Author: mathtuition88

Math and Education Blog

Latest Posts on Mathtuition88.blogspot.com

Recently, I have been blogging at http://mathtuition88.blogspot.com. Here are the latest posts that you may want to check out!

This is a JavaScript app that I wrote to perform the XOR function on two hexadecimal strings. This is to help solve one of the cryptography assignements on Coursera.

I am providing tuition for SMU Calculus module: Math 001. A previous student of mine passed the module, despite not having any H2 Maths background. The module is highly challenging, and includes multivariable calculus.

  • Dragon Curve and Jurassic Park
    This is to introduce two videos on the mysterious and fascinating fractal: The Dragon Curve. Not many people have heard about it!

Featured Book:

The Fractal Geometry of Nature

Review

“A rarity: a picture book of sophisticated contemporary research ideas in mathematics.”–Douglas Hofstadter, author of Godel, Escher, Bach

 

 

Free JavaScript App to split text every few characters

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

Site: http://mathtuition88.blogspot.sg/2015/01/javascript-application-to-split-text.html

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

Screenshot:

screenshot javascript

Important Guidelines For Cracking Interview In Finance Company

Hope this article will be useful for students wishing to enter into the highly popular but also competitive Finance Industry! Finance jobs are open to students who major in diverse disciplines, including Engineering.

Important Guidelines For Cracking Interview In Finance Company

Cracking an interview at times seems to be a daunting task. If you are facing the jitters because of the upcoming interview in the finance company, then the best way to do so is to be prepared for the interview. Though there is no on-stop solution for the same, but remembering few important points can help you to overcome the fear related to the interview. During the interview in the financial sector, the interviewers assess whether the candidate is appropriate for the job, both in the professional and personal level. It is important for the job-seekers to communicate their ideas clearly during the interview process so that the prospective employer can gage how the candidate will perform under pressure.

Few tips to remember

Some amount of research, planning and preparation is required to crack the interview. Adequateknowledge regarding the subject is the key to crack the interview. Following few simple tips can help you to master the interview.

  • Research about the company as the services and products that are catered by the company. You can go through the website of the company and have an insight of the same. Recent news, press releases and recent accomplishments can help you to stay abreast about the financial company.
  • Identify your character traits as the strength and weaknesses and assess whether you are suitable for the job. It is imperative to say that the recruiters emphasize on the skill set of the candidate while they describe a job responsibility. Prior to the interview, make sure that you go through the job responsibility so that you can gage the qualities that the recruiters are looking for. This will also give you the hint of the questions that they might ask you during the interview. So after you have identified your behavioral traits, you can determine the ways through which you can add value to the company.
  • Interview gives the applicants the platform to showcase their skills and knowledge. So, make sure that you carry a detailed portfolio. This will include two copies of the resume, and along with the different certificates that will reflect your credentials. Make sure that you have these documents in one folder so that you can produce them with ease without going through piles of paper. Prepare the documents in accordance to the job description and the requirement of the job and the company. This also reflects your professionalism. If you have prior experience of working in any financial company, it is wise to showcase that.
  • Your appearance and presentation are also importance for creating an impression on the recruiters. Your attire affects the psyche of the recruiters, so pay heed to what you wear for your interview. If you are wearing any perfume, make sure that it is not too strong.
  • It is important to be polite during the interview. Make sure that you communicate clearly with the interviewer. Remember the way you present yourself will create a negative or positive impression about you. Convey your dedication towards your work and also your pride. Refrain from interrupting your recruiters as this might irk them.
  • While responding to the questions maintain a decent way. Your posture and gait also createsa positive impression on the recruiter.
  • Reach the venue of the interview ahead of the scheduled interview in formal attire.Great the receptionist or the concerned person on meeting them.
  • You can prepare a list of questions that are likely asked in the interviews and practice the same.

Knowing these tricks will help you to answer the questions asked during the interview seamlessly. It is important to remember that the key to cracking the interview is to stay positive and remain cool all through.

