Math Blog

Mystery numbers : 370 & 153

tomcircle's avatarMath Online Tom Circle

Just can’t imagine how strange a plane MH370 could just disappear in the air, no explosion, no terrorists (?) although 2 Iranian passengers with stolen passports from an Italian and an Austrain.

Malaysian Flight: MH 370

Departure : Passengers, among them the majority are 153 Chinese, boarded on 3.7 (March 7) around 11 PM at Kuala Lumpur International Airport, disappeared 1 hour later in the air.

http://www.nst.com.my/latest/font-color-red-missing-mh370-font-timeline-of-flight-mh370-1.507516

Just notice 370 is a strange number:

$latex boxed { (3)^{3} + (7)^{3}+ (0)^{3} = 370}$

A lot of mystery numbers have such behaviors when decompose the digit, then each powered by 3, sum them up, you get back the mystery number itself.

Bible Math: 153 St. Peter Fish
[John 21:3-11]
3  So they went out and got into the boat, but that night they caught nothing.
6 He said, ”Throw your net on the right side of the boat and you will find some.” When…

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Bayesian Probability Could Help Search MH370 Missing Plane

tomcircle's avatarMath Online Tom Circle

https://mathtuition88.com/2014/03/13/math-equation-missing-plane/

Ref:

See also Bayesian Probability applied in 911 World-Trade Center Tragedy:

http://tomcircle.wordpress.com/2013/07/10/911-wtc-attack-probability/

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Math equation could help find missing MH370 plane

Math equation could help find missing Malaysian plane

Source: http://america.aljazeera.com/articles/2014/3/12/mathematical-equationcouldhelpfindmissingmalaysianplane.html

Bayes’ Theorem helped researchers locate Air France Flight 447’s black box in 2011

(Video: How Bayesian Search found the USS Scorpion)

Days after a Malaysian airliner with 239 people aboard went missing en route to Beijing, searchers are still struggling to find any confirmed sign of the plane. Authorities have acknowledged that they didn’t even know what direction it was heading when it disappeared.

As frustrations mount over the failures of the latest technology in the hunt for Malaysia Airlines Flight MH370, some scientists say an 18th-century mathematical equation – used in a previous search for an Air France jetliner’s black box recorder – could help pinpoint the location of the Malaysian plane.

Indonesian Air Force officers examine a map of the Malacca Strait during a briefing following a search operation for the missing Malaysia Airlines Boeing 777, at Suwondo air base in North Sumatra, Indonesia, on Wednesday.

In 2009, Air France Flight 447 en route to Paris from Rio de Janeiro vanished over the Atlantic Ocean, triggering the most expensive and exhaustive search effort ever conducted for a plane. After two years, officials could only narrow the location of the plane’s black box down to an area the size of Switzerland.

But Flight 447’s black box was found in just five days after authorities contacted scientific consultants who applied a centuries-old equation called Bayes’ Theorem.

Read more at: http://america.aljazeera.com/articles/2014/3/12/mathematical-equationcouldhelpfindmissingmalaysianplane.html

What is Bayes’ Theorem

Mathematically, Bayes’ theorem gives the relationship between the probabilities of A and B, P(A) and P(B), and the conditional probabilities of A given B and B given A, P(A|B) and P(B|A). In its most common form, it is: (Wikipedia)

\displaystyle\boxed{P(A|B)=\frac{P(B|A)P(A)}{P(B)}}

(Check out this post on probability formulas to learn more about Probability)

Proof of Bayes’ theorem (Theorem useful for finding MH370 plane)

The proof of Bayes’ theorem is actually relatively simple, the only requirement is to know the formula for conditional probability (Learnt in H1/H2 Maths): \displaystyle \boxed{P(A|B)=\frac{P(A\cap B)}{P(B)}}

From this, we have \displaystyle \boxed{P(A\cap B)=P(A|B)P(B)}

Similarly, \displaystyle \boxed{P(B\cap A)=P(B|A)P(A)}

But since \displaystyle P(A\cap B)=P(B\cap A), we have P(A|B)P(B)=P(B|A)P(A). Dividing throughout by P(B) gives Bayes’ Formula: \displaystyle\boxed{P(A|B)=\frac{P(B|A)P(A)}{P(B)}}

Sincerely wishing that the MH370 plane will be found soon, and hopefully the passengers are still alive.

