Category: Uncategorized

Buy Math Notes with Exam Papers

We are selling Math Short Summarized Notes, and giving away Free Exam Papers bundled together! These two complement each other, the Short Condensed notes will help when doing the Exam Papers, and practice makes perfect for Maths.

Check out the Highly Condensed Math Notes at: https://mathtuition88.com/math-notes-worksheets-sale/

Currently, we have 4 products:

  • Highly Condensed E Math Notes (Bundled with E Maths Prelim Papers)
  • Highly Condensed A Math Notes (Bundled with A Maths Prelim Papers)
  • Chicken and Rabbit Worksheet Generator (Bundled with PSLE P6 Prelim Papers)
  • Multiplication Worksheet Generator (Bundled with Primary 4 Exam Papers)

All of them can be accessed from this page: https://mathtuition88.com/math-notes-worksheets-sale/

Many times, it is possible to be stuck on a Math Problem. I have personally been stuck on Math Problems many numerous times, for instance when doing the Math Problem of the Month! When you finally discover the solution by yourself, the feeling of accomplishment is like pure nirvana. There are some books that specifically address How to Solve Math Problems, one of them is How to Solve It: Modern Heuristics. Very highly rated on Amazon, this book describes modern methods to solve heuristics and optimization problems (suitable for students interested in Computer Science). Another well written book by Polya is How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library). This book is suitable for students who like challenging math problems to train their mathematical skills!

Page keywords: Buy Exam Papers Singapore, Buy Test Papers, Buy Prelim Papers

 

 

20% Discount on the following Math Resources!

I have recently revamped my Math Resources for Sale page, currently there are 6 products for sale! From the wacky Chicken and Rabbit Question Generator, to the very serious Highly Condensed Notes series for students preparing for exams!

For a limited time only, there is currently a 20% discount promotion on all the products on the page!

10% Discount Code: ilovemath

(This Discount Code is only known to my website viewers! :))

10% Social Discount: Tweet or Share on Facebook to get another 10% Discount

Do check out the Math Resources for Sale page!

 

GR0568 Q2 Solution (Tangent to Graph)

This is indeed a GRE Math question that even high school students can solve!

Q2) Which of the following is an equation of the line tangent to the graph y=x+e^x at x=0?

(A) y=x
(B) y=x+1
(C) y=x+2
(D) y=2x
(E) y=2x+1

Solution:

Firstly, at x=0, y=0+e^0=1.

\frac{dy}{dx}=1+e^x=1+e^0=2

Substituting these values into y=mx+c, we get

1=2(0)+c, hence c=1.

Thus, the equation is y=2x+1.

Answer: (E)

By the way, recently someone purchased a set of Copic Markers 36-Piece Sketch Basic Set from my website. Thanks! I was curious why a set of Copic Markers cost a whopping $150 USD, and thus went online to research. It seems that Copic Markers are one of the best markers on the market. If you are into animation / illustration, or just love drawing, Copic Markers will be the perfect choice. The difference between Copic Markers and ordinary markers is that Copic Markers are alchohol based, while usual markers are water based. Alchohol based markers mix better and can create rich blends, unlike water based markers which tend to oversoak the paper while blending.

GR0568 GRE Math Test Solutions

I have decided to post some solutions to the GRE Mathematics Test Sample Practice Past Year Papers that are available online. Hope it helps!

The GRE (Graduate Record Examinations) Mathematics Test is a standardized test by the company ETS (Educational Testing Service), and meant for students considering PhD in Math in the United States.

Question 1) In the xy-plane, the curve with parametric equations x=\cos t and y=\sin t, 0\leq t\leq\pi, has length

(A) 3
(B) \pi
(C) 3\pi
(D) \frac{3}{2}
(E) \frac{\pi}{2}

Solution:

Using the integral formula for arc length, \displaystyle s=\int_0^\pi \sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}\ dt, we obtain

\displaystyle \begin{aligned}\int_0^\pi \sqrt{(-\sin t)^2+(\cos t)^2}\ dt &=\int_0^\pi 1\ dt\\ &= \pi\end{aligned}

Thus, the answer is option (B).
Do check out this book Cracking the GRE Mathematics Subject Test, 4th Edition for more information about the GRE Math Subject Test, and how to crack it! It contains valuable and concise information on the topics tested in the GRE Mathematics Test.