Author Bio: Ralph Spencer is a career counselor, and he also writes blogs on the tips for a successful career. You can click here to know the tips of cracking an interview.

 

New Year Maths Movie to Watch: The Imitation Game

Reblogged from: http://mathtuition88.blogspot.sg/2015/01/math-movie-imitation-game.html

imitation game

 

Read more at: http://mathtuition88.blogspot.sg/2015/01/math-movie-imitation-game.html

Featured Book:

Alan Turing: The Enigma: The Book That Inspired the Film “The Imitation Game”

This book is currently ranked Top 100 book in the whole world! (#95 according to Amazon.com)

It is only a slight exaggeration to say that the British mathematician Alan Turing (1912-1954) saved the Allies from the Nazis, invented the computer and artificial intelligence, and anticipated gay liberation by decades–all before his suicide at age forty-one. This acclaimed biography of the founder of computer science, with a new preface by the author that addresses Turing’s royal pardon in 2013, is the definitive account of an extraordinary mind and life.

Capturing both the inner and outer drama of Turing’s life, Andrew Hodges tells how Turing’s revolutionary idea of 1936–the concept of a universal machine–laid the foundation for the modern computer and how Turing brought the idea to practical realization in 1945 with his electronic design. The book also tells how this work was directly related to Turing’s leading role in breaking the German Enigma ciphers during World War II, a scientific triumph that was critical to Allied victory in the Atlantic. At the same time, this is the tragic account of a man who, despite his wartime service, was eventually arrested, stripped of his security clearance, and forced to undergo a humiliating treatment program–all for trying to live honestly in a society that defined homosexuality as a crime.

The inspiration for a major motion picture starring Benedict Cumberbatch and Keira Knightley,Alan Turing: The Enigma is a gripping story of mathematics, computers, cryptography, and homosexual persecution.

Free Psychometric Career Matching Service

If you know or are a stressed teen, returning veteran, or a high school counselor then this free online service may be of great service to you. MyVerse is a free online service dedicated to psychometrically matching individuals to 1-5 careers via a color test. MyVerse will be a great first step towards a career path, and create a foundation for a person to build upon.

Right now 92% of high school seniors are not sure what career path they want to take and there is a 52% drop out rate among first year college students. MyVerse will help guide individuals along the correct path and give people a goal to achieve which will drastically reduce the dropout rates across the nation.

Right now MyVerse has a campaign on RocketHub found here. There you can contribute to the MyVerse campaign so we can see this awesome new online career service that has so much potential come to life.

myverse

The Significance of 8888: MH17+MH370+QZ8501

Although the QZ8501 plane is now confirmed to be in the Java Sea, we still hope that there may be some survivors, who may have possibly swum to a nearby island. Hopefully, the rescuers may be able to rescue some of the passengers.

This is a followup on the previous post on the Probability of adding up to 8888.

Other than the QZ 8501 incident, there are many other incidents that have relation to “8888” or “8” in general. Some of them are the “8888” Uprising in Myanmar, the May 12 Sichuan earthquake, the Blizzard of January 25, and the Tibetan Riots of March 14.

To read more, visit: http://mathtuition88.blogspot.sg/2014/12/the-significance-of-8888-mh17mh370qz8501.html

One special fact about 8, is that it is the only natural perfect power that is one less than another perfect power. (2^3=3^2-1) This is known as Catalan’s conjecture or Mihăilescu’s theorem.

Lastly, you may want to watch this video on Chinese Lucky Numbers by Numberphile.

Featured Book:

Biblical Numerology: A Basic Study of the Use of Numbers in the Bible

A sane explanation of biblical numerology. Davis explains the conventional, rhetorical, symbolic, and mystical use of numbers in this fascinating study of the structure and syntax of biblical numbers.

Numbers are present throughout the Bible, and do have some meanings. Why did God create the world in seven days? (rest on the seventh day) Why did Jesus have 12 disciples, not more or not less? Read this book to find out!

Math of QZ8501 (Sum of 3 numbers that add up to 8888)

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.

