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. 🙂

Sum of Cubes (A Maths Tuition)

What is tested for A Maths (Additional Maths) Exam

Just to share an A Maths question that is likely to come out for 2014 A Maths Exam. It is the brand new topic just added this year: Sum and difference of cubes.



Attached below is a practice question on Alpha Cube+Beta Cube question that may be likely to come out this year! After all, if it is just added in the syllabus it is highly likely that they will test it.

Alpha Beta Cube Question

Good luck for the exam!

Maths Tuition

For Mathematics Tuition, contact Mr Wu at:


Tutor profile: About Tutor

Featured book:

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


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

Lunes (Mathematics)

What are Lunes? Check out this absolutely interesting video:

The Lune of Hippocrates


Featured book:

A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus (Dover Books on Mathematics)

“As it is, the book is indispensable; it has, indeed, no serious English rival.” — Times Literary Supplement
“Sir Thomas Heath, foremost English historian of the ancient exact sciences in the twentieth century.” — Prof. W. H. Stahl
“Indeed, seeing that so much of Greek is mathematics, it is arguable that, if one would understand the Greek genius fully, it would be a good plan to begin with their geometry.”

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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Do you want to know which employer is the most suitable for you?

Please help to do this survey at:

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

Thanks for your help once again!

Holder’s Inequality for Lp Spaces

These are two excellent videos explaining Holder’s Inequality for Lp Spaces:

Featured book:

Divine Proportions: Rational Trigonometry to Universal Geometry

This revolutionary book establishes new foundations for trigonometry and Euclidean geometry. It shows how to replace transcendental trig functions with high school arithmetic and algebra to dramatically simplify the subject, increase accuracy in practical problems, and allow metrical geometry to be systematically developed over a general field. This new theory brings together geometry, algebra and number theory and sets out new directions for algebraic geometry, combinatorics, special functions and computer graphics. The treatment is careful and precise, with over one hundred theorems and 170 diagrams, and is meant for a mathematically mature audience. Gifted high school students will find most of the material accessible, although a few chapters require calculus. Applications include surveying and engineering problems, Platonic solids, spherical and cylindrical coordinate systems, and selected physics problems, such as projectile motion and Snell’s law. Examples over finite fields are also included.


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.


Fire HD Kids Edition Tablet: Educational Review

Fire HD Kids Edition Tablet
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This is a potential good alternative to the Ipad. Ipad is more for games, while the Fire HD Kids Edition Tablet is more educational, with a hand-curated subscription of over 5,000 kid-friendly books, movies, TV shows, educational apps, and games.

It will be out soon this October 2014! Pre-order now by clicking this link: Click here to Pre-order.

AlgTop1: One-dimensional objects

This is a continuation of the series of Algebraic Topology videos. Previous post was AlgTop 0.

Professor Wildberger is an interesting speaker. He holds some unorthodox views, for instance he doesn’t believe in “real numbers” or “infinite sets”. Nevertheless, his videos are excellent and educational. Highly recommended to watch!

The basic topological objects, the line and the circle are viewed in a new light. This is the full first lecture of this beginner’s course in Algebraic Topology, given by N J Wildberger at UNSW. Here we begin to introduce basic one dimensional objects, namely the line and the circle. However each can appear in rather a remarkable variety of different ways.

Featured book:

Divine Proportions: Rational Trigonometry to Universal Geometry

Author: NJ Wildberger

This revolutionary book establishes new foundations for trigonometry and Euclidean geometry. It shows how to replace transcendental trig functions with high school arithmetic and algebra to dramatically simplify the subject, increase accuracy in practical problems, and allow metrical geometry to be systematically developed over a general field. This new theory brings together geometry, algebra and number theory and sets out new directions for algebraic geometry, combinatorics, special functions and computer graphics. The treatment is careful and precise, with over one hundred theorems and 170 diagrams, and is meant for a mathematically mature audience. Gifted high school students will find most of the material accessible, although a few chapters require calculus. Applications include surveying and engineering problems, Platonic solids, spherical and cylindrical coordinate systems, and selected physics problems, such as projectile motion and Snell’s law. Examples over finite fields are also included.

Books for Gifted Children

Featured book:

Match Wits With Mensa: The Complete Quiz Book

This is the #1 Top-Selling book recommended on my website! It includes Mathematical Logic Puzzles from Mensa. Highly recommended for gifted children. Parents, if your child is gifted and you want to stretch his or her learning potential, you may want to buy this book as it is the most complete quiz book on the market. It doesn’t matter whether you are in the Gifted Education Programme, as long as you have an interest in logic puzzles this book is for you.

Maths and Science is essentially about logical thinking, so logic puzzles will directly benefit studies in maths and science. Above all, logic puzzles are meant to be fun and a good and healthy pastime.

