Take advantage of all opportunities to build your knowledge and networks. Engage with peers in career fairs, conferences and other meet-up forums, and exchange ideas and experience. Also take advantage of such gathering to evaluate your work and gain tips on how they can be improved. Jealously nurture your offline relationships as you do the online relationships.

Author Bio

John Lewis has 5 years’ experience in internet marketing. For more information and guidance on internet marketing and to view and receive top web reviews for design work, contact us below



Free Career Analysis (With Prizes to be Won)

Free Career Analysis (With Prizes to be Won):
Are you a Careerist, Entrepreneur, Harmoniser, Idealist, Hunter, Internationalist, or Leader?

Find out by doing this Free Career Analysis by renowned survey company Universum:

Thanks a lot for your help! You will also benefit by finding out your Career Personality, which is released at the end of the survey!

1st prize: Win a week-long trip to Singapore, Stockholm, or New York.


Free JavaScript App to split text every few characters

This is a simple JavaScript application to split characters every few characters, separated by a comma. Useful to make long strings more easy to read.


This is a simple JavaScript application that can split text every “n” characters, and add a separator of your choice in between. (E.g. separated by comma, space, semicolon, etc.) For instance, given the input:”abcde12345″, separating using the default settings will output:”ab,cd,e1,23,45″. Hope it helps!


screenshot javascript

Math Formula in WordPress vs Blogspot

Refering to How to write Math Formulas on Blogspot / Blogger, Blogspot is also capable of rendering beautiful Math Equations based on LaTeX.

blogger latex
Produced by Blogspot using MathJax

Blogger uses MathJax for rendering the Math Formulas, which look like the ones shown above.

Let’s try the WordPress version and readers can judge for themselves which is better.

\displaystyle a^p \equiv a \pmod p

\displaystyle\int_0^{\frac{\pi}{2}} \sin x\ dx=1

My personal opinion is: they look the same to be honest. However, the Blogger way of typing is much more convenient, just using $ and $$, as opposed to WordPress requiring “$latex” and “$latex\displaystyle”, which is more cumbersome especially for long texts. However, experts like Terence Tao have opted for WordPress, which shows that WordPress does probably have some advantages.

Featured Book:

The LaTeX Companion (Tools and Techniques for Computer Typesetting)

Tuition News: Tuition for toddlers – necessary or over the top?

Tuition for toddlers – necessary or over the top?

Is tuition for toddlers necessary? Some food for thought.

As a tutor, I always try to value add and teach students something that is not taught in schools, for example tips or tricks in Math, or methods to check for careless mistakes.

Also certain key concepts may not be taught in school, even in elite schools. Many students, including students from the elite Nanyang Girls’ High School or ACS(I), have no idea initially that the discriminant b^2-4ac has something to do with the quadratic formula \displaystyle\frac{-b\pm\sqrt{b^2-4ac}}{2a}. After my explanation though, they are enlightened, and finally can understand why b^2-4ac<0 means that the quadratic has no real roots! 🙂

A good tutor can help find out what the student does not know, and teach to fill in the gaps of knowledge. Without a tutor, often a student does not know what he/she does not know! (until the exam comes)

A Maths exam is not an IQ test! It is a test of knowledge and preparation, whoever is more prepared (whether through tuition or self-studying) will get more marks.

Tuition, in the right format and spirit, is actually something good. Aristotle, the philosopher, was a tutor to Alexander the Great, one of the greatest kings that ever lived.

Featured Books:

Recommended Books for GEP

Tuition Database Singapore


File Photo of Children attending preschool/kindergarten AFP News/AFP File Photo – File Photo of Children attending preschool/kindergarten

As his tutor flashed one flashcard after another to him, little Gabriel Tan glanced longingly towards the door.

A sharp look from his mother put him back in focus, and he obediently repeated the words on the flashcards.

“Can I go to the playground now, mummy?” asked the little boy hopefully.

“No, you have to do your memory exercises next,” said his tutor, pre-empting the mother’s reply, and the boy’s face fell again.

Gabriel is only three years old, but he has been receiving hour-long tuition lessons three times a week after his nursery classes so that he can “keep up” when his mother finally enrolls him at the coveted primary school she is an alumnus of – Nanyang Primary.

“I don’t think he is very smart, so to make up for that, he has extra tuition…

View original post 52 more words

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.


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

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

  1. Fourier Series
  2. Laplace Transform
  3. Total and Partial Differentiation
  4. 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.

System of Equations Solver App / Widget

Just to test out this amazing System of Equations Widget by Wolfram Alpha:

It works! 🙂

widget wolfram alpha

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.

List of Schools Taught


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

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.


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:

Featured book:

Teaching STEM in the Early Years: Activities for Integrating Science, Technology, Engineering, and Mathematics

How are 3D cartoons made? (Hint: Math!)

Check out this very interesting video on how Pixar makes 3D Movies using Math. If you are a fan of Pixar cartoons, you must watch this! Eigenanalysis, a branch of Math mentioned in the video, seems to be related to the subject Linear Algebra, which is taught in undergraduate Math courses.

This is one of Pixar’s earlier short films, titled Geri’s game, which is also mentioned in the first video.

Featured book:

Geometric Modeling

Completely updated to include the most recent developments in the field, the third edition like the two previous editions, emphasizes clarity and thoroughness in the mathematical development of its subjects. It is written in a style that is free of jargon of special applications, while integrating the three important functions of geometric modeling: to represent elementary forms (curves, surfaces, and solids), to shape and assemble these into complex forms, and to determine geometric properties and relationships. With hundreds of illustrations, this unique book appeals to the readers visual and intuitive skills in a way that makes it easier to understand its more abstract concepts. Upper-division and graduate students, teachers, and professionals studying, teaching or practicing geometric modeling, 3D modeling, computational geometry, computer graphics applications, animation, CAD/CAM, and related subjects will find this to be a very valuable reference.

      Describes and compares all the important mathematical methods for modeling curves, surfaces, and solids.


