The WordPress.com stats helper monkeys prepared a 2014 annual report for this blog.
Here’s an excerpt:
The Louvre Museum has 8.5 million visitors per year. This blog was viewed about 200,000 times in 2014. If it were an exhibit at the Louvre Museum, it would take about 9 days for that many people to see it.
Source: http://mathtuition88.blogspot.sg/2014/12/math-of-qz8501-sum-of-3-numbers-that.html
We sincerely hope that Captain Iriyanto, the pilot of missing AirAsia flight QZ8501, and all other passengers survive and return safely. Hopefully the plane will be found soon.
Something mysterious about the recent missing airplanes is that their numbers add up to 8888, a mystical number in Chinese culture. MH17, MH370, QZ8501, 17+370+8501=8888.
We have calculated that it is not a common event at all, it is rarer than winning the top prize in 4D, a lottery in Singapore.
Probability of 3 random numbers (from 1 to 9999) adding to 8888: 0.0039497% , or around 1 in 25,000.
Probability of winning the First Prize in 4D: 0.01%, or 1 in 10,000.
Read more at: http://mathtuition88.blogspot.sg/2014/12/math-of-qz8501-sum-of-3-numbers-that.html
Featured Book:
Introduction to Probability, 2nd Edition
An intuitive, yet precise introduction to probability theory, stochastic processes, and probabilistic models used in science, engineering, economics, and related fields. The 2nd edition is a substantial revision of the 1st edition, involving a reorganization of old material and the addition of new material. The length of the book has increased by about 25 percent. The main new feature of the 2nd edition is thorough introduction to Bayesian and classical statistics.
With the Star Wars Episode 7 coming up, all Star Wars fans are really excited. The trailer alone has reached 50 million views, barely a month after it was released.
Wait, can Star Wars be related to Math? Yes it can! Check out The Math of Star Wars which describes a Math related question related to Star Wars! As a Math Tutor, I try my best to relate anything and everything to Math! 😛
Christmas is ending soon, and hope everyone had a nice day, and happy new Year!
Featured Book:
Star Wars Workbook: 1st Grade Math
Does your child love Star Wars but hate math? Well, this might just work! A highly rated Workbook based on Star Wars.
One of the pros of Blogger is that JavaScript is allowed, whereas for WordPress, JavaScript is not allowed for security reasons. JavaScript is a pretty cool add on to a website, it can do simple calculations.
I have written a JavaScript Applet to Guess Birthday Month based on First 4 NRIC Digits, at http://mathtuition88.blogspot.sg/2014/12/javascript-app-to-calculate-birthdate.html.
Do check it out if you are interested! (For fun only, it may not be 100% accurate).
The math theory is based on my earlier post at: Formula to guess Month of Birthday from Singapore NRIC.
Featured Post:
Mathematics for 3D Game Programming and Computer Graphics, Third Edition
Refering to How to write Math Formulas on Blogspot / Blogger, Blogspot is also capable of rendering beautiful Math Equations based on LaTeX.
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.
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)
In O Level E Maths, students are required to memorize the prefixes: kilo-, mega-, and giga-. For today’s computer literate generation, that should be no problem since kilobytes, megabytes, and gigabytes are used so commonly.
A practical usage of this is Computer Memory, and how to solve the dreaded Blue Screen of Death.
I have recently discovered a truly remarkable method on how to solve the Blue Screen of Death, using a free tool called Glary Utilities. Read more about it here and hope it helps!
Site: http://mathtuition88.blogspot.sg/2014/12/the-math-of-computer-memory-and-how-to.html
Featured Book:
Computer Math: Problem Solving for Information Technology with Student Solutions Manual (2nd Edition)
The following is a follow up video on my earlier post on Logarithm Question (Challenging).
The video is posted on: http://mathtuition88.blogspot.sg/2014/12/singapore-math-high-school-logarithm.html
Thanks for watching!
Featured Book:
John Napier: Life, Logarithms, and Legacy
Featured Posts:
Is Santa real? Can we prove it using Math that Santa exists / does not exist?
Check out this website at: http://mathtuition88.blogspot.sg/2014/12/the-math-of-santa.html
(Actually it is a sister website of Mathtuition88.com, I have decided to post more often there to build up the site.)
Featured Book:
Everyday Calculus: Discovering the Hidden Math All Around Us
Calculus. For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun, accessible, and surrounds us everywhere we go. In Everyday Calculus, Oscar Fernandez shows us how to see the math in our coffee, on the highway, and even in the night sky.
Free Career Analysis:
Are you a Careerist, Entrepreneur, Harmoniser, Idealist, Hunter, Internationalist, or Leader?
Find out by doing this Free Career Analysis by renowned survey company Universum:
http://uledge.co/ambWWCY
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!
Website: http://uledge.co/ambWWCY
This is a YouTube Video, based on my earlier post on Fibonacci Numbers and the Mysterious Golden Ratio!
Thanks for watching! Remember to speed up the video when necessary!