Puzzle fans have bought more than 650,000 copies of the Mensa Genius Quiz series—the only books that let readers “match wits with Mensa,” comparing how well they do against members of the famous high-IQ society. Here, in a giant omnibus edition, are four best-selling titles: The Mensa Genius Quiz Books 1 & 2, The Mensa Genius Quiz-A-Day Book, and The Mensa Genius ABC Book. Here are more than 800 fun mindbenders to exercise every part of your brain—word games, trivia, logic riddles, number challenges, visual puzzles—plus tips on how to improve your thinking skills. All the puzzles have been tested by members of American Mensa, Ltd., and include the percentage of Mensa testers who could solve each one, so that you can score yourself against some of the nation’s fittest mental athletes.

Snooze button good or bad? (Education, Productivity Tip)

The snooze button – one of life’s luxuries. But is it really helping you out, or making you more tired?

Start Maths Revision Early for the Best Results!

O Level Group Tuition @ Bishan starting in 2014!

Maths is a subject that requires students to start revision / practice early!

It needs consistent practice and last minute studying is not going to work well!

Many students have the wrong concept that they can start practising questions one or two months before the O Levels. The problem is, without constant practice, the questions from the Ten Year Series would be too difficult for students to even begin attempting the questions! This is especially true for Additional Mathematics. This leads to panic and is not the desired study strategy. This is the main reason why it is possible to score very low (less than 20 marks out of 100) in Maths, if the student does not have solid foundation or has lack of practice. To avoid this scenario, start practicing and revising Maths now! Many students already start studying / learning in advance during the December holidays. January is still a good time to start! As the Chinese proverb states: “一年之计在于春一日之计在于晨”, the best time to begin planning for a task is in Spring.

Also, the current O Level Maths is not like the O Level of the past! Due to higher education standards nowadays, and competition from foreigners (especially China students whose pet subjects are Maths and Chinese), the bell curve for E Maths has shifted very very high. Rumours have it that 90 marks is necessary for a guaranteed A1 in E Maths.

On the bright side, it is very possible to improve in Maths with practice. Look at the Mathematics questions in O Levels, one long question is around 10 marks. Answering that one question correctly will already boost your score by 10 marks. (2 grades). Answering two long questions correctly will boost score by a whopping 20 marks!

Hesitate no longer! Start revising for your Maths now!

O Level Group Tuition @ Bishan starting in 2014!

Secondary 4 O Level E Maths and A Maths Group Tuition, Bishan

Maths Tuition @ Bishan starting in 2014.

Secondary 4 O Level E Maths and A Maths.

Patient and Dedicated Maths Tutor (NUS Maths Major 1st Class Honours, Dean’s List, RI Alumni)


Maths Challenge

Hi, do feel free to try out our Maths Challenge (Secondary 4 / age 16 difficulty):

maths challenge

Source: Anderson E Maths Prelim 2011

If you have solved the problem, please email your solution to .

(Include your name and school if you wish to be listed in the hall of fame below.)

Students who answer correctly (with workings) will be listed in the hall of fame. 🙂

Hall of Fame (Correct Solutions):

1) Ex Moe Sec Sch Maths teacher Mr Paul Siew

2) Queenstown Secondary School, Maths teacher Mr Desmond Tay

3) Tay Yong Qiang (Waiting to enter University)

Mr Heng, however, noted that how well a child does in school depends on how motivated he is.


Minister for Education Heng Swee Keat has said parents should consider other factors apart from a school’s previous year cut-off point (COP) when helping their P6 children decide on which secondary school to choose.

          Minister for Education Heng Swee Keat (Photo: MOE)

SINGAPORE: Minister for Education Heng Swee Keat has said parents should consider other factors apart from a school’s previous year cut-off point (COP) when helping their P6 children decide on which secondary school to choose.

Writing on his Facebook page, Mr Heng said it would be good for parents to have an open talk with their children to know what type of secondary school they are interested in.

Mr Heng, however, noted that how well a child does in school depends on how motivated he is.

So he encourages parents to carefully consider the kind of environment that will best motivate their children, and enable them to develop themselves fully in the next four to five years.

Some children, he said, are late developers and the right environment helps them thrive.

Mr Heng urged parents to think of how best they can help their children develop confidence and enjoy the space to discover his talents and passions.

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Recommended Maths Olympiad Books for Self Learning / Domain Test

Math Olympiad Books are useful for GEP/DSA preparation. It is also useful for the latest type of test called Domain Tests, which is basically a subject test (Math included) for entry into top secondary schools like the Raffles / Hwa Chong family. There are different subject domains (depending on the school), ranging from General domain / Academic domain / CCA domain.

A First Step to Mathematical Olympiad Problems (Mathematical Olympiad Series)

The Art of Problem Solving, Vol. 1: The Basics

The first book is written by Professor Derek Holton. Prof Holton writes a nice column for a Math magazine, which gives out books as prizes to correct solutions.

GEP Math Olympiad Books

If you are searching for GEP Math Olympiad Books to prepare for the GEP Selection Test, you may search for Math Olympiad Books for Elementary School. Note that Math Olympiad Books for IMO (International Mathematics Olympiad) are too difficult even for a gifted 9 year old kid!