Also see: Bayesian search theory (Bayesian search theory is the application of Bayesian statistics to the search for lost objects. It has been used several times to find lost sea vessels, for example the USS Scorpion. It also played a key role in the recovery of the flight recorders in the Air France Flight 447 disaster of 2009.)

Fun Math Equals Better Student Participation

Fun Math Equals Better Student Participation

We are glad to have Mr Henry Thompson write a Math article on our blog. 🙂

Guest post by Henry Thompson of DegreeJungle.com:

One significant obstacle that students face when trying to understanding mathematics is that they devote a great deal of their energy to NOT enjoying themselves. Think about it; reading literature is satisfying, if the story is carefully chosen. Holding a conversation about up-to-date events in History, while studying critical analysis, is enjoyable. But, even for math teachers, working out a complex algebraic equation is simply not exciting.

Students rely on their professors to make mathematics convenient and more effortlessly appreciated. Thus, it makes good sense for educators to insert some sort of enjoyment into their math lessons as frequently as possible; particularly, if the diversion includes a little academic theory.

Today’s professors feel that great math education objectives should not only “address the program of study,” but should also present learners with new ways to discover life through the aperture of mathematics.

For this reason, groundbreaking educators around the globe have altered their approach to math education by leaving behind unimportant and boring learning objectives and implementing applicable and appealing math learning inside the classroom.

Yesteryear’s Math Programs Are Uninspiring

If teachers recall their pedagogic theories from college, they’ll remember that many lesson plans contained mathematical calculations at the hub of their programs.

Additionally, the framework in most old-school math textbooks contains terribly-fashioned word problems. It appears that a few textbook publishers hold fundamental challenges in developing math problems that are linked to real life.

Outdated textbooks only pay attention to computational formats as well, leaving out the reasoning that is produced behind the scenes, which is needed to solve math problems.

The folks at Degree Jungle recently talked to some math educators, who located their teaching credential programs through the infamous search engine, to find out what instructors in the twenty-first century should look for when analyzing conventionally-structured math programs.

A Brand-New Strategy for Teaching

A large number of math educators, today, recommend professors seek math learning-systems that guarantee relevancy, instead of those which put math calculations at the center of study; lessons that contain “real-life” relevance will most certainly motivate students to engage more.

The planet contains plenty of fascinating mathematic applications. A tree’s design is a consequence of fractional limb patterns. A tiny shellfish’s cask coils in an exquisite and attractive mathematical design. Profound mathematics dwells in the massive framework of the cosmos. Moreover, all things that folks explore throughout the day contain some sort of mathematical design.

Easy Tips for Applying Mathematics to the Real-World

Below are a handful of tips that educators can work with to help put real-world situations inside their educational math programs:

  • Instead of a worksheet that explains how to spend money, provide students with some real coins to count, or let them visit to the school store.
  • Cooking incorporates proportions and divisions.

Resources for Improving Engagement

Although adding real-world scenarios to math problems plays a vital part in ensuring an entertaining lesson, it is not the only unique educational approach for teaching math. There are countless mathematical strategies short of “real-life” applicability that are, nevertheless, exceptionally appealing.

  • Projecteuler.net delivers a collection of serious mathematical-CIS problems that will demand much more than just mathematical awareness to solve.
  • Fullerton IV Elementary School’s, Integers Across Disciplines, proposes another strategy. Educators there have developed tasks that force students to visit challenging mathematical problems and to discover that math demands practice and patience.
  • Euler’s graph theory using geography assists students in building mathematical tolerance and in discovering ways to conquer frustration. As an included reward, learners will understand that not all math problems have solutions.