      Prepares the reader for more advanced topics, such as 3D modeling, CAD/CAM, animation, and scientific visualization.


      Incorporates references throughout the text to direct the reader to more specialized treatments of the subjects.


      Carefully designed illustrations and exercises support each mathematical concept presented.
    Offers hundreds of exercises to test the readers comprehension.


College pays students for getting a ‘C’ in math

Interesting idea. Definitely a motivation for most students!


  • Hillsborough Community College will pay up to $1,800 in cash to students who make a C or higher in three semesters of math classes.
  • Students also have the to win free textbooks.
  • HCC funds part of this experiment with additional funding coming from a George Soros organization.

Florida community college is trying to inspire students to finish their degree by doling out up to $1,800 in cash to students who make a C or higher in three semesters of math courses.

The program, called Mathematic Access Scholarship Program (MAPS), has run at Hillsborough Community College (HCC) for the past three years and is spearheaded by Manpower Demonstration Research Corporation (MDRC).

“We hoped the incentives would inspire behaviors that would lead to increased student success.”

Featured book:

Great Jobs for Math Majors, Second ed. (Great Jobs For… Series)

“What can I do with a degree in math?”

You’ve worked hard for that math degree. Now what? Sometimes, the choice of careers can seem endless. The most difficult part of a job search is starting it. This is where Great Jobs for Math Majors comes in. Designed to help you put your major to work, this handy guide covers the basics of a job search and provides detailed profiles of careers in math. From the worlds of finance and science to manufacturing and education, you’ll explore a variety of job options for math majors and determine the best fit for your personal, professional, and practical needs.

Do you want to be an actuary? Work in the banking industry? Program computers? In this updated edition, you’ll find:

  • Job-search basics such as crafting résumés and writing cover letters
  • Self-assessment exercises to help determine your professional fit
  • Investigative tools to help you find the perfect job
  • Networking tips to get your foot in the door before your résumé is even sent
  • True tales from practicing professionals about everyday life on the job
  • Current statistics on earnings, advancement, and the future of the profession
  • Resources for further information, including journals, professional associations, and online resources

254A announcement: Analytic prime number theory

Bookmark Terence Tao’s site if you are interested in his notes on Analytic number theory! He will be placing lecture notes online on his blog.
This is a one-in-a-lifetime chance to learn Analytic Number Theory from a Master — Fields Medallist Terence Tao.

What's new

In the winter quarter (starting January 5) I will be teaching a graduate topics course entitled “An introduction to analytic prime number theory“. As the name suggests, this is a course covering many of the analytic number theory techniques used to study the distribution of the prime numbers $latex {{mathcal P} = {2,3,5,7,11,dots}}&fg=000000$. I will list the topics I intend to cover in this course below the fold. As with my previous courses, I will place lecture notes online on my blog in advance of the physical lectures.

The type of results about primes that one aspires to prove here is well captured by Landau’s classical list of problems:

  1. Even Goldbach conjecture: every even number $latex {N}&fg=000000$ greater than two is expressible as the sum of two primes.
  2. Twin prime conjecture: there are infinitely many pairs $latex {n,n+2}&fg=000000$ which are simultaneously prime.
  3. Legendre’s conjecture:…

View original post 3,927 more words

Math Olympiad Question: Sum of powers of two

Is there a number that is a sum of two powers of 2, and ends with 3 zeros?

The answer is yes!

For example, 2^3+2^{253}=14474011154664524427946373126085988481658748083205070504932198000989141205000

How about n zeroes?

Check out last month’s problem of the month at:




Featured book:

104 Number Theory Problems: From the Training of the USA IMO Team

This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.

Buy yourself a present! (and a mysterious Christmas Math Equation)

It has been a long 2014, yet time flies so quickly, and we are about to end this marvelous year.

Regardless of how the beginning of the year went, it is now time to reward yourself! Check out the amazing collection of holiday items at, and buy yourself a present!

amazon gift
Shop Amazon’s Electronics Holiday Gift Finder – Find the Perfect Gift for Loved Ones

As promised this is the mysterious Christmas Equation: \displaystyle y=\frac{\ln (\frac{x}{m}-sa)}{r^2}. Why is this the Christmas Equation? Check out the video below:

Exams are over! Book disproves evolution using Math!

Finally, after an arduous year, the exams are over (in Singapore). 🙂

It is now time for a period of rest and relaxation, to get ready for 2015, where everything starts again.

Students who are looking for an early headstart (a 1 month headstart is rather valuable) in subjects other than mathematics can check out Startutor: The best tuition agency in Singapore.

Recently, I chanced upon this book:

The Organized Universe: Exclusive Scientific Proof That Darwinism Is a Fraud

What strikes me is that the author is using a Mathematical Law (Benford’s Law) to prove that Darwinism is a fraud. It is pretty unique since other books usually rely on proofs based on physics, biology or chemistry.

The Theory of Darwinian Evolution is a Fraud! Finally, a long awaited secret of the Universe. For the first time, Man has scientific proof showing a pattern to all life. Can this be possible? In this ground breaking first book, veteran researcher and inventor/scientist Karl Dahlstrom and co-author C. Phillip Clegg have written an exceptionally readable, mind expanding and almost equation free account of how an accidental discovery of an obscure mathematical theorem came to overturn an established scientific paradigm. The best theories of the universe are beautiful, simple and profound just as Einstein’s famous formula, E=MC2. This book is elegant in its simplicity and yet complex in its scope of re-defining an ordered universe. This book zeros in on a 150 year old controversy of Darwinian Evolution and tears it apart with laser like precision such that the very core of that ‘theory’ is – to borrow a phrase from Descartes – “rent asunder”. There is nothing new under the sun. Since the Big Bang, an organizing principle of matter, embedded in the natural laws of physics, and eventually life itself, has manifested itself in a precise pattern such that it is found in literally everything – from the composition of meteorites to seawater, soil, and gasses here on earth as well as in tabulated data on everything from stock prices to river lengths. This discovery, called Benford’s Law, simply states that in any tabulated data set of natural numbers, the frequency of occurrence of the digits 1 through 9, as the first significant digit, will conform to a set pattern: 1 will occur 30.x% of the time; “2” will occur 17.x%, etc. with the frequency of each succeeding number being less than the preceding number. What does this scientific law of nature have to do with Darwin’s Evolution Theory?