8888

 

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.

Star Wars Math

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.

math of star warsWait, 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.

 

Guess Birthday Month based on First 4 NRIC Digits

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

Math Formula in WordPress vs Blogspot

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

blogger latex
Produced by Blogspot using MathJax

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

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

\displaystyle a^p \equiv a \pmod p

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

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

Featured Book:

The LaTeX Companion (Tools and Techniques for Computer Typesetting)

Math of Computer Memory and how to Solve the Blue Screen of Death (Windows)

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.

blue screen

 

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)

Singapore Math (High School): Logarithm Question

The following is a follow up video on my earlier post on Logarithm Question (Challenging).

singapore-math-logarithmThe 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:

Recommended Singapore Math Books

The Math of Santa Claus

santa

 

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 Survey

mathtuition88's avatarTuition Database Singapore

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

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YouTube Video: Fibonacci Numbers and the Mysterious Golden Ratio

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

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

Featured Book:

The Fabulous Fibonacci Numbers

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

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

NUS S/U Tips and Tricks from Provost

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.

The Art of S/U:

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)

 

Proof that Square Root of Two is Irrational [Rare Constructive Proof] (YouTube Video)

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.

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

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

This is my first video on YouTube! 🙂

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

Featured Book:

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

mathtuition88's avatarMathtuition88

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

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}
$

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Singapore Calendar 2015 (Printable)

mathtuition88's avatarTuition Database Singapore

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:
Chicken Soup for the Soul: Think Positive for Kids: 101 Stories about Good Decisions, Self-Esteem, and Positive Thinking

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.

View original post

Giant VS Golem: Clash of Clans Math

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

Giant VS Golem: Clash of Clans Math

Giant lvl7 Vs Golem5

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

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

Health

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

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

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

For pure tanking, nothing beats a max level Golem.

Golemite 1 and 2 cut out photo of Golemite Ssfang

Damage per second

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

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

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

NewGiantTroopInfoImage

Against Spring Traps

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

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

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

Conclusion: Golems are more resistant to Spring Traps.

Against Inferno Towers (Multi-mode)

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

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

Inferno3

Against Inferno Tower (Single Target)

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

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

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

Inferno3

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

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

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Intellectual wealth

An interesting news to share:

Source:http://www.thestandard.com.hk/news_detail.asp?we_cat=21&art_id=152297&sid=43527569&con_type=1&d_str=20141212&fc=8

Billionaire Ronnie Chan rather be mathematician or scientist if he could live life over

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

Tuition for toddlers – necessary or over the top?

Is tuition for toddlers necessary? Some food for thought.

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

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

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

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

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

Featured Books:

Recommended Books for GEP

mathtuition88's avatarTuition Database Singapore

Source: https://sg.news.yahoo.com/blogs/what-is-buzzing/tuition-for-toddlers-%E2%80%93-necessary-or-over-the-top-053116125.html

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

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

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

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

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

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

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

View original post 52 more words

A Difficult Problem: Are you not smart enough to solve it … or have you just not solved it yet?

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)

 

Mathematicians prove the Umbral Moonshine Conjecture

Source: Science Daily

Mathematicians prove the Umbral Moonshine Conjecture

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)

Review

“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

What do Mathematicians Eat for Breakfast? (Surprising Answers!)

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

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

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

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

Check out this interesting video on trisecting angles:

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

Featured Book:

Galois’ Theory Of Algebraic Equations

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

Liu Hong (Ancient Chinese Mathematician)

Source: Baidu Encyclopedia (Liu Hong)

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

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

liu hong

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

liu hong

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

Featured Book:

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

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

Discriminant of Quadratic Polynomial Olympiad Question

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

Question: bilkent nov 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

 

Coursera Course Review: An Introduction to Functional Analysis

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

How to Study after School

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

afterschool

What are the Main Careers in Automobile Industry?

This is an article describing careers in the automobile industry. Hope it is useful for students interested in this area of work! 🙂

What are the Main Careers in Automobile Industry?