A Mathematician’s Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form


A Mathematician’s Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

A Mathematician’s Lament is a short book on the pedagogics and philosophy of mathematics by Paul Lockhart, originally a research mathematician but for many years a math teacher at a private school. Characterised as a strongly worded opinion piece arguing for an intuitive and heuristic approach to teaching and the importance of mathematics teaching reforms, the book frames learning mathematics as an artistic and imaginative pursuit which is not reflected at all in the way the subject is taught in the American educational system.

The book was developed from a 25-page essay that was written in 2002, originally circulated in typewritten manuscript copies, and subsequently on the Internet.

A few analysis resources

Analysis resources by Timothy Gowers. Excellent post to revise mathematical analysis.

gowers's avatarGowers's Weblog

This will be my final post associated with the Analysis I course, for which the last lecture was yesterday. It’s possible that I’ll write further relevant posts in the nearish future, but it’s also possible that I won’t. This one is a short one to draw attention to other material that can be found on the web that may help you to learn the course material. It will be an incomplete list: further suggestions would be welcome in the comments below.

A good way to test your basic knowledge of (some of) the course would be to do a short multiple-choice quiz devised by Vicky Neale. If you don’t get the right answer first time for every question, then it will give you an idea of the areas of the course that need attention.

Terence Tao has also created a number of multiple-choice quizzes, some of which are relevant…

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Compound Interest (O Levels Maths Tuition)

Compound Interest

“Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.” – Albert Einstein

The formula for Compound interest is:

Total Amount = \displaystyle\boxed{P(1+\frac{i}{100})^n}

Where P=Principal amount (starting amount of money)

i = interest rate (in percent)

n = number of times compounded

We will illustrate this using an example:

Compound Interest Example Question

Source: Admiralty Secondary School Preliminary Examination 2011 Paper 2

Q: The cash price of a sports car is $420,000.

Mr Lionel buys it on compound interest loan terms. He pays a down payment of $300,000 and the balance at the end of 5 years with a compound interest rate of 5% per annum. Calculate the amount that Mr Lionel has to pay at the end of 5 years.

Solution:

Firstly, we have to find out what is the balance. The balance would be $420,000-$300,000=$120,000.

That is the Principal amount, i.e. P=120,000. The interest rate, i=5. n=5 since the number of times compounded is 5 (once each year).

Hence, Total Amount = \displaystyle\boxed{P(1+\frac{i}{100})^n=120000(1+\frac{5}{100})^5=153153.79}

In conclusion, he has to pay $153153.79 at the end of 5 years.

How is Compound Interest the Eighth Wonder of the World?

Imagine you have an amount of $1000. (P=1000)

And you manage to find a bank that pays 10% compound interest per annum. (i=10)

What happens after 50 years? (n=50)

Using the formula, Total Amount = \displaystyle\boxed{P(1+\frac{i}{100})^n=1000(1+\frac{10}{100})^{50}=117390.85}

The amount would become around $117,000! Isn’t it amazing? This is why Maths is useful and fun.

Check out our Cool Math page for more Math fun facts!

Books by Danica McKellar: Actress, Author & Mathematician

Who knew?  Danica McKellar AKA Winnie Cooper on the television hit the Wonder Years, is a published author and mathematician.  She showed up on WGN Noon News the other day promoting her latest book, Kiss My Math.  Just goes to show brains and beauty CAN go together.

Here is the complete list of Books by Danica McKellar (Top Sellers)


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

  2. Kiss My Math: Showing Pre-Algebra Who’s Boss

  3. Hot X: Algebra Exposed!

  4. Girls Get Curves: Geometry Takes Shape

The Math of Bitcoins

What is Bitcoin?

Bitcoin is a peer-to-peer payment system and digital currency introduced as open source software in 2009 by developer Satoshi Nakamoto. It is a cryptocurrency, so-called because it uses cryptography to control the creation and transfer of money.[5] Conventionally, the capitalized word “Bitcoin” refers to the technology and network, whereas lowercase “bitcoin” refers to the currency itself.[6] (Wikipedia)

How to mine for Bitcoins using Math?