I have read the preview on Amazon and it seems pretty interesting. 🙂

Also, just a reminder that the Free Career Analysis Quiz by renowned survey company Universum is still active for a limited time only! Do check it out before it ends.



Are you a Careerist, Entrepreneur, Harmoniser, Idealist, Hunter, Internationalist, or Leader?

Are you a Careerist, Entrepreneur, Harmoniser, Idealist, Hunter, Internationalist, or Leader?

Find out by doing this Free Career Analysis by renowned survey company Universum:

Thanks a lot for your help! You will also benefit by finding out your Career Personality, which is released at the end of the survey!

career types

Tips on Resume Writing

Writing a resume is an important skill, both for students (applying for scholarships) and adults (applying for jobs). Check out this article on how to write a good resume! 🙂

Resume checklist for beginners – How to write your resume if you have little or no experience

Writing out a resume when you are a student or fresh out of school with no experience to speak of can be quite scary. Naturally, it would be different from what you write in a normal resume; nevertheless it is a lot simpler that it seems to be.

The core objectives for your resume:

As a beginner, your focus is straightforward, and here are the points you should keep in mind:

  • Your resume must primarily be useful to whoever will read it. Give the information that the reader needs in a concise and factual manner. Avoid verbosity.
  • Keep in mind that every potential employer comes with specific recruitment requirements. Ensure that your resume fully addresses these requirements to avoid having your application discarded at the computer-screening phase.
  • Aside from your basic information, there is no such thing as having an ‘all-purpose resume’. Modify your resume to fit what your potential employer is looking for.
  • Ensure you express your career objective concisely in your resume. If you need some help writing objectives for different job positions in different industries, you can get a number of online resources to which you can refer.
  • Conduct your research on the prospective employer’s business. If you can find an inside person it would be even better. Get as much information as you can about the position you are seeking. This will help you draft a fitting resume and avoid blunders that could cost you an employment opportunity.
  • More is not always better. Stick to the facts and avoid unnecessary floweriness. Only give additional information where you feel it would increase your competitive advantage

How to format your resume

The way you lay out your resume will be doubly important when you are at the start of your career. Remember the following:

  • Ensure that the resume is easy to read. Put the readers’ needs in mind and avoid cramming too much information into any single section.
  • Instead of employing headings, have actual demarcated sections to split the different sections of your resume. This will allow the reader to concentrate on specific sections e.g. education, work experience, qualifications etc.
  • Ensure that the resume looks professional and credible. Use color markers to separate between sections. Invest time into making it look the best.
  • Consider how much space you have. You should not cram too much information into a small space. Choose the right line spacing to ensure your resume looks light. Use short sentences.
  • Include any information you consider high value – extra-curricular activities you shone in, projects to internships you undertook that will be relevant to the post you wish to apply for.

Final checklist

The most sacrilegious thing you can do is to send your employer a half-baked, incomplete resume you worked on in the wee hours of the morning. Don’t be cheated, an employer can tell whether you gave it some thought or you simply threw together a few lines to beat the deadline.

After writing it out, ensure you check the following before sending it out:

  • Have you addressed all employer requirements?
  • Have you checked for typos and grammar errors?
  • Does it look good?
  • Have you included all your top selling points?

There, you are good to go!

Author Bio

Jane Whitaker is a human resources expert with many years’ experience. For more information on resume writing or if you need some help writing objectives for your resume, just visit our site.

Featured book:

On the Job Math Mysteries: Real-life Math from Exciting Careers, Grades 4-8

Here’s a fun and engaging new math book from Prufrock Press. On-The-Job Math Mysteries has 70 plus pages of math problems and solutions that are based upon standards set by the National Council of Teachers of Mathematics. The problems are based on real people who use math in a variety of occupations. Black and white photographs of individuals at work add to the real-life theme. Some problems include helpful diagrams and charts.
The variety of occupations covered in this book is quite diverse. In addition to those positions already noted, kids can read about how math is useful to the organic farmer, beekeeper, heavy equipment operator, software engineer, kayak guide, air traffic controller, bush pilot, and more. There are 22 occupations mentioned in all. Kids who appreciate academic work that has a purpose and real life applications will love OTJ Math Mysteries! — Lorel Shea, Editor, BellaOnline, Gifted Education

About the Author
Marya Washington Tyler has a master’s degree in gifted and talented education from the University of Wisconsin and has taught gifted and talented students for 11 years. Tyler is the author of several Prufrock bestsellers, including Real Life Math Mysteries, It’s Alive!, and Extreme Math, which she cowrote with her husband Kip. They have four wonderful, spontaneous, gifted children scattered across the country. The Tylers live in Ketchikan, AK, where they kayak, mountain climb, snowshoe, beach comb, and otherwise explore, photographing and videotaping the wonders of the Alexander Archipelago and Tongass rainforest around them. Tyler presently is working on a sequel to Real Life Math Mysteries, which will feature the mathematics faced by real Alaskans: dog mushers, float plane pilots, Native carvers, sea kayak guides, and more.


Curious Number Pattern (O Level standard)

Recently, a reader of our blog asked the following question:


May I request your help in solving this number pattern?

7/8, 2/3, 1/2, 4/11, 1/4, ? , ?

Thanks and best regards

This is indeed a tricky and curious question. Scroll down after our recommended book to find out the answer…

Featured book:

Puzzles to Puzzle You

For many, mathematics is a scary subject that they have been taught to hate right from their childhood. The subject is often termed as hard and tedious, and people hardly take the time to delve into its formulae and theories. Mathematics can be fun, though, when approached in the right way. This puzzle book shows its readers delightful ways in which they can tease their brains and make them work, through solving some very interesting maths problems. Puzzles to Puzzle You features exciting and intriguing mathematical puzzles that will help readers sharpen their maths skills in a fun way. The puzzles here are devised and presented by Shakuntala Devi, the well-known mathematical genius from India. Matching wits with the genius and trying to solve the puzzles can be a very interesting and productive activity, especially for students, children, and professionals.