 

Exciting New Math Course at Probability, and Book by Eccentric Mathematician

Recently, I just finished my Coursera course on Cryptography, and I have started a brand new course on Probability. This is a rather introductory course on Probability, probably at the junior undergraduate level. However, looking at the course syllabus, later on in the course some deeper aspects of probability will be taught.

Welcome message from the Probability team:

Thank you for signing up for Probability!  This is a beguiling subject with a fascinating historical tradition and vibrant modern applications.  We are delighted that you are joining us in this journey of exploration.  And you are entitled to bask in the warm light of the realisation that you are one of the pioneers in a novel form of online learning!

Class has already begun, so please join us.  We are looking forward immensely to our journey together!

Best wishes,
The Probability Course Team

The course is based on the book by Professor Venkatesh: The Theory of Probability: Explorations and Applications. Rated 5/5 on Amazon, this book is a good read, and covers many aspects of probability theory.

Another new Math book on the international scene is Birth of a Theorem: A Mathematical Adventure by the eccentric French Mathematician Cédric Villani who received the Fields’ Medal in 2010. It contains the story of his life,  his favorite songs, his love of manga, and the imaginative stories he tells his children.

Cédric Villani

 

 

The Useless Number

In this exciting video, the “Useless Number” refers to complex numbers, which were first thought to be useless when first discovered. However, nowadays everyone knows that complex numbers are very useful in engineering, physics and science!

Also, check out these related posts on complex numbers:

An interesting book about complex numbers is An Imaginary Tale: The Story of [the Square Root of Minus One] (Princeton Science Library). Styled like a storybook, this book tells the history of the imaginary numbers, which was discovered as early as during ancient Egypt. However, people didn’t realize the immense usefulness of complex numbers until much later. Click the image below to read more!

Interesting but Hard to Understand Math Comic

Check out this interesting comic riddle from Spikedmath.com! The sky is the limit when it comes to Math!

Do give it a try, before scrolling down to view the answer.

Featured Amazon Product:

Buy yourself a gift from Amazon! Amazon Gift Card – Email is an excellent way to send a gift for any memorable event.

Answer: sky

First, we use L’Hopital’s Rule since the initial limit is a 0/0 indeterminate form.

\displaystyle \lim_{x\to k} \frac{sx^2y\sin (k-x)}{k^2-kx}=\lim_{x\to k}\frac{2xsy\sin (k-x)-sx^2y\cos (k-x)}{-k} (We have also used the product rule and chain rule in this step)

Substituting x=k into the expression, we get \frac{-sk^2y}{-k} which is equivalent to sky.

 

New Math Popular Books

It is written in Japanese, translated in Chinese (Taiwan).

tomcircle's avatarMath Online Tom Circle

image

結城 浩(1963 -) is a Japanese Math Popular Book Writer for Secondary and High School students. In the “Galois Theory” (Chapter 10) she boldly attempted to explain to them such complicated concepts: Quotient Group, Field Extension, Group Order, Normal Group, Solvable Group …

http://m.ruten.com.tw/goods/show.php?g=21437146332387

http://www.nh.com.tw/nh_bookView.jsp?cat_c=01&stk_c=9789866097010

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Driving Schools

Today we will introduce two driving schools for the benefit of our readers who live in Canada. Canadians are one of the top 10 countries who read our blog!

One of them is Driving school in Mississauga. Located in the city of Mississauga, one of Canada’s rising cities, this driving school has patient and friendly instructors. Learning driving is just like learning any subject, it requires patient and friendly teachers to make the whole process more enjoyable.

The next school is a Driving school in Kitchener. Also nicely located in Canada, this driving school teaches how to drive safely under winter conditions. Just like in Math, students need to know how to prevent careless mistakes, as road accidents can be deadly.

In case you need to know the address about where to find those Driving schools, I have provided the addresses below. Hope it helps and have fun learning driving!