Source: http://www.huffingtonpost.com/2013/12/02/bitcoin-basics-explained_n_4374031.html

Adding transactions to the block chain and updating a local copy of the block chain is part of a process called mining. At the same time that miners (nodes in the network) are doing the important work of processing and recording transactions, they are also competing in a race.  They are racing to “complete the current block” in order to win bitcoins.

Mining is a serious competition nowadays and it consumes large computing resources.  Although it’s possible to mine on a laptop, the math problems have become hard enough that a laptop’s CPU will likely never complete a block on its own.  The cost of the electricity needed to run the mining software would exceed the return for mining.  Macs and PC are certainly capable of computing hash functions, but are too slow compared to specialized mining hardware that is now available.

Bitcoin mining serves 2 purposes, it creates the general ledger of Bitcoin transaction and provides security.  The miners compile the transactions together into a “block” and add it to the “Bitcoin blockchain.”  If there was a central authority this would need to be done once and verified by that central authority.  However, there is no central authority in Bitcoin and these blocks need to verified in some way.  Many Bitcoin Miners all over the world are compiling these transactions.  At the end of the compilation they essentially print a lottery number at the bottom.  Each miner is doing this millions or billions of times per second. (Source: http://cointext.com/bitcoin-mining-whats-it-all-about/)

Life Skills Learned In Math Class

Life Skills Learned in Math Class: Excellent blog post on how Math is useful in real life.

Whit Ford's avatarMathMaine

One of the hardest questions for many math teachers to answer in a way that is relevant to students is: “why do I need to know this?”  “For the next course you take”, the easiest answer in many cases, does not answer the question that was usually being asked.

My answers to this question obviously depend on the topic being studied at moment, and I don’t have “good” answers for all topics…  but here is my list of key quantitative life skills I learned directly or indirectly from math class, with

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Jake: Math prodigy proud of his autism (Video)

At age two, Jake Barnett was diagnosed with autism and his future was unclear. Now at age 13, Jake is a college sophomore and a math and science prodigy. Jake says his autism is key to his success. Morley Safer reports.
The Spark: A Mother’s Story of Nurturing, Genius, and Autism (Book by Jake’s mother)

“It seems that for success in science or art a dash of autism is essential.” – Hans Asperger

Donate to St Andrew’s Autism Centre at: http://www.saac.org.sg/partnership_opp.html

Amazing Math Fact: There are always two opposite points on the Earth with the same temperature

There are always two points on opposite sides of the Earth with the exact same temperature. And we can prove that.

Temperature changes continuously. If a and b are on opposite sides of the equator and D(a) = T(a) – T(b) is positive, then D(b) = T(b) – T(a) is negative. That means there must be some point x on the equator where D(x) = 0. At that point the two opposite sides are the same temperature.

Mathematicians call this the Intermediate Value Theorem which means if there is a continuous function that changes from of a positive value to a negative value (or the other way around) then it must, at some point, pass through zero.

Singapore International School popular among Asian celebrities

Singapore International School popular among Asian celebs, Hong Kongers

Source: http://sg.news.yahoo.com/singapore-international-school-popular-among-asian-celebs–hong-kongers-023523503.html

In recent years, many Asian celebrities have relocated to Singapore, citing its lack of paparazzi culture and social stability.

For some of these stars who are also parents, Singapore’s world-class education system was also an important factor in making the move.

For example, Chinese action star Jet Li, who is also a Singapore citizen, has once said that he moved here for his children to get a good bilingual education with equal emphasis on English and Chinese.

Jet Li as Huo Yuanjia

While Hong Kong actress Cecilia Cheung, who relocated to Singapore last year, has sent her two sons to an international school in Singapore, she also sang praises of the country’s education system.

File:Cecilia Cheung 2012.jpg
Cecilia Cheung

Rumour has it that Hong Kong actor Francis Ng, who has a Singaporean wife, also intends to send his son to a local school in Singapore.

Francis Ng

Read more at: http://sg.news.yahoo.com/singapore-international-school-popular-among-asian-celebs–hong-kongers-023523503.html

 

NUS Top 21 in latest World Reputation Rankings

Source: http://www.channelnewsasia.com/news/singapore/nus-rises-one-spot-to-21/1022252.html

The National University of Singapore sits in 21st spot in the 2014 World Reputation Rankings published by the Times Higher Education, up one from last year’s 22nd place.