Here is the answer:

7/8, 2/3, 1/2, 4/11, 1/4

when put in another form is:

7/8, 6/9, 5/10, 4/11, 3/12

As we can see, the numerator is constantly decreasing by 1, while the denominator is increasing by 1.

Hence the next two terms are: 2/13, 1/14 respectively. 🙂


Recommended IB Math Books

The IB programme is gaining popularity throughout the world. In Singapore, some schools offer the IB Programme instead of the A Levels, most notably being ACS (International).

The IB Mathematics definitely has some interesting topics, including Number Theory, Graph Theory, and even Group Theory. These interesting topics are usually not learnt in JC.

Here are some Recommended IB Math Books from

Most popular IB Math Books


IB Mathematics Standard Level (Oxford IB Diploma Programme)


Barron’s IB Math SL


IB Mathematics Higher Level Course Book: Oxford IB Diploma Program (International Baccalaureate)


Workbook – IB Diploma Math SL part 1: This is a math workbook for students doing their IB diploma programme in math SL.


Barron’s IB Math Studies

Best Rubik’s Cube (Cheap and Good) — The Dayan Zhanchi?

The Rubik’s Cube is a famous puzzle, that is related to Math and Group Theory. (See this free introduction by MIT on the The Mathematics of the Rubik’s Cube)

Recently, I am thinking of buying a new Rubik’s Cube, and searched on the internet on what is the best brand of Rubik’s Cube. For Rubik’s Cube, smoothness while turning is really important, because it will simply be easier to turn the edges if the cube is smooth.

After researching online, I came to a very surprising conclusion: The “made in China” brand Dayan Zhanchi is supposedly much better than the official Rubik’s brand (and also other “Western” brands)!

Dayan ® ZhanChi 3x3x3 Speed Cube 6-Color Stickerless

This amazing superhuman World Record is set using the Dayan Zhanchi! (2013, Mats Valk)

Other than the Dayan series, another alternative is the V-cube series:

V-CUBE 3 White Multicolor Cube

However, the reviews on Amazon seem to indicate that the Dayan is superior in both smoothness and price!

If you have any recommendations on which Rubik’s Cube is best, please write in the comments below!

I will be buying the Dayan Cube soon (hopefully in time for Christmas 2014), and will post new updates! I am most probably buying the stickerless version since I have past experience of stickers falling off from my previous cubes. (Note: Stickerless Rubik’s Cubes are banned from competitions for the ridiculous reason that it is possible to “see what colors are behind through the cracks”, see So if your goal is to enter a competition, you may want to consider the sticker version of the Zhanchi.

For parents, buying a Rubik’s cube for your child is a great investment. Playing with the Rubik’s cube is a major intellectual challenge (it has 43 quintillion permutations, only 1 of which is correct), which will develop the child’s brain for logical thinking, which is especially useful for Math and Science. Most importantly, it is fun!

Dayan ® ZhanChi 3x3x3 Speed Cube 6-Color Stickerless

Special note for buying Dayan Zhanchi from Singapore:

If you are buying the Dayan Zhanchi from Singapore, at first it seems like the Dayan ZhanChi does not ship to Singapore. It actually does! We just have to choose the correct seller, Cube Puzl, which ships to Singapore.

other sellers

cube puzl

Looking for a reliable Tuition Agency?

Looking for a reliable Tuition Agency?

Its the holiday period now, and many parents are looking to find a tutor for the next academic year. Please look no further, as Startutor is the best tuition agency in Singapore, winning hands down. I have worked with Startutor both as a tutor and an affiliate, and am impressed by their professional website (one of the best website designs around), and their professional attitude.

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:,wwcsmt)

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Interesting articles about Grade Inflation and Math


The scandal at the University of North Carolina at Chapel Hill is principally about academic dishonesty. But it highlights an institutional failure at almost all American colleges that dissuades students from pursuing the best career possible. Some academic departments systematically inflate students’ grades. And many of those departments give students the least rigorous preparation for the labor market.

Part of college is learning what you’re good at. Students use freshman-year courses to gauge their interest and aptitude in different majors. A student who receives an A in writing and a B in calculus might conclude that she’s a better writer than mathematician. But what if she actually earned the average grade in both courses?

Plenty of students who start in difficult fields such as math decide to scale back their ambitions. That’s fine if it’s a personal choice–but not if they’re doing so because they got deceptive messages from their graders.


The latest research also suggests that there could be more subtle problems at work, like the proliferation of grade inflation in the humanities and social sciences, which provides another incentive for students to leave STEM majors. It is no surprise that grades are lower in math and science, where the answers are clear-cut and there are no bonus points for flair. Professors also say they are strict because science and engineering courses build on one another, and a student who fails to absorb the key lessons in one class will flounder in the next.

After studying nearly a decade of transcripts at one college, Kevin Rask, then a professor at Wake Forest University, concluded last year that the grades in the introductory math and science classes were among the lowest on campus. The chemistry department gave the lowest grades over all, averaging 2.78 out of 4, followed by mathematics at 2.90. Education, language and English courses had the highest averages, ranging from 3.33 to 3.36.

Ben Ost, a doctoral student at Cornell, found in a similar study that STEM students are both “pulled away” by high grades in their courses in other fields and “pushed out” by lower grades in their majors.

Featured book:

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


How to join 9 Dots using 4 Lines? (Advanced Version)

This is a humorous math comic based on the popular brainteaser: How do we join 9 dots using 4 lines?

(Hint: Think out of the box. See the solution here: Answer)

However, Spiked Math has added a new twist to the riddle. Enjoy the comic!