Featured Book:
The Fabulous Fibonacci Numbers
The most ubiquitous, and perhaps the most intriguing, number pattern in mathematics is the Fibonacci sequence. In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature – from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world.
With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples).
This is an example of Intro Video made using Flixpress!
Pretty easy to make, just take a few minutes. I will be adding more videos to my YouTube Channel soon.
Featured Page:
Source: http://blog.nus.edu.sg/provost/2014/12/23/su1101-the-science-and-art-of-the-su-option/
Check out this link by NUS Provost, Prof. Tan, who was also a Math Professor.
Now, which grades should you keep?
If you obtained A or A+, well done and keep the grade!
If you obtained B+ or A-, I would generally encourage you to keep the grade as well. For those who may be thinking of exercising S/U on a B+ to qualify for the Dean’s List, do note that there will NOT be Dean’s Lists for the first two semesters.
If you obtained Bs and Cs, it is a little tricky. In theory, you should exercise S/U on your worst grades. However, the challenge is to do so without foresight of the grades that you will get for subsequent semesters. You should base your decisions on your academic goals and your self-assessment of your expected academic performance for the rest of your candidature. If you do not have a goal right now, your first semester CAP (before any S/U options are exercised) may be a good guide.
The S/U option is really a lifesaver for those at the borderlines, for example Borderline First Class Honours (CAP around 4.5), or Borderline Second Upper (Cap around 4.0). It makes a difference to your final grades.
The S/U option will apply to all Level 1000 modules (with or without pre-requisites) and Level 2000 modules without other NUS modules as pre-requisites, unless otherwise stipulated by the Faculties/Departments.
Taken from: http://www.nus.edu.sg/registrar/edu/UG/graduation.html#SU
This is a great improvement from the earlier system, where students could only S/U non-core modules. New NUS students have it good!
Featured Book:
The Calculus Lifesaver: All the Tools You Need to Excel at Calculus (Princeton Lifesaver Study Guide)
This is my second ever YouTube Video, and it is about a rarely seen proof (Constructive) that Square Root of Two is irrational.
The video is based on my earlier post on: Constructive Proof that Square Root of Two is irrational
Thanks for watching! Please speed up the video according to your preference! You can speed up either 2x or 1.5x for best effect.
Featured Book:
The Irrationals: A Story of the Numbers You Can’t Count On
The ancient Greeks discovered them, but it wasn’t until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define–and why so many questions still surround them. Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.
The holiday season is here, and check out the deals on Groupon to save while buying presents or delicious food!
https://www.youtube.com/watch?v=buhghuawde0
This is my first video on YouTube! 🙂
Please subscribe to my channel for more Math Videos coming in the future!
Featured Book:
Algebra Survival Guide Workbook: Thousands of Problems To Sharpen Skills and Enhance Understanding
$latex (a-b)^3=a^3-3a^2b+3ab^2-b^3$
So,
$latex
begin{array}{rcl}
a^3-b^3&=&(a-b)^3+3a^2b-3ab^2
&=&(a-b)(a-b)^2+3a^2b-3ab^2
&=&(a-b)(a^2-2ab+b^2)+(a-b)(3ab)
&=&(a-b)(a^2+ab+b^2)
end{array}
$
Hi Readers,
Are you looking for a printable 2015 Calendar, specially tailored for Singapore?
Check out this PDF printable 2015 calendar: Calendar
(Generated by http://www.calendarlabs.com/pdf-calendar.php)
Happy new year!
Featured book:
Give a child gifts that will last a lifetime – self-esteem, tolerance, values, and inner strength. This book is filled with inspirational stories for children and their families to share, all about kids making good choices and doing the right thing.
The values that children learn today will stay with them for the rest of their lives. This collection gives kids positive role models to follow in its 101 stories about doing the right thing and making healthy choices. You and your child will enjoy discussing the stories, making it a family event. Great for teachers to share with students too.
My previous posts on Clash of Clans Math (on Mortar damage, and Gold mine) were fairly popular, so I have decided to write one more post! This shows that Math can be applied to almost everything, even games!
Vs 
Recently, players of COC will know that the Level 7 Giant has been released. For fans of the Giant (I am one of them), this is great news. The Giant is a cheap substitute for tanking vs the Golem, and can be used in many strategies for instance Giwipe (Golem, Wizard, Pekka), Garch (Giant archer), among many others.
In this post, I will use Math to concretely compare the Level 7 Giant and the Level 5 Golem. For fairness sake, we will compare 6 Giants with 1 Golem (since they take up 30 spaces). Sources are taken from http://clashofclans.wikia.com/.
Conclusion: Golem is around 30% better than Giants in term of HP.
Calculation: (8820-6600)/6600 x 100%=33.6%
For pure tanking, nothing beats a max level Golem.
Conclusion: Giants are 450% better than Golems in terms of DPS!
This can be quite significant, for example, when using Giants in Giwipe, often one does not even need to use wallbreakers, since the giants can break through the walls on their own. This frees up more spaces for wizards/other troops.
Spring Traps are the ultimate nemesis of Giants, since each Spring Trap can bounce 15 Housing spaces, or 3 Giants.