A suitable book would be The Original Collection of Math Contest Problems: Elementary and Middle School Math Contest problems. It covers the areas of Algebra, Geometry, Counting and Probability, and Number Sense, over 500 examples and problems with fully explained solutions.

Other Suitable Math Olympiad Books for GEP

These are some books that are very popular and highly rated on Amazon.

Challenging Problems in Algebra (Dover Books on Mathematics)

Challenging Problems in Geometry (Dover Books on Mathematics)
Math Circles for Elementary School Students: Berkeley 2009 and Manhattan 2011 (MSRI Mathematical Circles Library)

My Best Mathematical and Logic Puzzles (Dover Recreational Math)
The Moscow Puzzles: 359 Mathematical Recreations (Dover Recreational Math)

The Stanford Mathematics Problem Book: With Hints and Solutions (Dover Books on Mathematics)

The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics (Dover Books on Mathematics)

Math, Science, Reading Scores Show U.S. Schools Slipping Behind


Math, Science, Reading Scores Show U.S. Schools Slipping Behind

Posted: December 10, 2010 PRINTER FRIENDLY VERSION: PDF

The United States received a stark wake-up call this week with the release of international test results showing students in other countries are surpassing American students when it comes to math, science and reading. China and Australia outperformed the U.S. in each of the three subject areas tested.

The results of a major international education assessment show that American students are lagging behind many other countries in crucial skills like reading, math and science.

“The United States came in 23rd or 24th in most subjects. We can quibble, or we can face the brutal truth that we’re being out-educated,” said U.S. Education Secretary Arne Duncan.

Test compares U.S. to other countries

The PISA tests how advanced students are in science, math and reading compared to their peers around the world.

The test, known as the Program for International Student Assessment (PISA), directly assesses how prepared teenagers are in math, science and reading compared to their peers in other countries.
The test is translated into each country’s language, and officials from the participating countries are able to review questions before students take the exam to make sure each test is fair and unbiased.

In the U.S., the participating schools and students are randomly selected. On average, about 4,500 students are tested in each of the participating countries.

China and Finland lead the way

Chinese and Finnish students scored highest on the PISA test.

Each PISA subject area is scored on a scale where 500 points is the average. The results announced this week show many countries outperforming the U.S. Here’s a sample:

Math: China 600, Germany 513, United States 487 (31st place)

Reading: China 556, Korea 539, United States 500 (17th place)

Science: China 575, Finland 554, United States 502 (23rd place)

The results of a major international education assessment show that  American students are lagging behind many other countries in crucial skills like reading, math and science.

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Time needed for each O Level E Maths / A Maths Question

E Maths / A Maths: Maximum time per question

Paper 1: 2 hours (120 min) — 80 marks

Max. Time taken per mark: 1.5 min per mark

Paper 2: 2 hours 30 minutes (150 min) — 100 marks

Max. Time taken per mark: 1.5 min per mark

In O Levels Maths, speed and accuracy is very important indeed!

In China, all parents know that maths is the number one subject in schools


‘Above all, it is a cultural thing.” Professor Lianghuo Fan is reflecting on the differences he has noticed between maths education in China and Singapore, where he lived and taught for 40 years, and in Britain, where he is now based. “In China, all parents know that maths is the number one subject in schools, and they expect that in a modern society everyone must be comfortable with maths, even if that means they have to work hard at it.“That attitude is passed on to their children. But here in Britain, you can feel students’ attitude about mathematics is different. They feel all right if they say they don’t like mathematics.”

Professor Fan is not alone in highlighting this national phobia of ours about maths. The government has this week shown itself determined to tackle the problem head on with the unveiling of a new “back-to-basics” primary school maths curriculum, with a renewed emphasis on times-tables, mental arithmetic, fractions and rote learning.

Most people over 40 will see the proposals as a return to the classroom practice of their childhood – but in its introductory remarks the Department for Education claimed inspiration from Asian model that Professor Fan knows so well: “I never heard a child in China or Singapore say that they don’t like maths’,” he stresses, “without a sense of embarrassment.”

We are sitting in a café near Southampton University – where 50-year-old Professor Fan has been head of the Mathematics and Science Education Research Centre since 2010 – as we try to decide if anything lies behind the popular stereotype that Asian children are “naturally” better at maths than those in the West. It is, for example, in the core storyline of Safe, the recent Hollywood blockbuster, starring Jason Statham. An 11-year-old girl, Mei (played by Chinese-born actress Catherine Chan), is a maths prodigy who can decode number sequences at a glance – and therefore has to be protected from the baddies.

Math Mark

Formula to guess Month of Birthday from Singapore NRIC

Latest Update: We have created a JavaScript App to Guess Birthday Month from NRIC


Here is a Math Formula trick to have fun with your friends, to guess their Month of Birthday given their NRIC, within two tries.

(only works for Singapore citizens born after 1970)

The formula is: take the 3rd and 4th digit of the NRIC, put them together, divide by 10, and multiply by 3.