Featured book:

Comic-Strip Math: Problem Solving: 80 Reproducible Cartoons With Dozens and Dozens of Story Problems That Motivate Students and Build Essential Math Skills

Math + Comics = Learning That’s Fun! Help students build essential math skills and meet math standards with 80 laugh-out-loud comic strips and companion mini-story problems. Each reproducible comic and problem set reinforces a key math skill: multiplication, division, fractions, decimals, measurement, geometry, and more. Great to use for small-group or independent class work and for homework! For use with Grades 3-6.

The Math of Ebola


In the past week, world leaders have started using a mathematical term when they talk about the Ebola epidemic in West Africa.

“It’s spreading and growing exponentially,” President Obama said Tuesday. “This is a disease outbreak that is advancing in an exponential fashion,” said Dr. David Nabarro, who is heading the U.N.’s effort against Ebola.

Students who have learnt how the exponential graph looks like will know that the exponential function grows extremely quickly. exponential graph

In fact, for large enough x, the exponential function e^x will be larger than any polynomial function, say x^{100}. For example, when x=700, e^{700}=1.01\times 10^{304}, while 700^{100}=3.23 \times 10^{284}.

Fortunately, there is some good news:

Before we all start panicking (which I have been working hard not to do, myself), the world did get some welcome news this week. On Tuesday, President Obama announced plans for the U.S. military to provide 1,700 hospital beds in West Africa. It will also help set up training facilities for health care workers.

Featured book:

An Introduction to Bioinformatics Algorithms (Computational Molecular Biology)

This introductory text offers a clear exposition of the algorithmic principles driving advances in bioinformatics. Accessible to students in both biology and computer science, it strikes a unique balance between rigorous mathematics and practical techniques, emphasizing the ideas underlying algorithms rather than offering a collection of apparently unrelated problems.The book introduces biological and algorithmic ideas together, linking issues in computer science to biology and thus capturing the interest of students in both subjects. It demonstrates that relatively few design techniques can be used to solve a large number of practical problems in biology, and presents this material intuitively.An Introduction to Bioinformatics Algorithms is one of the first books on bioinformatics that can be used by students at an undergraduate level. It includes a dual table of contents, organized by algorithmic idea and biological idea; discussions of biologically relevant problems, including a detailed problem formulation and one or more solutions for each; and brief biographical sketches of leading figures in the field. These interesting vignettes offer students a glimpse of the inspirations and motivations for real work in bioinformatics, making the concepts presented in the text more concrete and the techniques more approachable.PowerPoint presentations, practical bioinformatics problems, sample code, diagrams, demonstrations, and other materials can be found at the Author’s website.

The Making of a Mile of Pi – Numberphile

This guy (from the Youtube channel Numberphile) actually printed a million digits of Pi! Check out how long the piece of paper actually is!

Longer Version (30 minutes):

Featured book:

Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing
This book provides a fun, hands-on approach to learning how mathematics and computing relate to the world around us and help us to better understand it. How can reposting on Twitter kill a movie’s opening weekend? How can you use mathematics to find your celebrity look-alike? What is Homer Simpson’s method for disproving Fermat’s Last Theorem? Each topic in this refreshingly inviting book illustrates a famous mathematical algorithm or result–such as Google’s PageRank and the traveling salesman problem–and the applications grow more challenging as you progress through the chapters. But don’t worry, helpful solutions are provided each step of the way.

Math Bytes shows you how to do calculus using a bag of chocolate chips, and how to prove the Euler characteristic simply by doodling. Generously illustrated in color throughout, this lively and entertaining book also explains how to create fractal landscapes with a roll of the dice, pick a competitive bracket for March Madness, decipher the math that makes it possible to resize a computer font or launch an Angry Bird–and much, much more. All of the applications are presented in an accessible and engaging way, enabling beginners and advanced readers alike to learn and explore at their own pace–a bit and a byte at a time.

Topics coming out for A Maths Paper 2

Recently, the A Maths Paper 2 just finished (today), and the A Maths Paper 2 is hot on its heels, coming tomorrow!

Usually, topics tested in Paper 1 will most likely not come out again in Paper 2, so students doing their last minute revision can use this fact to focus their revision.

Topics that came out in Paper 1:

  1. Binomial Theorem
  2. Trigonometry (Addition Formula, find exact value)
  3. Rate of change
  4. Partial Fractions
  5. Linear Law
  6. Prove Trigonometry
  7. Coordinate Geometry
  8. Integrate & Differentiate Trigonometric Functions
  9. Discriminant (b^2-4ac)
  10. Stationary Points
  11. Tangent/Normal
  12. Quadratic/Modulus

Topics likely to come out in Paper 2:

  1. Indices/Surds
  2. Polynomials
  3. Exponential / Logarithmic Equations
  4. R-formula
  5. Sketching of Trigonometric Graphs
  6. Circles
  7. Proofs in plane geometry
  8. Integration as the reverse of differentiation
  9. Area under curve
  10. Kinematics

All the best for those who are taking the A Maths Paper 2 exam tomorrow. 🙂

Undergraduate Level Math Book Recommendations

Highly Recommended Math Books for University Self Study

Recently, a viewer of my website asked if I was able to suggest any undergraduate level university textbooks for self study that follows the university curriculum.

Self-study is challenging but not impossible. Choosing a good and appropriate book of the right level is of crucial importance. For instance, for beginners to Calculus, I wouldn’t recommend Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics) by Rudin. It is simply too difficult for beginners or even intermediate students. Any book by Bourbaki is also not suitable for beginners, for instance.

Update: I recently found a book that is a better alternative to Rudin: Mathematical Analysis, Second Edition by Apostol! Many online sources have very positive reviews on Apostol’s Analysis book. I have read it and found it much more readable than Rudin.

I would like to suggest the following books (mainly for Pure Mathematics). Ideally, the motivated student is able to self study and obtain the knowledge equivalent to a 4 Year course at a university.

The recommendations are divided into Year 1, Year 2, Year 3 and Year 4.