To avoid Spring Traps, place a few barbarians before sending out your giants. Hopefully the barbarians will activate (and waste) a few spring traps.
Conclusion: Golems are more resistant to Spring Traps.
Conclusion: Superficially, it seems good that Golems take 80% less damage than giants from Multi-mode Infernos. However, a bit of thinking reveals that the inferno in multi-mode will be attacking your other troops (for example wizards) instead, together with the 1 Golem. Hence, in other words, Golems also tank 80% less damage than giants from Multi-mode Inferno towers.
This calculation gets a little complicated. The inferno (Level 3) has 36 DPS initially, then 140 DPS after 2 seconds, then a whopping 1400 DPS after 5 seconds.
Conclusion: Giants survive 260% longer than Golems under Inferno (Single Target) Fire!
Other last points to note are that everytime a giant dies, there is a switch of targets, potentially attacking weak but crucial units like wizards or witches. This is a downside of giants.
Featured Product:
Fans Game Design Men T Shirts – O Collar T-Shirt
An interesting news to share:
Billionaire Ronnie Chan Chi-chung seems to have it all figured out. Were the Hang Lung Properties chairman to live his life over again, it would not be as a businessman — he’d be a mathematician or scientist instead.
Chan, who offered this little gem during a speech at the Hang Lung Mathematics Awards ceremony, said he may have more material wealth than famed mathematician Yau Shing-tung but much less intellectual wealth.
As co-founder of the awards, which were set to encourage secondary school students to pursue maths and sciences, Chan urged youngsters to go the extra mile and become mathematicians or scientists as they can contribute more to society than what a businessman can.
Read more at: http://www.thestandard.com.hk/news_detail.asp?we_cat=21&art_id=152297&sid=43527569&con_type=1&d_str=20141212&fc=8
Hopefully this can encourage students currently studying Maths, be it O Level Maths, JC H1 or H2 Maths, or even University Maths!
Featured Book:
The Shape of Inner Space: String Theory and the Geometry of the Universe’s Hidden Dimensions
New Scientist
“It is a testimony to [Yau’s] careful prose (and no doubt to the skills of co-author Steve Nadis) that this book so compellingly captures the essence of what pushes string theorists forward in the face of formidable obstacles. It gives us a rare glimpse into a world as alien as the moons of Jupiter, and just as fascinating…. Yau and Nadis have produced a strangely mesmerizing account of geometry’s role in the universe.”
Nature
“Physicists investigate one cosmos, but mathematicians can explore all possible worlds. So marvels Fields medalist Shing-Tung Yau…. Relating how he solved a major theoretical problem in string theory in the 1970s, Yau explains how the geometries of the vibrating multidimensional strings that may characterize the Universe have implications across physics.”
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
has something to do with the quadratic formula
. After my explanation though, they are enlightened, and finally can understand why
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
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
Watch this very inspirational video about learning.
When students encounter a difficult Math problem, there are two ways to approach it. Are you not smart enough to solve it … or have you just not solved it yet? The mindset the student adopts can make a huge difference in the learning effectiveness.
The key point is that there is great power of believing that you can improve. Adopting a growth mindset enables students to transcend their initial limitations and improve to a new level.
Featured Book:
Self-theories: Their Role in Motivation, Personality, and Development (Essays in Social Psychology)
Source: Science Daily
Date: December 15, 2014
Source: Emory University
Summary: Monstrous moonshine, a quirky pattern of the monster group in theoretical math, has a shadow — umbral moonshine. Mathematicians have now proved this insight, known as the Umbral Moonshine Conjecture, offering a formula with potential applications for everything from number theory to geometry to quantum physics.
“We’ve transformed the statement of the conjecture into something you could test, a finite calculation, and the conjecture proved to be true,” says Ken Ono, a mathematician at Emory University. “Umbral moonshine has created a lot of excitement in the world of math and physics.”
Co-authors of the proof include mathematicians John Duncan from Case Western University and Michael Griffin, an Emory graduate student.
“Sometimes a result is so stunningly beautiful that your mind does get blown a little,” Duncan says. Duncan co-wrote the statement for the Umbral Moonshine Conjecture with Miranda Cheng, a mathematician and physicist at the University of Amsterdam, and Jeff Harvey, a physicist at the University of Chicago.
Ono will present their work on January 11, 2015 at the Joint Mathematics Meetings in San Antonio, the largest mathematics meeting in the world. Ono is delivering one of the highlighted invited addresses.
Read more at: Science Daily
Featured Book:
Moonshine beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics (Cambridge Monographs on Mathematical Physics)
“An excellent introduction to this area for anyone who is looking for an informal survey… written in a lively and readable style.”
R.E. Boucherds, University of California at Berkeley for the Bulletin of the AMS
“It is written in a breezy, informal style which eschews the familiar Lemma-Theorem-Remark style in favor of a more relaxed and continuous narrative which allows a wide range of material to be included. Gannon has written an attractive and fun introduction to what is an attractive and fun area of research.”