For an example, if a person’s NRIC is S8804xxxx, we take 04, divide by 10 to get 0.4

Then, 0.4 multiplied by 3 gives 1.2

Then, guess that the person is either born in January (round down 1.2 to 1) or February (round up 1.2 to 2). There is a high chance that you are right! Usually, round up for the first six months (Jan to Jun), and round down for the last six months (Jul to Dec).

This formula was developed and tested by me. There are some exceptions to the rule, but generally it works fine especially for people born from 1980 to 2000.

Hope you have fun with maths, and impress your friends!


Maths Skills to be a Doctor

Doctor and Lawyer are the top two favourite careers in Singapore. Do doctors need to use Maths? Read the below to find out.

Even if Maths is not directly needed, the logical thinking skills learnt in Mathematics will definitely be of great use. 🙂

I am not a medical doctor, but my two younger siblings are medical students, and the Mathematical knowledge and thinking skills have definitely helped them in their medical studies.


Functional numeracy is as essential to an aspiring medical professional as functional literacy. As a physician, perhaps the most important mathematical skills you will need are:

1. Basic mathematical knowledge sufficient to calculate drug doses, concentrations, etc.

2. An understanding of the core statistical concepts most commonly represented in the medical literature.

3. Knowledge of algebra to understand calculations of acid–base status, etc.

4. Ability to appreciate whether or not results are mathematically plausible.    (Nusbaum, 2006)

The careful logical reasoning that is necessary for the study of mathematics is an essential element of clinical reasoning. Although you do not need higher mathematics to get through medical school, you will need the ability to manipulate numbers, including fractions, ratios, powers of 10 and logarithms. You will also need a basic understanding of probability, graphs and simple algebra. You will need to rearrange equations and convert between units of measure.



It’s often unclear from your interactions with a doctor how much math she is using in order to treat you. While not all doctors have to use math as directly and frequently as engineers do, all of them must understand the complex mathematical equations that inform different medical treatments in order to administer treatments correctly.

Dosages and Half-Life

One of the most common ways in which doctors use mathematics is in the determination of medicine prescriptions and dosages. Doctors not only have to use basic arithmetic to calculate what dosage of a particular drug will be effective for your height and body type over a specific period of time, they will also have to be aware of the medicine’s cycle through the body and how the dosage of one drug compares with the dosage of a similar type of drug. Sometimes doctors have to use calculus to figure out the right dosage of a drug. Calculus is the study of how changing variables affect a system. In the human body, the kidney processes medicine. However, people’s kidneys are at varying levels of health. Doctors can designate the kidney as a changing function in a calculus equation known as the Cockroft-Gault equation. This equation uses the level of creatine in a patient’s blood to find the level of the kidney’s functioning, which allows the doctor to determine the appropriate dose.

Cancer Treatment

When a doctor administers radiation therapy to a cancer patient, the radiation beams have to cross each other at specific angles, so that they harm the cancerous tumor without harming the surrounding healthy tissue. The precise numbers for these angles must be calculated mathematically. Cancer tends to respond to any drug by mutating so that its DNA is no longer affected by that drug. Oncologists and medical scientists have decided to target cancerous tumors with many different kinds of drugs at once so that the cancer is unable to respond adequately. They use complex mathematical models that plot the speed and timing of the cancer’s different mutations to figure out what combinations and dosages of different drugs should be used.

Medical Images and Tests

Doctors in medical imaging use two-dimensional images of a patient’s body taken from thousands of angles to create a three-dimensional image for analysis. Determining what angles should be used and how they will fit together requires mathematics. Medical researchers who study disease will analyze the mathematical dimensions of these images. Neurologists who run EEGs on patients to measure their brain waves must add and subtract different voltages and use Fourier transforms to filter out signal static. Fourier transforms are used to alter functions in calculus.

Treatment Research

Medical scientists working with cardiologists use differential equations to describe blood flow dynamics. They also build sophisticated computer models to find the ideal size of an artificial aorta and where to place it in an infant pending a heart transplant. Doctors have to read medical journals to keep up on the latest scientific findings for the benefit of their patients. In addition to describing the calculus used to model health conditions, medical journal studies also make heavy use of statistics and probability to describe the health conditions of whole populations and the likelihood that different treatments will be effective.

Maths Skills to be a Good Lawyer

Doctor and Lawyer are the top two favourite careers in Singapore. On the surface, Lawyers seem not to need much maths, but recent research shows that Mathematics skills and thinking may be crucial to becoming a better Lawyer.


There is a “highly significant relationship” between law students’ math skills and the substance of their legal analysis, according to research from Arden Rowell, a professor of law and the Richard W. and Marie L. Corman Scholar at Illinois.

CHAMPAIGN, Ill. — The stereotype of lawyers being bad with numbers may persist, but new research by two University of Illinois legal scholars suggests that law students are surprisingly good at math, although those with low levels of numeracy analyze some legal questions differently.