If you have any other recommendations, please feel free to comment below!

Year 1

Introduction to Pure Math and Proofs:

How to Prove It: A Structured Approach


Thomas’ Calculus (12th Edition)

Linear Algebra:

Linear Algebra and Its Applications, 4th Edition

Multivariable Calculus:

Thomas’ Calculus, Multivariable (13th Edition)

Year 2

Linear Algebra II (Second Year Course):

Linear Algebra, 4th Edition

Analysis I: 

Introduction to Real Analysis

Abstract Algebra I:

A First Course in Abstract Algebra (3rd Edition)

This book will be an introduction to Group Theory.


Introduction to Probability, 2nd Edition

Analysis II:

Calculus, 4th edition

(Note: Despite the title “Calculus”, this book is actually a rather rigorous book on Analysis, suitable as a second course textbook)

Complex Analysis I:

Complex Variables and Applications (Brown and Churchill)

Year 3

Analysis III:

Introductory Real Analysis (Dover Books on Mathematics)

ODE (Ordinary Differential Equations):

Ordinary Differential Equations (Dover Books on Mathematics)

Graph Theory:

A First Course in Graph Theory (Dover Books on Mathematics)

Algebra II:

Abstract Algebra, 3rd Edition

Algebra II will usually be a course on Rings, Modules.

(Note: You can use this book for learning Galois Theory too)

Differential Geometry:

Differential Geometry of Curves and Surfaces

Year 4 

Number Theory:

An Introduction to the Theory of Numbers

Galois Theory:

Abstract Algebra, 3rd Edition

(Note: Same textbook as for Algebra II)

PDE (Partial Differential Equations):

A First Course in Partial Differential Equations: with Complex Variables and Transform Methods (Dover Books on Mathematics)


A Beginner’s Guide to Mathematical Logic (Dover Books on Mathematics)

Functional Analysis:

Introductory Functional Analysis with Applications


Topology (2nd Edition)

(Note: See also my book review on Topology by Munkres)

Measure and Integration:

The Elements of Integration and Lebesgue Measure

Congratulations for reaching the bottom of this long list!

All the best for your studies in Mathematics. 🙂

Python Math Programming

Recently, I am thinking of learning the Python language for Math programming.

An advantage for using Python for Math Programming (e.g. testing out some hypothesis about numbers), is that the Python programming language theoretically has no largest integer value that it can handle. It can handle integers as large as your computer memory can handle. (Read more at:

Other programming languages, for example Java, may have a maximum integer value beyond which the program starts to fail. Java integers can only have a maximum value of 2^{31}-1 \approx 2.15 \times 10^9, which is pretty limited if you are doing programming with large numbers (for example over a trillion). For instance, the seventh Fermat number is already 18446744073709551617. I was using Java personally until recently I needed to program larger integers to test out some hypothesis.

How to install Python (free):

Hope this is a good introduction for anyone interested in programming!

Featured book:

Learning Python, 5th Edition

Get a comprehensive, in-depth introduction to the core Python language with this hands-on book. Based on author Mark Lutz’s popular training course, this updated fifth edition will help you quickly write efficient, high-quality code with Python. It’s an ideal way to begin, whether you’re new to programming or a professional developer versed in other languages.

Complete with quizzes, exercises, and helpful illustrations, this easy-to-follow, self-paced tutorial gets you started with both Python 2.7 and 3.3— the latest releases in the 3.X and 2.X lines—plus all other releases in common use today. You’ll also learn some advanced language features that recently have become more common in Python code.

  • Explore Python’s major built-in object types such as numbers, lists, and dictionaries
  • Create and process objects with Python statements, and learn Python’s general syntax model
  • Use functions to avoid code redundancy and package code for reuse
  • Organize statements, functions, and other tools into larger components with modules
  • Dive into classes: Python’s object-oriented programming tool for structuring code
  • Write large programs with Python’s exception-handling model and development tools
  • Learn advanced Python tools, including decorators, descriptors, metaclasses, and Unicode processing

Pick’s Theorem Proof (Video)

This is an excellent video I found on Youtube by Professor Wildberger on the proof of Pick’s Theorem. It is easy enough for a high school student to understand!

Pick’s Theorem is a formula A=I+\frac{B}{2}-1 which gives the area of a simple polygon whose vertices lie on points with integer coordinates. Surprisingly, it is a relatively modern theorem, the result was first described by Georg Alexander Pick in 1899.

Using Pick’s Formula, the area of the above polygon is A=I+\frac{B}{2}-1=7+\frac{8}{2}-1=10. We can also see that it is the sum of two triangles A=\frac{1}{2}(4)(2)+\frac{1}{2}(4)(3)=10.

Amazing Formula!


Featured book:

Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers (MSRI Mathematical Circles Library)

A recent visitor to my website bought this book. Highly interesting and suitable for parents of young children. Three to seven is a critical period where the brain develops, hence learning about how to teach math to preschoolers is of great significance for young parents.

This book is a captivating account of a professional mathematician’s experiences conducting a math circle for preschoolers in his apartment in Moscow in the 1980s. As anyone who has taught or raised young children knows, mathematical education for little kids is a real mystery. What are they capable of? What should they learn first? How hard should they work? Should they even “work” at all? Should we push them, or just let them be? There are no correct answers to these questions, and the author deals with them in classic math-circle style: he doesn’t ask and then answer a question, but shows us a problem–be it mathematical or pedagogical–and describes to us what happened. His book is a narrative about what he did, what he tried, what worked, what failed, but most important, what the kids experienced. This book does not purport to show you how to create precocious high achievers. It is just one person’s story about things he tried with a half-dozen young children. Mathematicians, psychologists, educators, parents, and everybody interested in the intellectual development in young children will find this book to be an invaluable, inspiring resource. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

Educational Math Cartoons at

Are you looking for Educational Math Cartoon Videos?

Recently I came upon this site, which is funded by the Goldman Charitable Foundation in partnership with the University of Central Florida.