Geoffrey Mason, Mathematical Reviews
“Gannon wants to explain to us “what is really going on.” His book is like a conversation at the blackboard, with ideas being explained in informal terms, proofs being sketched, and unknowns being explored. Given the complexity and breadth of this material, this is exactly the right approach. The result is informal, inviting, and fascinating.”
Fernando Q. Gouvea, MAA Reviews
Are you curious what do Mathematicians eat for breakfast? 🙂
Featured Book:
The Math of Food (Integrating Math in the Real World Series)
How can math help you improve your diet?
Sharpens math skills from whole-number operations through basic algebra and geometry
Builds problem-solving and critical-thinking skills
Includes teacher notes, concepts and skills covered, relevant Internet sites, and more
In O Level E Maths, we learn how to bisect an angle using compass and straightedge (ruler). However, is it possible to trisect an angle?
It turns out it is impossible! This took 2000 years to prove, and requires the use of a very difficult theory called Galois Theory.
Check out this interesting video on trisecting angles:
It turns out it is possible to trisect angles using Origami though:
Featured Book:
Galois’ Theory Of Algebraic Equations
Galois’ Theory of Algebraic Equations gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The main emphasis is placed on equations of at least the third degree, i.e. on the developments during the period from the sixteenth to the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as “group” and “field”. A brief discussion on the fundamental theorems of modern Galois theory is included. Complete proofs of the quoted results are provided, but the material has been organized in such a way that the most technical details can be skipped by readers who are interested primarily in a broad survey of the theory. This book will appeal to both undergraduate and graduate students in mathematics and the history of science, and also to teachers and mathematicians who wish to obtain a historical perspective of the field. The text has been designed to be self-contained, but some familiarity with basic mathematical structures and with some elementary notions of linear algebra is desirable for a good understanding of the technical discussions in the later chapters.
Source: Baidu Encyclopedia (Liu Hong)
刘洪(约公元130～210)，字元卓，东汉泰山郡蒙阴县（今山东省临沂市蒙阴县）人，东汉鲁王刘兴后裔，我国古代杰出的天文学家和数学家，珠算发明者，被后世尊为“算圣”。
Liu Hong (Year 130~210) was an ancient Chinese Mathematician who studied astronomy and mathematics. He was the inventor of the art of abacus arithmetic, and hence was given the title of “Sage of Arithmetic”.
Recently, I was fortunate to visit a statue of Liu Hong at his birthplace (modern day Linyi).
(Me beside statue of Liu Hong at Linyi People’s Square, Shandong)
Featured Book:
How To Use A Chinese Abacus: A step-by-step guide to addition, subtraction, multiplication, division, roots and more.
This book will teach you step-by-step how to perform addition, subtraction, division, multiplication, square roots and cube roots on a Chinese abacus. It also explains the ancient ‘extra bead’ method and the ‘suspended bead’ method. Great for both children and adults. Clearly explained with text and pictures throughout every stage of your calculation.
The discriminant of a quadratic polynomial (
Question: 
Solution: http://www.fen.bilkent.edu.tr/~cvmath/Problem/1411a.pdf
One of the above people who answered correctly, Toshihiro Shimizu, is an IMO Gold Medalist from Japan.
Featured Book:
Mathematical Olympiad Challenges
Highly Rated on Amazon!
Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory
Historical insights and asides are presented to stimulate further inquiry
Emphasis is on creative solutions to open-ended problems
Recently, I completed an excellent Coursera Course: An Introduction to Functional
Analysis, offered by École Centrale Paris.
Although challenging, it was a fun and interesting course, thanks to the effort by Professors John Cagnol and Anna Rozanova-Pierrat. Functional Analysis is a pretty difficult topic, and it was great to have two good professors explain it.
This course is actually more suitable for students who have some mathematical background, especially in mathematical analysis. New students may find it too hard to follow it from scratch. It is excellent as a review course for students who have taken functional analysis a few years ago but have forgotten some of it.
Featured Book:
Introductory Functional Analysis with Applications
Here are some tips to organize your studying time!
How to Better Organize After School Studying?
The key to achieving success in every academic discipline is practice, practice and more practice. However, this is where many students struggle the most: finding the time and the right methods to study after school. If you want to help your child study better, here is a simple to-do list:
Find the best method for your kid
Children have their own individual studying patterns, some of them prefer to study by themselves, some kids learn more when they participate in study groups, while other children, especially students with learning difficulties, might require a help of a professional tutor. You have to first recognize your child’s needs, try different methods and evaluate the results. Remember that the key to successful studying is regularity: even the best tutor will not be able to help your child, if they meet sporadically. Schedule a time for after school studying every week and check if your child adheres to it.
Take regular breaks
It is good to have a strict studying schedule, but breaks are also important. Regular breaks help boost child’s creativity and approach the task at hand with more enthusiasm.