Read more at: http://www.channelnewsasia.com/news/singapore/nus-rises-one-spot-to-21/1022252.html

 

Singapore Free Education?

Source: http://www.oyetimes.com/news/asia/59957-free-education-the-debate-over-singapore-budget-2014

Nominated MP Laurence Lien debated over the ever increasing managing costs of the Singaporeans. He stated that lower costs would allow lower income to seem enough for a small family. He tried to convince the government to provide free education for children between three and eighteen years of age. “Tertiary education fees can be chargeable in the form of a loan whose repayment is a proportion of what the graduate actually earns in the workforce. Those going into lower paid professions, like in the non-profit sector, can receive loan forgiveness if they are unable to make full payment at the end of their loan tenure.”

Read more at: http://www.oyetimes.com/news/asia/59957-free-education-the-debate-over-singapore-budget-2014

Education Minister outlines key goals to bring out best in every child

Source: http://www.channelnewsasia.com/news/singapore/education-minister/1024500.html

The key goal of the Education Ministry is to bring out the best in every child, whatever his or her starting point, assures Education Minister Heng Swee Keat on Friday at his ministry’s Committee of Supply debate in Parliament.

SINGAPORE: The key goal of the Education Ministry is to bring out the best in every child, whatever his or her starting point.

Speaking during his ministry’s Committee of Supply debate in Parliament on Friday, Minister for Education Heng Swee Keat provided this assurance and outlined the ministry’s commitment to support every student’s different needs in doing so.

Read more at: http://www.channelnewsasia.com/news/singapore/education-minister/1024500.html

Midpoints, midpoints, everywhere!

Interesting post about Quadrilateral Midpoint Theorem (QMT), which states that if you connect, in order, the midpoints of the four sides of a quadrilateral–any quadrilateral–even if the quadrilateral is concave or if its sides cross–the resulting figure will always be a parallelogram.

chrisharrow's avatarCAS Musings

I didn’t encounter the Quadrilateral Midpoint Theorem (QMT) until I had been teaching a few years.  Following is a minor variation on my approach to the QMT this year plus a fun way I leveraged the result to introduce similarity.

In case you haven’t heard of it, the surprisingly lovely QMT says that if you connect, in order, the midpoints of the four sides of a quadrilateral–any quadrilateral–even if the quadrilateral is concave or if its sides cross–the resulting figure will always be a parallelogram.

Parallel1

Parallel2

Parallel3

This is a cool and easy property to explore on any dynamic geometry software package (GeoGebra, TI-Nspire, Cabri, …).

SKETCH OF THE TRADITIONAL PROOF:  The proof is often established through triangle similarity:  Whenever you connect the midpoints of two sides of a triangle, the resulting segment will be parallel to and half the length of the triangle’s third side…

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Deepest condolences to the loved ones of Math major Philip Wood on board Malaysia Airlines Flight MH370

Deepest condolences to the loved ones of Math major Philip Wood on board Malaysia Airlines Flight MH370

Source: http://edition.cnn.com/2014/03/08/world/asia/malaysia-airlines-plane-passengers/

“We extend our deepest condolences to the loved ones of those on board Malaysia Airlines Flight MH370,” U.S. State Department spokeswoman Jen Psaki said. “Officials from the U.S. Embassies in Kuala Lumpur and Beijing are in contact with the individuals’ families. Out of respect for them, we are not providing additional information at this time.”

Among them is Philip Wood, who graduated from Oklahoma Christian University in 1985 according to school spokeswoman Risa Forrester. He earned a bachelor of science degree, concentrating in math and computer science, and belonged to the Delta Gamma Sigma service organization, Forrester said.

On Oklahoma Christian’s Facebook page, one woman lamented the “heartbreaking news” while a man remembered Wood as “gentle, kind, had great taste in music and was a wonderful artist.”