According to research from Arden Rowell and Jessica Bregant, there is a   “highly significant relationship” between law students’ math skills and the substance of their legal analysis, suggesting that legal analysis – and by extension, legal advice – may vary with a lawyer’s native math skills.

What the research shows is that math matters to lawyers more – and for different reasons – than people have realized,” said Rowell, a professor of law and the Richard W. and Marie L. Corman Scholar at Illinois. “People are only now starting to pay attention to the fact that lawyers and judges who are bad at math can make mistakes that ruin people’s lives. That implicates numeracy as a neglected but potentially critical aspect of legal education, because it’s not something that law schools have traditionally focused on when selecting students.”

JC Cut Off Points

JC Cut Off Points (COP)

To sign up for JC Tuition (subjects other than Math, e.g. GP Tuition): Check out this recommended tuition agency: StarTutor!

Aggregate Scores of Junior Colleges (JC) 

Outliers: The Story of Success This is a very inspirational book on why do some people succeed, and what makes high-achievers different? Famous author Malcolm Gladwell reveals the secret and how it is possible for average ordinary people to achieve the same results. (Best Seller on

Check out our post on Recommended Graphical Calculator for JC.

Also check out our post on: Which JC is Good?

  1. RJC Cut Off Points: Arts 3, Science 3
  2. HCI Cut Off Points: Arts 3, Science 3
  3. VJC Cut Off Points: Arts 5, Science 4
  4. NJC Cut Off Points: Arts 5, Science 5
  5. ACS(I) Cut Off Points: Science 5
  6. ACJC Cut Off Points: Arts 7, Science 6
  7. TJC Cut Off Points: Arts 7, Science 6
  8. AJC Cut Off Points: Arts 10, Science 8
  9. MJC Cut Off Points: Arts 9, Science 9
  10. NYJC Cut Off Points: Arts 9, Science 9
  11. SAJC Cut Off Points: Arts 9, Science 9
  12. CJC Cut Off Points: Arts 10, Science 10
  13. SRJC Cut Off Points: Arts 13, Science 13
  14. TPJC Cut Off Points: Arts 13, Science 14
  15. JJC Cut Off Points: Arts 13, Science 16
  16. PJC Cut Off Points: Arts 16, Science 16
  17. YJC Cut Off Points: Arts 20, Science 20
  18. IJC Cut Off Points: Arts 20, Science 20

L1R5 aggregate scores/ Cut Off Points (with bonus points) of students admitted to JCs in the 2012 Joint Admissions Exercise (JAE).

Junior College



Anderson JC



Anglo-Chinese JC



Anglo-Chinese School (Independent)


Catholic JC



Hwa Chong Institution



Innova JC



Jurong JC



Meridian JC



Nanyang JC



National JC



Pioneer JC



Raffles Institution



Serangoon JC



St. Andrew’s JC



St. Joseph Institution

Tampines JC



Temasek JC



Victoria JC



Yishun JC




JC Cut Off Points (Bonus Points)

For students seeking admission to JC/Poly/ITE and with the following CCA grades:a. Grades of A1 – A2 (2 points)b. Grades of B3 – C6 (1 point)
For students seeking admission to JC/MI courses and with grades of A1 to C6 in both their first languages (i.e. English and a Higher Mother Tongue). This is provided that these choices come before any Poly/ITE choices.(2 points)
For students seeking admission to JC/MI courses and with grades of A1 to C6 in Malay/Chinese (Special Programme) (MSP/CSP) or Bahasa Indonesia (BI) as their third language. This is provided that these choices come before any Poly/ITE choices.(2 points)
For students from feeder schools if they choose their affiliated Junior College course(s) as their:a. 1st choice, or b. 1st and 2nd choices. (2 points)

The bonus points can be deducted from their total points, and will be helpful to enter the JC (depending on the JC’s Cut Off Points). Theoretical Minimum Score is 0 points (if under CLEP or MLEP programme), otherwise minimum score is 2 points.

Teachers have profound effect on students, says Heng Swee Keat


Education Minister Heng Swee Keat said teachers “grow knowledge, instill beliefs, inculcate values, nurture passion, and in so doing, they shape the future” of students.

          File photo: Minister for Education Heng Swee Keat

SINGAPORE: Education Minister Heng Swee Keat said on Thursday “teachers affect all of us more deeply” than one can know.

In a Facebook post ahead of Teachers’ Day on Friday, Mr Heng sent his warmest thoughts and admiration to all teachers who dedicate themselves to bringing out the best in children.

In the tribute to all teachers, Mr Heng said they “grow knowledge, instill beliefs, inculcate values, nurture passion, and in so doing, they shape the future” of their students.

He added that every child who grows up confident and compassionate has been affected by a caring teacher in some way.

Mr Heng said in order to give every child a profound educational experience, every teacher must be a caring educator.

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数学补习 (碧山)


教O Level E Maths 和 A Maths.