Intensify as the exam approaches
If the after school studying is meant as a preparation for the upcoming exam, remember to start studying early and intensify as the day of the exam approaches. For example, start from doing simple Singapore Math exercises a few weeks before the day of the exam and progress to more complex issues, while increasing the workload. Never let your child study overnight before the exam, it will only make him feel more tired and stressed out on the day of the exam, plus this kind of behavior supports bad studying habits and false convictions that everything can be mastered within a few hours and there is no need to learn on a day to day basis.
Resource: http://eastwestmath.com
Here is a helpsheet that I created on the topic of Domain and Range of Inverse Functions, a topic no longer in O Levels but still in IP Math.
Featured Book:
This is an article describing careers in the automobile industry. Hope it is useful for students interested in this area of work! 🙂
What are the Main Careers in Automobile Industry?
The automobile industry contributes greatly to the employment of many citizens in the country. It is one industry, which supports just any other industry you might think of. Many people feel its influence – the people commuting to work, the drivers who deliver goods to customers, the emergency services engineers, technicians, and mechanics. As one way of promoting the growth of the automobile industry, the Ideal Auto USA provides direct and indirect employment through selling some of the eco-friendly cars in the industry.
Careers in the automobile industry
There are many kinds of employment opportunities in this industry often employing some of the brightest minds like the engineers. Because there is a wide array of jobs, one would have to find a suitable choice based on his or her interest and qualifications. If you have the right training, you can easily advance higher in the positions. The technicians are responsible for things like replacing air filters, changing oils, and balancing wheels. These technicians handle many other maintenance tasks such as doing tune ups and changing the brake pads.
Apart from the technicians, there are the mechanics that repair cars. These workers are categorized one or two levels up the employment ladder from the technicians. At times, people confuse the mechanics with technicians, but the reality is that mechanics are more advanced than automobile technicians are.Besides performing many of the tasks done by technicians, they have knowledge on how to repair cars and work on engines.
While mechanics may work for companies or other people, when they have the business skill and the required capital, they can set up their own business. A repair shop is certainly one rewarding business, which can help mechanics further their career.
The automakers and car dealers employ many workers from the cleaners, service team, the mechanics, engineers, sales persons, drivers, and managers. All these people and their families get support from the industry. There are also indirect jobs, which come with this industry such as the workers employed in steel plants, glass making plants, or computer chip makers, which make the materials for manufacturing cars.
Salary range for automobile careers
According to Bureau of Labor Statistics, the automotive service technicians as well as the mechanics earned an average wage of about $38,560 as in May 2011 while the average salary for the mechanical engineers who work in the automobile manufacturing was at averagely $95,080. These figures show that the workers especially those with some skill in the automobile sector command quite a substantial pay.
If you want to make a living when working in the automobile industry, you might want to get some education be it in sales and marketing, engineering, motor vehicle mechanics, or even a driver. With Ideal Auto USA, it offers the best cars in the industry, which is a way of expanding the career market as more workers get employment as drivers and mechanics.
Tim Bryson is a practising automobile mechanic and has been working in this industry for more than 8 years. For the best eco-friendly cars that will drive the automobile industry, you can visit Ideal Auto USA.
These are some Fourier Series (learnt in University Maths courses) videos from YouTube. Very interesting and enlightening!
The gist of the theory of Fourier Series is that a function (periodic) can be expressed as an infinite sum of sine and/or cosine functions.
Featured Book:
Fourier Analysis: An Introduction (Princeton Lectures in Analysis)
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences–that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.
Students studying Mathematics at university will sooner or later hear of the famous eccentric Mathematician Paul Erdos, and the concept of Erdos Number. People who have written a paper with Erdos have a Erdos number of 1. People who have cowritten with the above people (with Erdos number 1), have Erdos number 2. Unfortunately, it is now impossible to get Erdos number 1, as Paul Erdos has passed away.
But what is an Imaginary Erdos Number?
This YouTube channel Numberphile has really succeeded in making Maths interesting! I watch almost every new episode that comes out, and will feature it on my website.
Featured Book:
MY BRAIN IS OPEN: The Mathematical Journeys of Paul Erdos
Paul Erdõs, one of the greatest mathematicians of the twentieth century, and certainly the most eccentric, was internationally recognized as a prodigy by age seventeen. Hungarian-born Erdõs believed that the meaning of life was to prove and conjecture. His work in the United States and all over the world has earned him the titles of the century’s leading number theorist and the most prolific mathematician who ever lived. Erdõs’s important work has proved pivotal to the development of computer science, and his unique personality makes him an unforgettable character in the world of mathematics. Incapable of the smallest of household tasks and having no permanent home or job, he was sustained by the generosity of colleagues and by his own belief in the beauty of numbers.
Witty and filled with the sort of mathematical puzzles that intrigued Erdõs and continue to fascinate mathematicians today, My Brain Is Open is the story of this strange genius and a journey in his footsteps through the world of mathematics, where universal truths await discovery like hidden treasures and where brilliant proofs are poetry.
There are pros and cons of taking H1 or H2 Maths:
H1 Maths is an easier version, and will definitely take less time to study. This time can be used for studying other subjects. Also, it covers statistics which can come in handy for majors like Psychology, Social Science, or Business. Students who take A Maths in O Level will find that the Pure Math part of H1 Maths is basically the same, if not even easier than O level A Maths.