The automobile industry contributes greatly to the employment of many citizens in the country. It is one industry, which supports just any other industry you might think of. Many people feel its influence – the people commuting to work, the drivers who deliver goods to customers, the emergency services engineers, technicians, and mechanics. As one way of promoting the growth of the automobile industry, the Ideal Auto USA provides direct and indirect employment through selling some of the eco-friendly cars in the industry.

Careers in the automobile industry

There are many kinds of employment opportunities in this industry often employing some of the brightest minds like the engineers. Because there is a wide array of jobs, one would have to find a suitable choice based on his or her interest and qualifications. If you have the right training, you can easily advance higher in the positions. The technicians are responsible for things like replacing air filters, changing oils, and balancing wheels. These technicians handle many other maintenance tasks such as doing tune ups and changing the brake pads.

Apart from the technicians, there are the mechanics that repair cars. These workers are categorized one or two levels up the employment ladder from the technicians. At times, people confuse the mechanics with technicians, but the reality is that mechanics are more advanced than automobile technicians are.Besides performing many of the tasks done by technicians, they have knowledge on how to repair cars and work on engines.

While mechanics may work for companies or other people, when they have the business skill and the required capital, they can set up their own business. A repair shop is certainly one rewarding business, which can help mechanics further their career.

The automakers and car dealers employ many workers from the cleaners, service team, the mechanics, engineers, sales persons, drivers, and managers. All these people and their families get support from the industry. There are also indirect jobs, which come with this industry such as the workers employed in steel plants, glass making plants, or computer chip makers, which make the materials for manufacturing cars.

Salary range for automobile careers

According to Bureau of Labor Statistics, the automotive service technicians as well as the mechanics earned an average wage of about $38,560 as in May 2011 while the average salary for the mechanical engineers who work in the automobile manufacturing was at averagely $95,080. These figures show that the workers especially those with some skill in the automobile sector command quite a substantial pay.

If you want to make a living when working in the automobile industry, you might want to get some education be it in sales and marketing, engineering, motor vehicle mechanics, or even a driver. With Ideal Auto USA, it offers the best cars in the industry, which is a way of expanding the career market as more workers get employment as drivers and mechanics.

AuthorBio

Tim Bryson is a practising automobile mechanic and has been working in this industry for more than 8 years. For the best eco-friendly cars that will drive the automobile industry, you can visit Ideal Auto USA.

Fourier Series Videos

These are some Fourier Series (learnt in University Maths courses) videos from YouTube. Very interesting and enlightening!

The gist of the theory of Fourier Series is that a function (periodic) can be expressed as an infinite sum of sine and/or cosine functions.

Featured Book:

Fourier Analysis: An Introduction (Princeton Lectures in Analysis)

This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences–that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.

 

Imaginary Erdős Number: What is that?

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.

Should I take H1 or H2 Maths?

There are pros and cons of taking H1 or H2 Maths:

H1 Maths is an easier version, and will definitely take less time to study. This time can be used for studying other subjects. Also, it covers statistics which can come in handy for majors like Psychology, Social Science, or Business. Students who take A Maths in O Level will find that the Pure Math part of H1 Maths is basically the same, if not even easier than O level A Maths.

H2 Maths is the harder version, more difficult than even the O Level A Maths. New and interesting topics like Complex Numbers and Vectors will lay a good foundation for University majors like Engineering and Physics. Try not to forget what you have learnt in O Level A Maths, it will come in handy.

Students who wish to enter SMU & take H1 Maths in JC may want to note that SMU has a introductory module on calculus which is pretty much compulsory, even for majors like social science. I have taught a student from SMU, and would say that the content is heavier than even H2 Math Calculus; there is multivariable calculus in the SMU Course.

Featured Book:

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

Graphic design & Fashion degree Programmes

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!

fashion poster

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

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

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

All the above topics are rather challenging and deep. Fortunately, for most engineering students, application of the theorems would suffice, the deep proofs are not really necessary. It would be good to know them though.