These videos are designed to be used as collateral material for mathematics courses on the K-12 and college levels, and to be a resource for informal independent study. Rather than focusing on procedural problem solving, the objective is to give insight into theconcepts on which the rules of mathematics are based. Once a student has gained a strong conceptual foundation, the material presented in math textbooks is much easier to digest and retain

An example of their Math cartoon on Infinite Series:

Hope you enjoy their videos!

Featured Book:

The Joy of x: A Guided Tour of Math, from One to Infinity

“Delightful . . . easily digestible chapters include plenty of helpful examples and illustrations. You’ll never forget the Pythagorean theorem again!”—Scientific American

Many people take math in high school and promptly forget much of it. But math plays a part in all of our lives all of the time, whether we know it or not. In The Joy of x, Steven Strogatz expands on his hit New York Times series to explain the big ideas of math gently and clearly, with wit, insight, and brilliant illustrations.

Whether he is illuminating how often you should flip your mattress to get the maximum lifespan from it, explaining just how Google searches the internet, or determining how many people you should date before settling down, Strogatz shows how math connects to every aspect of life. Discussing pop culture, medicine, law, philosophy, art, and business, Strogatz is the math teacher you wish you’d had. Whether you aced integral calculus or aren’t sure what an integer is, you’ll find profound wisdom and persistent delight in The Joy of x.

Math Olympiad Integer Sequence Question

Check out this interesting Math Olympiad Integer Sequence Question! (September 2014 Math Problem of the Month)

Main Page:




Featured book: 

Fifty Lectures for American Mathematics Competitions: Volume 2

While the books in this series are primarily designed for AMC competitors, they contain the most essential and indispensable concepts used throughout middle and high school mathematics. Some featured topics include key concepts such as equations, polynomials, exponential and logarithmic functions in Algebra, various synthetic and analytic methods used in Geometry, and important facts in Number Theory.

The topics are grouped in lessons focusing on fundamental concepts. Each lesson starts with a few solved examples followed by a problem set meant to illustrate the content presented. At the end, the solutions to the problems are discussed with many containing multiple methods of approach.

I recommend these books to not only contest participants, but also to young, aspiring mathletes in middle school who wish to consolidate their mathematical knowledge. I have personally used a few of the books in this collection to prepare some of my students for the AMC contests or to form a foundation for others.

By Dr. Titu Andreescu
US IMO Team Leader (1995 – 2002)
Director, MAA American Mathematics Competitions (1998 – 2003)
Director, Mathematical Olympiad Summer Program (1995 – 2002)
Coach of the US IMO Team (1993 – 2006)
Member of the IMO Advisory Board (2002 – 2006)
Chair of the USAMO Committee (1996 – 2004)

I love this book! I love the style, the selection of topics and the choice of problems to illustrate the ideas discussed. The topics are typical contest problem topics: divisors, absolute value, radical expressions, Veita’s Theorem, squares, divisibility, lots of geometry, and some trigonometry. And the problems are delicious.

Although the book is intended for high school students aiming to do well in national and state math contests like the American Mathematics Competitions, the problems are accessible to very strong middle school students.

The book is well-suited for the teacher-coach interested in sets of problems on a given topic. Each section begins with several substantial solved examples followed by a varied list of problems ranging from easily accessible to very challenging. Solutions are provided for all the problems. In many cases, several solutions are provided.

By Professor Harold Reiter
Chair of MATHCOUNTS Question Writing Committee.
Chair of SAT II Mathematics committee of the Educational Testing Service
Chair of the AMC 12 Committee (and AMC 10) 1993 to 2000.

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Featured book:

Coding the Matrix: Linear Algebra through Applications to Computer Science

Google’s signature ranking algorithm “PageRank” is heavily based on linear algebra! Read the above book to find out more!

An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by doing, writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google’s ranking algorithm), and cancer detection from cell features. A companion web site,

provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant xkcd comics.

Chapters: The Function, The Field, The Vector, The Vector Space, The Matrix, The Basis,Dimension, Gaussian Elimination, The Inner Product, Special Bases, The Singular Value Decomposition, The Eigenvector, The Linear Program

Gmail iOS update adds iPhone 6 support and a math joke

Just to share, interesting Math Joke by Google Gmail!


Gmail iOS update adds iPhone 6 support and a math joke

You may need to brush up on your math if it seems odd to you that Google just updated the iOS Gmail app to version 3.1415926.

But Google is definitely not the type of company that turns down an opportunity to make a math joke, even when that joke is as simple as naming an app update after pi.

Besides that, the Gmail for iOS update has a single improvement: support for the iPhone 6 and iPhone 6 Plus.

Read more at:


You may want to buy this Spigen Tough Armor Case if you are buying the new “flexible” iPhone 6 / 6 plus!

iPhone 6 Plus Case, Spigen® [KICK-STAND] iPhone 6 Plus (5.5) Case Protective [Tough Armor] [Gunmetal] Dual Layer EXTREME Protection Cover Heavy Duty Kick-Stand Feature Case for iPhone 6 Plus (5.5) (2014) – Gunmetal (SGP11053)

  • TPU + Polycarbonate = Dual Protection
  • Advanced Shock Absorption Technology: Web Pattern TPU case
  • Drop Protection with AIR CUSHION Corners
  • Built in Kick-Stand for Hands-Free Viewing
  • Compatible with Apple iPhone 6 Plus (5.5″) Only – 2014

Education Info

Confused About What to Do After 12th Standard?

So, your +2 level exams are over, and you are looking forward to join a college, but you do not really know which stream to choose. You, inevitably, have different people in your life, suggesting different streams to you, leaving you even more confused. While one stream brings you more money, the other one gives you a much stress-free life. Do not worry. Here is a guide through the tricky path. Following are some fine points of the streams available for graduation.