H2 Maths is the harder version, more difficult than even the O Level A Maths. New and interesting topics like Complex Numbers and Vectors will lay a good foundation for University majors like Engineering and Physics. Try not to forget what you have learnt in O Level A Maths, it will come in handy.
Students who wish to enter SMU & take H1 Maths in JC may want to note that SMU has a introductory module on calculus which is pretty much compulsory, even for majors like social science. I have taught a student from SMU, and would say that the content is heavier than even H2 Math Calculus; there is multivariable calculus in the SMU Course.
Featured Book:
Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks
To all Singaporean readers and parents,
We are proud to recommend some excellent Graphic Design and Fashion Degree Programmes, by First Media Design School. The degree is being conferred by the University of the West of England, Bristol.
For those who are interested to enroll in this school, please contact me (Mr Wu) at mathtuition88@gmail.com. I have some extra information booklets about the course provided by the company, and will be pleased to guide you in the registration process.
Once again, if you are interested to enroll, please contact me as soon as possible. Thanks!
Some of the Maths topics that Engineering Students need to learn are:
All the above topics are rather challenging and deep. Fortunately, for most engineering students, application of the theorems would suffice, the deep proofs are not really necessary. It would be good to know them though.
Featured Book:
Schaum’s Outline of Advanced Mathematics for Engineers and Scientists (Schaum’s Outline Series)
This is the book you are looking for, if you are looking for a book to help ace Engineering Maths.
Just to summarize the 10 Surprising Facts:
Read more at: http://www.takepart.com/photos/ten-surprising-facts-finlands-education-system-americans-should-not-ignore/more-languages
Featured book:
This book is highly recommended for those who are interested in the 4 Temperaments and related research (Introvert, Extrovert, Sanguine, Choleric, Melancholic, Phlegmatic, etc.)
Source: http://www.math.illinois.edu/~verahur/18.024/notesSD.pdf
Excerpt:
Proof of the second-derivative test. Our goal is to derive the second-derivative test, which determines the nature of a critical point of a function of two variables, that is, whether a critical point is a local minimum, a local maximum, or a saddle point, or none of these. In general for a function of n variables, it is determined by the algebraic sign of a certain quadratic form, which in turn is determined by eigenvalues of the Hessian matrix [Apo, Section 9.11]. This approach however relies on results on eigenvalues, and it may take several lectures to fully develop. Here we focus on the simpler setting when n = 2 and derive a test using the algebraic sign of the second derivative of the function.
The full proof can be found in the featured book below: T. Apostol, Calculus, vol. II, Second edition, Wiley, 1967
Featured book:
Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability (Volume 2)
Sounds bizarre, but it is true! Something “uniquely Singapore” as 92 marks is usually the top echelon for most other countries.
Students need not be disappointed, as 88 to 92 marks is already a very respectable score. Most important is to understand the subject well, and try to improve.
Source: http://news.asiaone.com/news/education/tuition-no-enough
Despite scoring between 88 and 92 marks for his subjects, he was placed in the third quartile of his cohort.
“Which means he was not among the top 50 per cent,” says his mum, Mrs Jaclyn Chew, 41.
Her son, who attends an all-boys school in north-eastern Singapore, was crestfallen after he asked his parents how he fared.
“I had to tell him the truth about where he stood compared to his peers,” Mrs Chew says.
“It’s just bizarre that with his grades and the tuition, he’s still in the lower half of the grade spectrum.”
– See more…
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Source: Spiked Math
Can you guess what are the names of the movies above (phrased in terms of Math).
Some hints:
are some of them.
You may discuss in the comments below!
At the undergraduate level, sometimes functions are of two variables (x,y). How do we find the maximum or minimum points of such a function?
Read the following PDF to find out!
Recommended Book:
Multivariable Calculus, 7th Edition
This is a highly practical book on Multivariable Calculus. It is also suitable for Engineers / Physics Majors. I learnt Multivariable Calculus from this book. 🙂
Here is a Integration by Parts helpsheet I created and uploaded on Scribd. Integration by Parts is a really useful technique, in fact it is one of the two key integration techniques in H2 Maths. The other technique is Integration by Substitution.
Featured book:
The Humongous Book of Calculus Problems
This book is really “humongous”. If you need to source for practice problems for Calculus, this is a good place to start. 🙂
Translation: How do we move only 1 matchstick to make the equation valid?
(“Not Equals” sign 
This is a really tricky question… Hint: Need to think in Chinese, this is a Chinese joke 😛
Featured Post:
The Motivational Books recommended in the above post seems to be very popular with readers on this site. Many readers (presumably parents) have bought the books! Buy a Christmas present for yourself this Xmas. 🙂
“It is more blessed to give than to receive.” – Acts 20:35
Source: http://www.bbshare.sg/
Join the Boys’ Brigade in spreading the Christmas cheer to needy families in Singapore.
To most of us, items like rice and biscuits are ordinary and common, but to the needy and elderly in Singapore, they are necessities and much needed items.