Featured Book:

Schaum’s Outline of Advanced Mathematics for Engineers and Scientists (Schaum’s Outline Series)

This is the book you are looking for, if you are looking for a book to help ace Engineering Maths.

Finland’s Education System: 10 Surprising Facts That Americans (or Singaporeans) Shouldn’t Ignore

mathtuition88's avatarTuition Database Singapore

Source: http://www.takepart.com/photos/ten-surprising-facts-finlands-education-system-americans-should-not-ignore/finland-knows-whats-best

Just to summarize the 10 Surprising Facts:

  1. School Starts Later
  2. More Recess
  3. No Testing (and little homework)
  4. Extra Teachers for Struggling Students
  5. More Languages
  6. Instruction Guidelines, Not Prescriptions
  7. Less Teaching
  8. Professional Teacher
  9. Teachers Stick with Students
  10. 43 Percent Attend Vocational School

More Languages

Read more at: http://www.takepart.com/photos/ten-surprising-facts-finlands-education-system-americans-should-not-ignore/more-languages

Featured book:
The Temperament God Gave Your Kids: Motivate, Discipline, and Love Your Children

This book is highly recommended for those who are interested in the 4 Temperaments and related research (Introvert, Extrovert, Sanguine, Choleric, Melancholic, Phlegmatic, etc.)

View original post

Second-derivative Test For Extrema Of Functions Of Two Variables

Source: http://www.math.illinois.edu/~verahur/18.024/notesSD.pdf

Excerpt: 

Proof of the second-derivative test. Our goal is to derive the second-derivative test, which determines the nature of a critical point of a function of two variables, that is, whether a critical point is a local minimum, a local maximum, or a saddle point, or none of these. In general for a function of n variables, it is determined by the algebraic sign of a certain quadratic form, which in turn is determined by eigenvalues of the Hessian matrix [Apo, Section 9.11]. This approach however relies on results on eigenvalues, and it may take several lectures to fully develop. Here we focus on the simpler setting when n = 2 and derive a test using the algebraic sign of the second derivative of the function.

The full proof can be found in the featured book below: T. Apostol, Calculus, vol. II, Second edition, Wiley, 1967

Featured book:

Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability (Volume 2)

 

 

Tuition News: 92 Marks ranks student in bottom 50%

mathtuition88's avatarTuition Database Singapore

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…

View original post 153 more words

Undergrad Math Tuition: Maxima and Minima (Multivariable Calculus)

At the undergraduate level, sometimes functions are of two variables (x,y). How do we find the maximum or minimum points of such a function?

Read the following PDF to find out!

Recommended Book:

Multivariable Calculus, 7th Edition

This is a highly practical book on Multivariable Calculus. It is also suitable for Engineers / Physics Majors. I learnt Multivariable Calculus from this book. 🙂

 

H2 Maths Tuition: Integration by Parts

Here is a Integration by Parts helpsheet I created and uploaded on Scribd. Integration by Parts is a really useful technique, in fact it is one of the two key integration techniques in H2 Maths. The other technique is Integration by Substitution.

Featured book:

The Humongous Book of Calculus Problems

This book is really “humongous”. If you need to source for practice problems for Calculus, this is a good place to start. 🙂

Matchstick Problem

matchstick quiz

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

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

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

Featured Post:

Motivational Books for Students (Educational)

The Motivational Books recommended in the above post seems to be very popular with readers on this site. Many readers (presumably parents) have bought the books! Buy a Christmas present for yourself this Xmas. 🙂

Boys’ Brigade Share-a-Gift (BBSG)

mathtuition88's avatarTuition Database Singapore

“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:

  1. Volunteer to Deliver Food Hampers
  2. Donate Essential Items
  3. Online Donation

Wishing all our readers a Merry Christmas!

Featured Book:
Bright Minds, Poor Grades: Understanding and Motivating your Underachieving Child

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…

View original post 13 more words

College Students Career Guide

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.