Ultimate Drivers – Driving School Mississauga
3173 Erindale Station Rd #101
Mississauga, ON
(905) 848-6565

Ultimate Drivers – Driving School Kitchener
301 King St E #319, Kitchener, ON N2G 2L3
(519) 954-2266

Fun IQ Math

tomcircle's avatarMath Online Tom Circle

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7+2+5 = ?
(Test the logic pattern)

Ans: (Scroll below — only after you have tried to solve it )
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7+(2)+5= 143547
7×2=14
7×5=35
14 + 35 – (2)=47

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Free Audiobooks by Amazon (Audible)

Are you a auditory learner? (one who learns best through hearing) Do you wish you could listen to some books on your long journey to work or school? Try Audible and Get Two Free Audiobooks! Audible is a company owned by Amazon, and a provider of audio books.

Some other interesting blog posts you may want to check out are:

I have also set up a page to promote Singapore Math Books hopefully to a global audience!

Mental Math

tomcircle's avatarMath Online Tom Circle

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No equation, no formula, no calculator, no writing on paper, just do mental calculation.

What is the answer  in the last diagram ?

Scroll down to see the answer, but not until you have tried yourself.
(There are many methods, but one is the fastest and the best !)
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Ans:
Add the first 3 diagrams: 10+20+24 = 54 for 2x (Dog + Cat + Rabbit).

Dog + Cat + Rabbit = 54/2 = 27

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Mental ‘Abacus’ Calculation Technique

tomcircle's avatarMath Online Tom Circle

Amazing calculation technique of Indian kids:

It is the advanced level of abacus calculator, where the physical abacus is replaced by a virtual abacus in the mind — see the kids need to move their fingers in the air, as if they touch a real abacus. This is different from the mental calculation sans a real electronic calculator, in which case no fingers playing the pressing buttons of an electronic calculator.

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Logic or ‘Think Out of the Box’

tomcircle's avatarMath Online Tom Circle

image

How nice it would be if yesterday were tomorrow, then today would be Friday.

What is ‘today’ here ?

Answer:
A. Wednesday;
B. Thursday;
C. Friday;
D. Sunday

Hints:
either use left brain (by logic) or
right brain (by EQ, after a Sunday evening).

Try before scrolling below for answers:
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Answer (1) : by logic (algebra)
Today = Wednesday

image
Let today = d
If d-1 = d+1 (yesterday = tomorrow)
Then d = d+2 (today = the day after tomorrow)
and d+2= 5 (today =…

View original post 40 more words

Crows Are Problem Solvers

tomcircle's avatarMath Online Tom Circle

Are crows the ultimate problem solvers?

Scientists have also discovered crows can count up to 3. Weren’t human primitives so too ? In Chinese, English, French, etc, anything upto 3 is equivalent to many.

Crows are ugly black birds, found commonly in the hawker centers here scrounging left over food on the tables or rubbish dumps. They are good children with strong filial piety, bringing food back to feed old parents. Below is a Tang dynasty poem by Bai Juyi白居易 (800AD) praising the crows:

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Building a strong career in Logo Design

This is for student inclined in arts and graphic designing. Hope it is helpful! 🙂

Building a strong career in Logo Design

Before you seek to make a career in logo designing, you should determine whether your interests and skills are aligned to those required for a logo designer. The following are the basic interests and inclinations that a logo designer should have:

  • Superior ability with the use of Photoshop, Adobe Illustrator and other graphic design software suites
  • Ability to concentrate on work that needs visual precision
  • Interest in working with computers and employing your creative abilities in the process
  • Ability to hold concentration on a single task for long periods
  • Excellent communication skills to gain understanding of client requirements and project needs
  • Interest in a career that gives the flexibility of formal or self-employment

Skills necessary for a career in logo design

There is a set of skills that will ensure that you perform the best in your career should you choose to pursue logo design. The core point of having these skills is to be equipped to work competently, combining natural abilities with school knowledge and in-field experience.

Design skills – Logo designers will tend to have an artistic inclination, with the flare for design in particular. Aside from that, they should be equipped with operative knowledge of graphic design software such as Photoshop, and Adobe Illustrator, among others.

Communication skills – it is important to have the skills required to gain a comprehensive understanding of client or employer requirements, and for that you’ll need superior communication skills. You also should be able to explain clearly why each design element was chosen over other options. If you’re a freelancer, communication skills will be invaluable when you are building networks and selling your business to potential clients.