There are 3 ways to help:
Wishing all our readers a Merry Christmas!
Featured Book:
For any parent who has ever been told, “your child isn’t performing up to his or her potential,” this book has the answer. Renowned clinical psychologist Michael Whitley, Ph.D. offers a proven ten-step program to motivate underachieving children. This easy-to follow book identifies the six types of underachievers from the procrastinator to the hidden perfectionist to the con artist, and it…
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Just to share a career guide, for those students about to graduate. Hope it helps!
Launch Your Career with Salesforce Award-Winning Recruitment Programs for College Students
It is never too early to start building your career, especially if you have certain goals you intend to achieve by certain landmark years. It is therefore important to look for a place where you can feel challenged to grow in your career and as an individual in a stimulating and supportive environment. Well, the good news is that Salesforce has not only one but also two programs that you can plug into to get your career moving.
Award-winning recruitment
These are not your ordinary, run-of-the-mill types of college recruitment programs. Both programs have won the Best Places to Work for Recent Grads awards three times (2011, 2012 and 2014) and the Indiana Intern.net Employer of the Year award twice (2011 and 2012). However, what are these programs that I’m harping about here?
First, you have the Catapult Rotational Program. This is a summer internship for undergraduate and graduate students. How does it work?
You choose a track that you would like to receive training in; whether in Business, Technology or Consulting (your college degree should give you a hint here).
Then you rotate among three teams for three months each where you will develop your main professional skill along with obtaining valuable experience in related departments.
At the end of the nine months, you will be absorbed into a full-time, permanent position in your specific department, where you will enjoy all the benefits of being a full-time employee of the ExactTarget Marketing Cloud (there’s dental too)
The other program is the Slingshot Internship program,which also runs during the summer for graduates and undergraduates who are in their sophomore, junior or senior year in college. This offers a real-world feel of what you can expect in your field of expertise.
You will have the opportunity for some hands-on work like working on the Salesforce metadata api and you will be required to complete two projects worthy of being included in your resume within the stipulated time of internship. You get the opportunity to network with the executive team and shadow an individual in your preferred career.
It’s not all work though. There are social events and philanthropic outings plus you receive a house stipend and competitive pay for all your hard work.
Not a dull moment
Regardless of the program that you choose, you have a guarantee that no two days will be the same. These programs expose you to the reality of life in your chosen career and get you more than ready for what is to come. It is very high octane and you are going to love it!
How do I get in?
Application for the programs begin in August and as you can imagine they fill in quite quickly so it is advisable to keep tabs on when the application process opens so that you can get yours in as fast as you can.
As expected, there are also certain qualifications that you have to meet and you can take a look at them on their website or through their college recruitment program FutureForce which has accounts on Twitter and Instagram.
It is an overall excellent opportunity that you should certainly look into.
Author Bio
Brennan Booth is a careers blogger in the field of technology. She is trained as a software engineer with lots of experience in the industry. To read more about Salesforce metadata api click the link.
Do you want to be a tutor, but find tuition agencies’ 50% commission too high?
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Good news for you who are interested in Cryptography, which is at the intersection of mathematics and computer science. Highly useful both in everyday life and also in top secret projects, like the cracking of the Enigma machine during World War II.
URL: https://www.coursera.org/course/crypto
The course is starting next year Jan 5, so bookmark the page if you are interested!
I will be joining the course too.
Featured book:
The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography
In his first book since the bestselling Fermat’s Enigma, Simon Singh offers the first sweeping history of encryption, tracing its evolution and revealing the dramatic effects codes have had on wars, nations, and individual lives. From Mary, Queen of Scots, trapped by her own code, to the Navajo Code Talkers who helped the Allies win World War II, to the incredible (and incredibly simple) logisitical breakthrough that made Internet commerce secure, The Code Book tells the story of the most powerful intellectual weapon ever known: secrecy.
Throughout the text are clear technical and mathematical explanations, and portraits of the remarkable personalities who wrote and broke the world’s most difficult codes. Accessible, compelling, and remarkably far-reaching, this book will forever alter your view of history and what drives it. It will also make yo wonder how private that e-mail you just sent really is.
Source: http://en.wikipedia.org/wiki/Mathematical_coincidence
If you have a calculator, check out the value of 
Why is it so close to the integer 20? Is it a coincidence (few things in Math are coincidence), or is it a sign of something deeper? e and Pi are two very fundamental numbers in Math, and the very fact that 
This was observed by a few mathematicians (Conway, Sloane, Plouffe, 1988) many years ago, but till this day there is no answer.
Do give it a thought!
Featured book:
Pi: A Biography of the World’s Most Mysterious Number
We all learned that the ratio of the circumference of a circle to its diameter is called pi and that the value of this algebraic symbol is roughly 3.14. What we weren’t told, though, is that behind this seemingly mundane fact is a world of mystery, which has fascinated mathematicians from ancient times to the present. Simply put, pi is weird. Mathematicians call it a “transcendental number” because its value cannot be calculated by any combination of addition, subtraction, multiplication, division, and square root extraction.