Arts or Humanities

If you are someone who has completed your schooling with an Arts background, you need to choose a course that suits your talent profile. It does not matter if you choose an academic course or a professional one; you need to be sure about your career goals. The stream of Arts offers you a wide array of courses which must be analysed properly before taking admission in any one of them. These courses include plain and simple B.A. or Bachelor of Arts, Hotel Management, Event Management, Fashion Designing, Mass Communication, and many more. All these courses offer lucrative career opportunities in the best industries worldwide. Besides, you can also go for Foreign Language Courses; these are high in demand, and help you get a job in multinational companies. The most frequently opted for foreign language courses are Spanish, French, Russian, Korean and Japanese.


Science happens to offer the widest number of courses after 12th. If you have had a science background at school, your first two preferences would likely be Medicine and Engineering. Besides these, you can also opt for B.Sc degree in Physics, Chemistry, Biology or Mathematics; a degree in Agriculture, Forensic Science, Bio Technology, Geology, etc.

As Medicine and Engineering happen to be popular choices, we are going to elaborate on these two courses. If you choose Medicine, you can opt for any one of the following- Bachelor of Medicine and Bachelor of Surgery (MBBS), Bachelor of Physiotherapy, Bachelor of Ayurveda Medicine and Surgery (BAMS), Bachelor of Science in Optometry, Bachelor of Dental Surgery (BDS) and Bachelor of Pharmacy.

As far as Engineering is concerned, there is wide array of options, which include Aeronautical Engineering, Automobile Engineering, Civil Engineering, Electrical and Electronics Engineering, Computer and Communication Engineering, Information Technology Engineering, Mechanical Engineering, Chemical Engineering, Biomedical Engineering, etc.


In case you are a Commerce student, it is quite likely that ‘Chartered Accountancy’ is what strikes your head. However, you need to begin with graduation. Courses such as BCom, BBA, BBS, BMS, etc., are some of the options Commerce students choose for their graduation. Besides, you can also opt for a diploma or certificate course in Taxation, Accounting, Applied Managerial Economics, Micro Finance, Banking and Insurance, Stock Market, Micro Finance, etc. Specialising in Commerce makes you eligible for jobs like that of Account Analyst, Account Assistant, Accounting Coordinator, Financial Consultant, Accounting Coordinator, Financial Auditor, Accounting Clerk, etc.

Think before you choose

There is no harm in taking others’ suggestions, but the ultimate decision must be yours. Nobody, but you know what you are comfortable at. It does not matter how much your parents coax you to take up Engineering, if you find Literature more interesting, go for it. After all, it is you who have to study the subject for the next three or four years, and build a future on the same. So, nobody but you can decide which course is best for you.

Also keep in mind that the course you choose gives you a good scope as far as career options are concerned. What you choose now will decide the shape of your future. So, please choose wisely.

Author’s bio: Jeff Traven is a professor at a well-known university is California. During his spare time, he likes to blog on various kinds topics that help young students choose the right courses after 12th, so that they can have a bright and prosperous future.

Why do Exterior Angles add up to 360 degrees?



This is the real reason why exterior angles of a polygon add up to 360 degrees! If you shrink the polygon (which doesn’t affect the sum of exterior angles), the exterior angles eventually meet at a point, and the sum of angles at a point is 360 degrees.

This is some cool math to think about!

Featured book:

Math Appeal: Mind-Stretching Math Riddles

NEW YORK TIMES bestselling author Greg Tang challenges kids to solve problems creatively in this follow-up to MATH FOR ALL SEASONS.

In this book you’ll learn to see
How very clever you can be.


Universum Survey (Please help to do!)

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It is a Career Test by Universum. Participate to reveal your career type and discover the optimal employers for you!

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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.


The Three Square Geometry Problem – Numberphile

Watch this interesting video about the “Three Square Geometry Problem”!

Theoretically, a fifth-grader or P5/PSLE student can solve it! The featured solution is truly brilliant and requires one to “think out of the box”.

Featured book:

Tutor in a Book’s Geometry

Need help with Geometry? Designed to replicate the services of a skilled private tutor, the new and improved Tutor in a Book’s Geometry is at your service! TIB’s Geometry is an extremely thorough, teen tested and effective geometry tutorial.

TIB’s Geometry includes more than 500 of the right, well-illustrated, carefully worked out and explained proofs and problems. Throughout TIB’s Geometry, there is ongoing, specific guidance as to the most effective solution and test taking strategies. Recurring patterns, which provide solutions to proofs, are pointed out, explained and illustrated using the visual aids that students find so helpful. Also included are dozens of graphic organizers, which help students understand, remember and recognize the connections between concepts.

TIB’s author Jo Greig intended this book to level the playing field between the students who have tutors and those that don’t. As a long time, very successful private mathematics tutor and teacher, Jo Greig knew exactly how best to accomplish this! TIB’s Geometry 294 pages are packed with every explanation, drawing, hint and memory tool possible! Not only does it have examples of the right proofs and problems, it also manages to impart every bit of the enthusiasm that great tutors impart to their private tutoring students. Ms. Greig holds a bachelors’ degree in mathematics. Dr. J. Shiletto, the book’s mathematics editor, holds a Ph.D in mathematics.

Stable Marriage Problem – Numberphile

This is an interesting problem in the topic of combinatorics and graph theory. It can be phrased in the context of arranging stable marriages.

Nice animation and clear explanation! Watch part 2 too for the mathematical explanation.

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!



Happy Teacher’s Day!

Glad to receive some Teacher’s Day cards and presents from my students!

teacher's day cardWishing all teachers a happy Teacher’s Day this Friday, and also wishing students all the best for their upcoming exams.

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!

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

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. 🙂


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
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
SINGAPORE — The Government’s plan to enhance housing, healthcare and education benefits for operationally ready national servicemen has …

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Welcome to the Teach100 community!

Recently, I added the Maths Blog to the Teach100 website. Glad to know that the blog has been approved!

“Thank you for submitting Singapore Maths Tuition to the Teach100! Your blog has been approved and is currently ranked at #427 of 601 blogs. Congratulations! We recently reached our 500th blog, and are excited to add your blog to our growing community!”