O Level E Maths and A Maths Tuition starting next year at Bishan

O Level E Maths and A Maths Tuition starting next year at Bishan
View Mr Wu’s GEP Testimonial at

Despite being in the Gifted Education Programme (GEP), Mr Wu is just an ordinary Singaporean. His secret to academic success is hard work and the Maths Techniques he has discovered by himself while navigating through the education system.

He would like to teach these techniques to students, hence choosing to become a full-time Mathematics tutor. Mr Wu has developed his own methods to check the answer, remember formulas (with understanding), which has helped a lot of students. Many Math questions can be checked easily, leading to the student being 100% confident of his or her answer even before the teacher marks his answer, and reducing the rates of careless mistakes.

Mr Wu’s friendly and humble nature makes him well-liked by students. Many of his students actually request for more tuition by themselves! (not the parents)

O Level E Maths and A Maths Tuition starting next year at Bishan, the best location in Central Singapore.

Timings are Monday 7-9pm, Thursday 7-9pm. Perfect for students who have CCA in the afternoon, or students who want to keep their weekends free.

Register with us now by email ( Vacancies will be allocated on a first-come-first-serve basis.

Thanks and wishing all a nice day.

Standard matrix in mathematics
Standard matrix in mathematics (Photo credit: Wikipedia)

Additional Maths — from Fail to Top in Class

Really glad to hear good news from one of my students.

From failing Additional Maths all the way, he is now the top in his entire class.

Really huge improvement, and I am really happy for him. 🙂

To other students who may be reading this, remember not to give up! As long as you persevere, it is always possible to improve.

Understanding the Birthday Paradox


23 people. In a room of just 23 people there’s a 50-50 chance of two people having the same birthday. In a room of 75 there’s a 99.9% chance of two people matching.

Put down the calculator and pitchfork, I don’t speak heresy. The birthday paradox is strange, counter-intuitive, and completely true. It’s only a “paradox” because our brains can’t handle the compounding power of exponents. We expect probabilities to be linear and only consider the scenarios we’re involved in (both faulty assumptions, by the way).

Let’s see why the paradox happens and how it works.

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Missing dollar riddle; Maths Group Tuition 2014

Ad: Maths Group Tuition starting in 2014

Maths can be fun too!
Build up interest in Mathematics by trying out some of these interesting Maths Riddles.


The riddle

Three guests check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn’t know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 for himself. Each guest got $1 back: so now each guest only paid $9; bringing the total paid to $27. The bellhop has $2. And $27 + $2 = $29 so, if the guests originally handed over $30, what happened to the remaining $1?

Try it out before looking at the answer!

5 awarded prestigious President’s Scholarship at Istana ceremony

Maths Group Tuition starting in 2014


SINGAPORE – Five government scholarship recipients, including a missionaries’ child who grew up in Papua New Guinea and a Youth Olympic Games triathlete, have been awarded the prestigious President’s Scholarships this year, at a ceremony at the Istana on Friday evening.

Get the full story from The Straits Times.

Here is the full speech by President Tony Tan:

Deputy Prime Minister Teo Chee Hean and Mrs Teo

Minister for Education Heng Swee Keat


Chairman and Members of the Public Service Commission

Ladies and Gentlemen

Good evening.

Each year, the Public Service Commission awards scholarships to outstanding young men and women who want to serve Singapore and Singaporeans through a career in the Public Service. The most prestigious undergraduate scholarship awarded by the Commission is the President’s Scholarship.

It is awarded to young Singaporeans who have the integrity and commitment to work for Singapore’s continued success. To be awarded a President’s Scholarship, one must demonstrate more than just excellence in academic and non-academic pursuits. One must also show a strong ethos for public service, impeccable character, remarkable leadership and dedication towards improving the lives of Singaporeans.

2013 President’s Scholars This evening, the President’s Scholarship is awarded to five exceptional young individuals who have distinguished themselves based on their leadership capabilities and calibre, and their passion to bring the nation forward.

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You can reach for the stars with Jaws, Braille and determination, mathematics whiz Yeo Sze Ling tells HELLEN TAN

Maths Group Tuition starting in 2014!


Counting on her mind

1,248 words 24 May 2005 Digital Life English (c) 2005 Singapore Press Holdings Limited

You can reach for the stars with Jaws, Braille and determination, mathematics whiz Yeo Sze Ling tells HELLEN TAN

Given that multiple degrees are common today, the fact that Miss Yeo Sze Ling has two degrees in mathematics, and is working on her doctorate in the same field, is probably not news.

Until you find out that she is blind.

The 27-year-old who earned her Bachelor’s degree (Honours) and a Master’s degree from National University of Singapore (NUS) is now into research on coding mathematics theories and cryptography.

These are used in computing algorithms to protect passwords or data from being stolen when they are zipped from computer to computer.

The field is an interest she shares with John Nash Jr, a mathematical genius who won a Nobel Prize, portrayed in the Oscar-winning movie, A Beautiful Mind.

Certainly, like Nash, her achievements should mean a lot.

He was a schizophrenic who thought he was doing secret cryptography work for the American government.