Business skills – logo design is a very business oriented field. As a freelance logo designer, you should have the skill to build various aspects of your business, including marketing yourself to new clients, maintaining relationships with existing clients and having the time management and planning skills to coordinate multiple projects within the time and budgetary allocations for each project. You should be able to plan your finances also so that you can grow your business and knowledge.

Practical/physiological abilities – A logo designer will probably spend a good portion of their life staring at a computer screen. You should be physically and mentally prepared to put in the long work hours and have a long concentration span. Your eyesight should also be very good, since logo design demands a high level of precision.

Personality traits – There are certain demands of the Logo Design profession that should be ingrained in your character to help you succeed in your career and live through the various challenges presented on the job:

  • Innate creativity and passion for design
  • Willingness to keep yourself informed on the changes in the industry, and learn new skills that are required to remain relevant
  • Precise and unerring attention to detail, so that you can present work that you and your client are proud to own and display
  • Discipline to plan and deliver projects on time and within budget, especially when you have the flexibility of being self-employed or working from home

Author Bio

John Lewis has 5 years’ experience in logo design at http://bigdropinc.com/. For more information and guidance on logo design and to view and receive top reviews for design work, contact us below

 

Buy New Car or Extend 5 More Years Old Car

tomcircle's avatarMath Online Tom Circle

Assumptions:
1. Class A (< 1600 cc) Old car (10 years expiring soon) is in good condition:
♢ Less than 200,000 KM
♢ Certified safe by qualified workshop

2. COE last-3-month average price ~$ 60,000 (10 years)
=> $30,000 (5 years)

3. New Car market price of $100,000

4. Parf rebate $7,000 (forfeited if extend car beyond 10 years)

5. Monthly Car Loan (@2.88% for max. bank loan 60% & max 5 years = $60k) = $1,144 (= interest + capital)
5-year car loan = $1,144 x12x5 = $ 68,640
Downpayment Cash = $40,000 (or $20,000 for 5-year Cost of Ownership )

image
Compare Buy or Extension (Both 5 years)

Description Buy Extension
1. Car Price (down payment) for 5 years $20,000$…
2.COE (5-Yrs)$…$ 30,000
3. Car Loan (5 Yrs) = car price + COE $ 68,640 $…
4. Parf rebate$7,000 – $ 7,000
Cost of Ownership…

View original post 46 more words

Circle & Hidden 9

tomcircle's avatarMath Online Tom Circle

‘9’ is the biggest number in the digits {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.

9 is reserved for the ancient Chinese Emperors whose robes were sewn with 9 dragons, and the palace roof top decorated with 9 dragons too.

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http://mp.weixin.qq.com/s?__biz=MzA3MjE0ODAzMw==&mid=204651538&idx=1&sn=33027a35921519fe42c647e1f5a4dadc&scene=1&from=groupmessage&isappinstalled=0#rd

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Free Career Analysis (With Prizes to be Won)

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

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

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

Website: http://uledge.co/ambWWCY

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

 

 

PSLE Maths

tomcircle's avatarMath Online Tom Circle

This is Singapore PSLE (Primary School Leaving Exams) Maths for 12- year-old kids.

It is not difficult for adults, but I wonder most kids have such analytical skill ?

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Answers below (scroll far behind….)
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(1)

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(2):
R – B = 1 for every suite of 5 cards
If R-B = 36
36×5= 180 cards

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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.

 

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

Calendar 2015 = 1997

tomcircle's avatarMath Online Tom Circle

Interesting thing about saturday in 2015
4/4/2015 saturday
6/6/2015 saturday
8/8/2015 saturday
10/10/2015 saturday
12/12/2015 saturday

Calendar of 2015 is same as calendar of 1997

Date & Day even Festivals are same,

Who told history doesn’t repeat ?

So

We are back in 90s

Have a Blessed Happy New Year!

Calendar Math explains:

http://tomcircle.wordpress.com/2013/03/30/calendar-math/

View original post

记乘法表 Multiplication Table

tomcircle's avatarMath Online Tom Circle

女童记不住乘法表崩溃大哭”三五太難了”:

This 4-year-old Chinese girl cried when her mother ‘tortured’ her to recite Multiplication table by rote learning. She always got stuck at 3 x 5= ?
She complained it is too difficult.

Most parents are teaching the kids Mathematics the wrong way! No wonder they grow up with hate and fear for Maths subject throughout the entire life.