In this delightful layperson’s introduction to one of math’s most interesting phenomena, Drs. Posamentier and Lehmann review pi’s history from prebiblical times to the 21st century, the many amusing and mind-boggling ways of estimating pi over the centuries, quirky examples of obsessing about pi (including an attempt to legislate its exact value), and useful applications of pi in everyday life, including statistics.
This enlightening and stimulating approach to mathematics will entertain lay readers while improving their mathematical literacy.
Also check out: Recommended Books for GEP
PSLE Results will be out tomorrow!
Wishing all students and parents all the best. 🙂
Currently, the PSLE Top Scorer is not released in mainstream media unlike in the past. It is perhaps a good thing too, to make PSLE less stressful.
PSLE is a stepping stone for students, it is important to remember that there is still a long way ahead. Many students who didn’t do well in PSLE end up excelling in O Levels. Education is really about lifelong learning.
1The results of the 2014 Primary School Leaving Examination (PSLE) will be released on Friday, 21 November 2014. Students may obtain their result slips from their respective primary schools from 11.00 am on 21 November 2014.
Read more at: http://www.moe.gov.sg/media/press/2014/11/release-of-2014-psle-results-and-2014-secondary-one-posting.php
Featured book:
Math Doesn’t Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail
Recently I have started accepting some sponsored posts and family-friendly advertisements on my blog: https://www.fiverr.com/mathtuition88/put-permanent-link-on-my-pagerank-4-site?funnel=2014112008100627112079920
Education related guest posts are welcome.
Need to be family-friendly sites. 🙂
Link will be put on my website: http://mathtuition88.com with PageRank 4, and over 500 unique views per day.
Do check out the widely acclaimed portal Fiverr: https://www.fiverr.com/mathtuition88/put-permanent-link-on-my-pagerank-4-site?funnel=2014112008100627112079920 for more details.
Due to the educational nature of this blog, I will only accept family-friendly and kid-friendly advertisements. 🙂
Advertisements related to education will almost certainly be approved as it fits the theme of our blog.
WordPress.com accepts Sponsored Posts: http://en.support.wordpress.com/sponsored-posts/ and it is one of the ways to fund the hosting of websites. Do give it a try if you have a blog to0. 🙂
Just to test out this amazing System of Equations Widget by Wolfram Alpha:
It works! 🙂
Featured book:
Linear Algebra For Dummies
An easy-to-follow guide to practical, real-world applications of linear algebra Linear algebra is a branch of mathematics that uses matrices to solve systems of linear equations; it has applications in many disciplines, from sociology and game theory to computer programming, engineering, and business.
Here is a guide for preparing for interviews, for students about to graduate. Also useful for those applying for scholarship interviews. 🙂
Guide for Preparing for Interviews
Preparation is a vital aspect of any successful interview. After receiving an invite to attend an interview, you need be prepared in order for you to make the right kind of impression on the interviewer. This will make it possible for you to express how you will be a worthwhile addition to the company. You need to do a number of things before the interview. One of the most crucial steps towards a successful interview is research and implementing the tips on validatejob.com.
Carry out Research
Carry out enough research regarding the role you have applied for as well as what the organization does. Find out the terms of the position in regards to aspect such as whether it will be an hourly job or part time job. During this process, you will be able to establish whether you have the right set of skills and experience for the job or not. You need to find out exactly what the employer needs from you and on how you can fulfill this need through your expertise in a particular field.
Before the interview, it is a good idea to anticipate what kind of questions you should expect and practice how you will answer them. Make an effort to find out what kind of interview it will be in terms of where and how the employer will conduct it. Proper planning will ensure that you arrive at the interview earlier than expected. Give yourself enough time to get to the location of the interview and have a moment to relax before the interview starts.
Dress Appropriately and Arrive on Time
Be fully aware of what you will wear to the interview and make sure that your choice is appropriate for the day. Wear the right kind of clothes and shoes to ensure that you look professional without compromising on comfort. It is advisable for you to get enough rest before the day of the interview. You are more likely to perform well if you have enough hours of sleep.
Making a positive impression during the interview will depend on factors such as how early you arrive as well as your level of organization. You will stand out from the rest of the candidates if you arrive on time or earlier than scheduled. You will also make a long lasting impression if you show how organized you are by ensuring that you carry all relevant documentation with you.
Pay Attention and Communicate Effectively
When the interviewer asks questions, pay attention and listen keenly. This will make sure that you give the right answers and address the concerns of the interviewer. Your answers should be informative but not too long or too short. Maximize on the opportunity by ensuring that the employer knows what your best qualities are as well as their relevance to the role that you are aspiring for.
Both verbal and non-verbal communication will have an effect on the interviewer. Speak confidently and make eye contact while maintaining good posture. Your actions should mirror your words because interviewers are generally observant in regards to body language. It is normal for people to be nervous before and during interviews. However, you need to find a way to overcome your nervousness in order for you to excel at the interview. Ample preparation and practice will help to ease your nerves and calm you down.
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Mathtuition88 