She has been blind from the age of about four when glaucoma struck. Glaucoma is a condition that increases pressure within the eyeball causing sight loss.

Technology has come in handy.

On campus, she totes a laptop.

At home in a four-room HDB flat in Bishan, her desktop Compaq PC holds today’s tech staples – e-mail and MSN Messenger for exchanging notes with friends.

The Internet is her source for research as well as for online newspapers or electronic books like A Beautiful Mind.

Continue reading at,%2024%20May%20-%20Counting%20on%20her%20mind%20-%20Yeo%20Sze%20Ling.htm

Rote learning has to make way for digital literacy: Heng Swee Keat


Education Minister Heng Swee Keat has said that with information readily available, rote learning has to make way for digital literacy.

SINGAPORE: Education Minister Heng Swee Keat has said that with information readily available, rote learning has to make way for digital literacy.

Speaking at the Second International Summit of the Book on Friday, Mr Heng said there is a need to place greater emphasis on critical and inventive thinking.

Whether it is a papyrus, print or the iPad, it seems that books are here to stay.

Professor Tommy Koh, chairman of the Organising Committee of the Second International Summit of the Book, and Ambassador-at-Large, said: “I think the book will endure to the end of time.

“But the form of the book has changed and will change. The container will change, the platform on which we read the book will also change.

“My children, for example, prefer to read the book either on the computer, on the iPad, on the tablet and other electronic forms. I still prefer the printed book. But in one form or another, the book will endure. There can be no human civilisation without books.”

But the question is whether readers are able to discern truths from untruths, especially in an era that is inundated with information.

Mr Heng said: “Some fear that the technologically sophisticated books of the future will dull the mind, as we no longer bother to use our imagination to render words into sounds and images.

“They worry too that we will forget to think for ourselves after we close the book because social media offers such an array of ready-made opinions that we will just pick one off the virtual shelf rather than form our own.

“We need to place greater emphasis on critical and inventive thinking, so that we may go on to imagine and create new insights.

“At the workplace, as the information revolution transforms the nature of work, our ability to move from theory to practice, to apply learning imaginatively in different contexts, and to create new knowledge, will become increasing valuable.”

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Sergey Brin, co-founder of Google, studied Mathematics!

Maths Group Tuition to start in 2014!


Sergey Mikhaylovich Brin (Russian: Сергей Михайлович Брин; born August 21, 1973) is an American computer scientist and Internet entrepreneur who, with Larry Page, co-founded Google, one of the most profitable Internet companies.[4] As of 2013, his personal wealth was estimated to be $22.8billion.[2] Together, Brin and Page own about 16 percent of the company.

Brin immigrated to the United States with his family from the Soviet Union at the age of six. He earned his undergraduate degree at the University of Maryland, following in his father’s and grandfather’s footsteps by studying mathematics, as well as computer science. After graduation, he moved to Stanford University to acquire a Ph.D. in computer science. There he met Larry Page, with whom he later became friends. They crammed their dormitory room with inexpensive computers and applied Brin’s data mining system to build a superior search engine. The program became popular at Stanford and they suspended their PhD studies to start up Google in a rented garage.

The Economist newspaper referred to Brin as an “Enlightenment Man“, and someone who believes that “knowledge is always good, and certainly always better than ignorance”, a philosophy that is summed up by Google’s motto “Organize the world’s information and make it universally accessible and useful”[5][6] and “Don’t be evil“.

Education in the United States

Brin attended grade school at Paint Branch Montessori School in Adelphi, Maryland, but he received further education at home; his father, a professor in the department of mathematics at the University of Maryland, encouraged him to learn mathematics and his family helped him retain his Russian-language skills. In September 1990 Brin enrolled in the University of Maryland to study computer science and mathematics, where he received his Bachelor of Science in May 1993 with honors.[14]

Sergey Brin Ted 2010.jpg

Studying at NUS Mathematics Department

Maths Group Tuition to start in 2014!


The history  of the Department of Mathematics at NUS traces back to 1929, when science  education began in Singapore with the opening of Raffles College with less than  five students enrolled in mathematics. Today it is one of the largest  departments in NUS, with about 70 faculty members and       teaching staff supported  by 13 administrative and IT staff.  The Department offers a wide selection  of courses (called modules) covering wide areas of mathematical sciences with  about 6,000 students enrolling in each semester. Apart from offering B.Sc.  programmes in Mathematics, Applied Mathematics and Quantitative Finance, the  Department also participates actively in major interdisciplinary programs,  including the double degree programme in Mathematics/Applied Mathematics and  Computer Science, the double major       programmes in Mathematics and Economics as  well as with other subjects, and the Computational Biology programme. Another  example of the Department’s student centric educational philosophy is the   Special Programme in Mathematics (SPM), which is specially designed for a  select group of students who have a strong passion and aptitude for  mathematics. The aim is to enable these students to build a solid foundation  for a future career in mathematical research or state-of-the-art applications  of mathematics in industry.