Same in schools and universities, Maths are taught the wrong ways by incompetent Math educators.

View original post

Mind, Brain And Education

tomcircle's avatarMath Online Tom Circle

Mind, Brain And Education
1. Spaced Repetition
2. Retrieval Practice

Tool: Test
Not to assess what students know, but to reinforce it.
Memory is like a storage tank, a test as a kind of dipstick that measure how much information we’ve put in there.

But that’s not how the brain works.

Every time we pull up a memory, we make it stronger and more lasting, so that testing doesn’t just measure, it changes learning.

Simply reading over materials to be learnt, or even taking notes and making outlines, as many homework assignments require, doesn’t have this effect.

Language learner: 80% retained.
Science: 50% retained.

Self-quizzing (focus less on input of knowledge by passive reading, focus more on output by calling out that same information from brain.)

Cognitive disfluency:
Tough topic, recall better.
Interleaved assignment: mix up different kinds of problems instead of grouping by type.

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Worldwide Student Homework Hours

tomcircle's avatarMath Online Tom Circle

Weekly Homework (hours)

A recent survey in 44 OECD countries reveals for 15-year-old students an average of 5 hours / week of homework.

CountryHomework HrsExtra Hrs PISA
Shanghai14 Tuitions1
Singapore9.4 Tuitions2
Hong Kong6 Tuitions3
Korea2.7Tuitions 4
Japan3.8Tuitions5
Taipei5.9Tuitions6
Finland2.87
England4.926

PISA 2012:
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PISA is like the Army IPPT Test on physical fitness. A fit soldier and a weak soldier go to war, whether he can fight with courage under duress to win the battle, has nothing to do with his IPPT scores.

Same for PISA scores…that explains why Americans are poor in PISA but produce many entrepreneurs, Nobel prize / Fields scientists, whereas China, Singapore, Korea, HK have only few.

image

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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)

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)

 

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.

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无状元老师, 有状元学生

Chinoiseries2014's avatarChinoiseries 《汉瀚》［中/英/日/韩/法］

从来没有状元的老师, 却能培养出状元学生。中国历史的状元, 都是在科举失败的穷秀才教导出来的。看今日的Fields Medalists / Nobel Prize winners, 他们的指导教授多数没拿过这大奖。

法国有两位世界级的数学大师Evariste Galois, Charles Hermite,  相隔15年,同是一位中学数学老师培养。Mr. Richard  是巴黎路易大帝中学(Lycée Louis Le Grand) 的数学老师, 他能创新课材, 加上他本身是”数学迷”, 对学生因材施教, 慧眼视英雄于微时。Galois13 岁前是由妈妈家教(home-schooling), 中一才上学校。Richard看出他有数学天才, 个别教他读当代数学大师的书, 其他科目的老师却视他为功课低劣学生。

结果Galois发现群论 (Group Theory), 开创”抽象代数” (Abstract Algebra)。Galois不被世人接受, 因为他的理论太玄奥 (至今还是数学硕士班的难题), Cauchy, Fourier, Poissons,  Gauss… 这些世界数学泰斗也看不懂! 他的悲剧是法国大革命, 因枪斗而死, 才21岁的生命。可是他对人类的贡献是”Larger than Life”.

Richard 收集Galois的作业, 留给15年后同一班另一学生Charles Hermite, 也是个数学天才。他比Galois的命运好一点, 考进Ecole Polytechnique (X),是排最后一名及格, 好过Galois重考2年都进不了。可是他的脚有问题, X第一年学生是军官训练, 他被X踢出校门。讽刺的是, 很多年后他回校被聘为教授。

Charles Hermite 证明 e是超函数 (Transcendental), 他的学生德国人Lindermann如法炮制, 证明pi也是transcendental. 

Lindemann 从Hermite接过法国数学火种, 回去德国成为一代宗师, 培养了很多大师级的学生 (Félix Klein, Dirichlet, Jacobi, Gauss, …), 20世纪德国数学Gottingen University取代巴黎成为数学王国, 直至二战德国犹太数学家(Émile Noether, Artin, …)逃去美国, 才轮到Princeton University.

一位默默无名的中学/高中数学老师Richard, 百年树人, 改变了世界数学史!

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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.”

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.