“Philip Wood was a man of God, a man of honor and integrity. His word was gold,” his family said in a statement. “Incredibly generous, creative and intelligent, Phil cared about people, his family, and above all, Christ.

Malaysia Airlines is asking for prayers from around the world for Flight 370.

10 Biggest Mathematical Disasters in the World

Interesting Blog Post about the 10 Biggest Mathematical Disasters in the World

mathspig's avatarMathspig Blog

tulip graph Correction The millennium bug or the Y2K bug was going to cause planes to fall from the sky, bank accounts to be wiped out, electricity grids to cease functioning, trains to crash, cars to collide as stop lights stopped functioning, life support units to malfunction and computers to crash around the globe. For years leading up to midnight on New Years eve 1999 consults were paid extraordinary amounts of money to solve the problem.  When the clock ticked over to 1 st Jan 2000 nothing much happened. It was, indeed, a non-event, an error in logic. y2k digyourowngrave.com  (Pic from, appropriately, digyourowngrave.com)  

y2k2The Maths Error: Guessing the Answer.

Computer programmers represented the year in the date of many programs using two digits but claimed logical errors would arise upon “rollover” from x99 to x00.

While consultants claimed their advice saved the world from catastrophe countries that spent very little on the…

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Dr. Adrian Yeo Ning Hong’s Math Books

tomcircle's avatarMath Online Tom Circle

Dr. Yeo Ning Hong was the former cabinet Minister of Singapore. He wrote a few Math books after retirement to teach his grand-daughters in primary schools – on Trigonometric Identity Proofs !!!
Yes!
He has wonderful tricks to make such difficult Secondary 3 Math easy for kids, and of course, also helps the weak Math teenagers.

Interesting !
Trig Or Treat: An Encyclopedia of Trigonometric Identity Proofs With Intellectually Challenging Games

The other books by him are:

The Pleasures of Pi,e and Other Interesting Numbers

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Ring Memorize Trick

tomcircle's avatarMath Online Tom Circle

Memorize Trick For Ring:

1. Ring (R) is for Marriage with 2 operations: + (addition of kids), * (multiply asset).

2. (R , +) is Commutative Group
Analogy: your kids are also your wife’s kids, vice versa.

3. (R ,*) is Semi-Group (only closure & associative)
Analogy: your asset to multiply (*) is semi (50%) owned by your wife.

4. Fair distributive law for * with respect to +
=> distribute your asset (a) to your kids (k) & wife (w):
a*(k+w) = a*k + a*w

5. No division (/) operation => Ring can’t be broken.

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Do you need a maths degree to teach maths?

Excellent post on teaching Maths.
The basic requirements for teaching Maths are:
1: You must like maths.
2: You must have a good knowledge of maths.

srcav's avatarcavmaths

A few weeks ago I wrote a post in shock at the fact that a number of schools in the locality had been teaching rounding wrongly. By this I don’t mean I took issue with their pedagogical approach, but rather that the method of rounding they were teaching was wrong and would result in the wrong answer in some instances. This post received the following comment from Old Andrew (@andrewolduk):

“Is anybody going to raise the obvious issue here that a lot of maths teachers don’t have maths degrees? In recent years the rise of “conversion courses” means that many have a background that isn’t in the least mathematical.”

This stirred up some quite strong feelings on both sides. Sophie Skinner (@miss_skinner) wrote this excellent piece stating her views, and Dave Gale (@reflectivemaths) wrote this piece reflecting his view. Twitter has been buzzing with conversation on the matter, and…

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Sushi Monster – delicious math practice!

Free Math Game App!

jwu2713's avatarEducational Apps for Elementary Teachers & Students

Image

Description: *FREE app at time of post *  Sushi Monster is a ridiculously cute and engaging way to practice math fact fluency (addition and multiplication)!  Students must use their critical thinking and reasoning skills to strategically decide which sushi pieces (each has a number above it) to add/multiply together to feed the monster the total he desires.  Within each round, students see all the upcoming totals in the top left-hand corner so they can plan ahead.  Next to this bar is a Number Sentence bar that builds the addition/multiplication sentence as the student chooses sushi.  If it’s wrong, the monster throws a fit and tosses the sushi plates back!  (What a picky monster…)  Levels within this app are sequenced so that they become progressively more difficult as the student completes them.