The  Department is ranked among the best in Asia in mathematical  research.   It offers a diverse and vibrant program in graduate  studies, in fundamental as well as applied mathematics. It promotes  interdisciplinary applications of mathematics in science, engineering and  commerce. Faculty members’ research covers all major areas of contemporary  mathematics. For more information, please see research overview, selected publications, and research     awards.

Academic grading in Singapore: How many marks to get A in Maths for PSLE, O Levels, A Levels

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Singapore‘s grading system in schools is differentiated by the existence of many types of institutions with different education foci and systems. The grading systems that are used at Primary, Secondary, and Junior College levels are the most fundamental to the local system used.

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Primary 5 to 6 standard stream

  • A*: 91% and above
  • A: 75% to 90%
  • B: 60% to 74%
  • C: 50% to 59%
  • D: 35% to 49%
  • E: 20% to 34%
  • U: Below 20%

Overall grade (Secondary schools)

  • A1: 75% and above
  • A2: 70% to 74%
  • B3: 65% to 69%
  • B4: 60% to 64%
  • C5: 55% to 59%
  • C6: 50% to 54%
  • D7: 45% to 49%
  • E8: 40% to 44%
  • F9: Below 40%

The GPA table for Raffles Girls’ School and Raffles Institution (Secondary) is as below:

Grade Percentage Grade point
A+ 80-100 4.0
A 70-79 3.6
B+ 65-69 3.2
B 60-64 2.8
C+ 55-59 2.4
C 50-54 2.0
D 45-49 1.6
E 40-44 1.2
F <40 0.8

The GPA table differs from school to school, with schools like Dunman High School excluding the grades “C+” and “B+”(meaning grades 50-59 is counted a C, vice-versa) However, in other secondary schools like Hwa Chong Institution and Victoria School, there is also a system called MSG (mean subject grade) which is similar to GPA that is used.

Grade Percentage Grade point
A1 75-100 1
A2 70-74 2
B3 65-69 3
B4 60-64 4
C5 55-59 5
C6 50-54 6
D7 45-49 7
E8 40-44 8
F9 <40 9

The mean subject grade is calculated by adding the points together, then divided by the number of subjects. For example, if a student got A1 for math and B3 for English, his MSG would be (1+3)/2 = 2.

O levels grades

  • A1: 75% and above
  • A2: 70% to 74%
  • B3: 65% to 69%
  • B4: 60% to 64%
  • C5: 55% to 59%
  • C6: 50% to 54%
  • D7: 45% to 49%
  • E8: 40% to 44%
  • F9: Below 40%

The results also depends on the bell curve.

Junior college level (GCE A and AO levels)

  • A: 70% and above
  • B: 60% to 69%
  • C: 55% to 59%
  • D: 50% to 54%
  • E: 45% to 49% (passing grade)
  • S: 40% to 44% (denotes standard is at AO level only), grade N in the British A Levels.
  • U: Below 39%

Featured Mathematician of the Day: Shing-Tung Yau

Maths Group Tuition starting in 2014!


Shing-Tung Yau (Chinese: 丘成桐; pinyin: Qiū Chéngtóng; Cantonese Yale: Yāu Sìngtùng; born April 4, 1949) is a Chinese-born American mathematician. He won the Fields Medal in 1982.

Yau’s work is mainly in differential geometry, especially in geometric analysis. His contributions have had an influence on both physics and mathematics and he has been active at the interface between geometry and theoretical physics. His proof of the positive energy theorem in general relativity demonstrated—sixty years after its discovery—that Einstein‘s theory is consistent and stable. His proof of the Calabi conjecture allowed physicists—using Calabi–Yau compactification—to show that string theory is a viable candidate for a unified theory of nature. Calabi–Yau manifolds are among the ‘standard toolkit’ for string theorists today.

Yau was born in Shantou, Guangdong Province, China with an ancestry in Jiaoling (also in Guangdong) in a family of eight children. When he was only a few months old, his family emigrated to Hong Kong, where they lived first in Yuen Long and then 5 years later in Shatin. When Yau was fourteen, his father Chiou Chenying, a philosophy professor, died.

After graduating from Pui Ching Middle School, he studied mathematics at the Chinese University of Hong Kong from 1966 to 1969. Yau went to the University of California, Berkeley in the fall of 1969. At the age of 22, Yau was awarded the Ph.D. degree under the supervision of Shiing-Shen Chern at Berkeley in two years. He spent a year as a member of the Institute for Advanced Study, Princeton, New Jersey, and two years at the State University of New York at Stony Brook. Then he went to Stanford University.

Since 1987, he has been at Harvard University,[1] where he has had numerous Ph.D. students. He is also involved in the activities of research institutes in Hong Kong and China. He takes an interest in the state of K-12 mathematics education in China, and his criticisms of the Chinese education system, corruption in the academic world in China, and the quality of mathematical research and education, have been widely publicized.

Shing-Tung Yau at Harvard Law School dining hall
Shing-Tung Yau at Harvard Law School dining hall (Photo credit: Wikipedia)