Compatible with the following device(s): iPad, iPod Touch, and iPhone

Implementation in classroom:

– Activity idea:  This is a…

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Math Jokes

This is the ultimate source of Math Jokes on the Internet: http://www.math.utah.edu/~cherk/mathjokes.html

Know any other funny Math Jokes? Post it in the comments below! 🙂

Top 5 Math Jokes:

  1. A mathematician, a physicist, and an engineer were traveling through Scotland when they saw a black sheep through the window of the train.
    “Aha,” says the engineer, “I see that Scottish sheep are black.”
    “Hmm,” says the physicist, “You mean that some Scottish sheep are black.”
    “No,” says the mathematician, “All we know is that there is at least one sheep in Scotland, and that at least one side of that one sheep is black!”
  2. The physicist and the engineer are in a hot-air balloon. Soon, they find themselves lost in a canyon somewhere. They yell out for help: “Helllloooooo! Where are we?”
    15 minutes later, they hear an echoing voice: “Helllloooooo! You’re in a hot-air balloon!!”
    The physicist says, “That must have been a mathematician.”
    The engineer asks, “Why do you say that?”
    The physicist replied: “The answer was absolutely correct, and it was utterly useless.”
  3. There are three kinds of people in the world; those who can count and those who can’t.
  4. Salary Theorem The less you know, the more you make. Proof:
    Postulate 1: Knowledge is Power
    Postulate 2: Time is Money

    As every engineer knows: Power = Work / Time And since Knowledge = Power and Time = Money It is therefore true that Knowledge = Work / Money . Solving for Money, we get: Money = Work / Knowledge Thus, as Knowledge approaches zero, Money approaches infinity, regardless of the amount of Work done.

  5. An insane mathematician gets on a bus and starts threatening everybody: “I’ll integrate you! I’ll differentiate you!!!” Everybody gets scared and runs away. Only one lady stays. The guy comes up to her and says: “Aren’t you scared, I’ll integrate you, I’ll differentiate you!!!” The lady calmly answers: “No, I am not scared, I am e^x .”

Math Quotes

Famous Math Quotes

  1. If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.  ~John Louis von Neumann
  2. Pure mathematics is, in its way, the poetry of logical ideas.  ~Albert Einstein
  3. A mathematician is a device for turning coffee into theorems. ~Paul Erdos
  4. Give me a place to stand, and I will move the earth. ~ Archimedes
  5. Mathematics is the door and key to the sciences. ~ Roger Bacon
  6. The essence of mathematics is its freedom. ~ Cantor
  7. A youth who had begun to read geometry with Euclid, when he had learnt the first proposition, inquired, “What do I get by learning these things?” So Euclid called a slave and said “Give him threepence, since he must make a gain out of what he learns.” ~ Euclid
  8. Mathematics is the queen of the sciences and number theory is the queen of mathematics. ~ Gauss
  9. Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country. ~ Hilbert
  10. When you can measure what you are talking about and express it in numbers, you know something about it. ~ Kelvin

 

Randomly Generated Math Research Papers

Randomly Generated Math Research Papers

Want to write your own randomly generated Math Research Papers that look professional but is actually full of Math humour (aka Abstract Nonsense)?

Check out: http://thatsmathematics.com/mathgen/

Sample paper generated: Random Math Paper

 

Singapore Math by The Khan Academy

Singapore Math by The Khan Academy

Site: https://www.udemy.com/singapore-math/

We will (eventually) do all of the lectures in the Singapore Math curriculum (which we like). You can follow along through the workbooks available at singaporemath.com.

Check out their website for more details!

Our Daily Story #12: The Vagabond Mathematician Paul Erdős

tomcircle's avatarMath Online Tom Circle

http://en.m.wikipedia.org/wiki/Paul_Erd%C5%91s

What is Erdős Number ?

image

Amazon Book: “My Brain Is Open”

Paul Erdős (er-dish) was one of the greatest mathematicians in 21st Century, a Jewish Hungarian, single and no home. He traveled around the world in one small suitcase containing his mathematical papers. He would knock at the door of his former students or math collaborator impromptu, started working and published the papers, then moved on to next destination the moment his overstay became unwelcome by the host’s wife. In this way he published 1,500 articles in his lifetime.

image

Example:

Einstein had the Erdős Number 2 , through his assistant who co-wrote a paper with Paul Erdős.

Ref:

http://tomcircle.wordpress.com/2013/03/30/paul-erdos/

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Harvard Online Course: Abstract Algebra

For Junior College students after getting your A-level result this month, if you want to further study Math (or Science, Engineering) in the top universities overseas after your National Service, e.g. USA (Harvard, MIT, Stanford, Princeton, …), or France (where their modern math standard in French Baccalaureate – not the Singapore IB – is much higher than the GCE A level).
Attend this video up to the first 15 lectures will prepare you a good Modeen Math foundation, which is seriously lacking in our Singapore JC Math syllabus (regardless whether you get distinction in GCE A level Math)

tomcircle's avatarMath Online Tom Circle

Prof Benedict Gross is one of the best Algebra professors I have seen – he can explain so well the abstract concepts, without injecting fear and confusion to the students.

As Prof Gross had brilliantly said in the beginning of this Lecture 1:

Algebra is the language of Math.

Since Math is the language of science,
therefore any serious Science needs to speak in Algebra language.

Today, if you read a research paper on any math (or Computer Science, Mathematical Physics…) topic, hardly you can avoid these “basic” algebraic lingoes: Group, Ring, Field, Vector Spaces, Quotient Group, Ideal, …

I strongly recommend to anyone who likes to study Modern Algebra but afraid of the abstractness, this is the course (free) for you. I can guarantee you by the halfway (15th lecture) you will have a solid foundation, and by the last lecture you will be able to follow high-level…

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Fun Math Games for Kids

Fun Math Games for Kids

Math Board Games

Site: http://0b4b4eghj3ow8u1ctvk2o9ns5l.hop.clickbank.net/?tid=SEAEAGLEMATHGAME

Dear Friend,

Let’s face it, math can be fun but not all kids think it is. Kids are used to being entertained and expect everything that you want them to do, to be just as entertaining as their favorite pastimes.

What worked in the past, doesn’t necessarily work today. Many kids don’t want to learn math or practice math, they’d rather be watching DVD’s or playing with computer games.

No wonder you feel frustrated!

You know that math skills will be vital to every child’s future. It helps them in school… at work… in social situations… in all areas of life. You simply cannot get along without it. But many kids struggle with math and don’t enjoy it at all.

But it doesn’t have to be like this!

Imagine being able to get kids so engaged with math that they don’t even want to stop even when you ask them to. Wouldn’t that be great?

Read more at: http://0b4b4eghj3ow8u1ctvk2o9ns5l.hop.clickbank.net/?tid=SEAEAGLEMATHGAME

 

Our Daily Story #11: The Anonymous Mathematician “Nicolas Bourbaki”

tomcircle's avatarMath Online Tom Circle

The romantic gallic Frenchmen like to joke and give pranks. We have already seen the Number 1 Mathematical ‘prank’ in Our Daily Story #1 (The Fermat’s Last Theorem), here is another 20th century Math prank “Nicolas Bourbaki” – the anonymous French mathematician who did not exist, but like Fermat, changed the scene of Modern Math after WW II.

http://en.m.wikipedia.org/wiki/Nicolas_Bourbaki

image

André Weil (not to confuse with Andrew Wiles of FLT in Story #2 ) and his university classmates from the Ecole Normale Supérieure (Évariste Galois‘s alma mater which expelled him for involvement in the French Revolution), wanting to do something on the outdated French university Math textbooks, formed an underground ‘clan’ in a Parisian Café near Jardin du Luxembourg. They met often to brainstorm and debate on the most advanced Math topics du jour. Finally they decided to totally re-write the foundation of Math based on Set…

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