I was taught how to find area of a circle when in school. The teacher wrote down the formulae on the blackboard and I accepted it as absolute truth.
Later in my life I used integral calculas to derive the formulae for the area of a circle, but I never found a way to explain it to a 11 year old, till recently.
At my son’s primary school , the maths teacher explained why the area of a circle is pr2 by cutting a pair of cardboard discs. Apparently it was first derived by Archimedes. I was amazed at the beauty and the simplicity of the proof . Why didn’t they teach it in our schools ?
By our third year, most of us will have learned to count. Once we know how, it seems as if there would be nothing to stop us counting forever. But, while infinity might seem like an perfectly innocent idea, keep counting and you enter a paradoxical world where nothing is as it seems.
Mathematicians have discovered there are infinitely many infinities, each one infinitely bigger than the last. And if the universe goes on forever, the consequences are even more bizarre. In an infinite universe, there are infinitely many copies of the Earth and infinitely many copies of you. Older than time, bigger than the universe and stranger than fiction. This is the story of infinity.
Georg Ferdinand Ludwig Philipp Cantor (/ˈkæntɔr/ KAN-tor; German: [ˈɡeɔʁk ˈfɛʁdinant ˈluːtvɪç ˈfɪlɪp ˈkantɔʁ]; March 3 [O.S. February 19] 1845 – January 6, 1918[1]) was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are “more numerous” than the natural numbers. In fact, Cantor’s method of proof of this theorem implies the existence of an “infinity of infinities”. He defined the cardinal and ordinal numbers and their arithmetic. Cantor’s work is of great philosophical interest, a fact of which he was well aware. (Wikipedia)
This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world’s leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music–and much, much more.
Tung Soo Hua (Chinese: 董素华; pinyin: Dǒng Sùhúa, Dong Suhua) is an award-winning television news anchor and current affairs presenter with MediaCorp TV Channel 8 and Channel U. (Wikipedia)
Tung won the Best Chinese-language News Presenter award for Star Awards in 2004, 2005, 2006, 2007, 2009 and 2011 Star Awards.
Tung studied in Nanyang Girls’ High School, and graduated with a Masters degree in Social Sciences (International Studies) from the National University of Singapore, after obtaining her first Honours Bachelor of Science degree in Mathematics.
Presenter/Senior Producer, Chinese News, MediaCorp Pte Ltd
Ms Tung Soo Hua is an award-winning television news and current affairs presenter with MediaCorp, Singapore’s leading media company. Currently, she co-hosts “Evening News at 10pm” on the most watched Mandarin channel in Singapore, Channel 8, and fronts “Money Week”, a weekly financial programme on Channel U. She started her journalism career in MediaCorp as a Chinese-language news producer in 1997.
Ms Tung was named the “Best News/Current Affairs Presenter” for six times between 2004 and 2011 in “Stars Awards”, which is MediaCorp’s gala event recognising its talents for their excellence. She graduated with a Masters degree in Social Sciences (International Studies) from the National University of Singapore, after obtaining her first Honours Bachelor of Science degree in Mathematics.
Currently in its eighteenth printing in Japan, this best-selling novel is available in English at last. Combining mathematical rigor with light romance, Math Girls is a unique introduction to advanced mathematics, delivered through the eyes of three students as they learn to deal with problems seldom found in textbooks. Math Girls has something for everyone, from advanced high school students to math majors and educators.
This is a very interesting video on the Infinite Hotel Paradox from Youtube. One of the best videos on the mysterious Infinity that I have ever watched. Do check it out!
The Infinite Hotel, a thought experiment created by German mathematician David Hilbert, is a hotel with an infinite number of rooms. Easy to comprehend, right? Wrong. What if it’s completely booked but one person wants to check in? What about 40? Or an infinitely full bus of people? Jeff Dekofsky solves these heady lodging issues using Hilbert’s paradox.
Lesson by Jeff Dekofsky, animation by The Moving Company Animation Studio.
Many people take math in high school and promptly forget much of it. But math plays a part in all of our lives all of the time, whether we know it or not. In The Joy of x, Steven Strogatz expands on his hit New York Times series to explain the big ideas of math gently and clearly, with wit, insight, and brilliant illustrations.
This is a great introduction to LaTeX, a mathematical typesetting language that can be used to write Math equations. LaTeX can be used on WordPress too!
What happens if light slows down – A Beginner’s Guide to Relativity and Light
In the beginning God created the heavens and the earth. And God said, “Let there be light,” and there was light. Light is one of the most ubiquitous things that we see, and it is also one of the oldest – it existed since the beginning of mankind. However, light is also mysterious in that no one really understands what it is and how it is rectilinearly propagated. Nevertheless, the speed of light plays an important part in physics, and it is one of the more often quoted constant. What will happen then, if the speed of light suddenly changes from 300000000m/s to a fraction of its original self –3000 m/s? (It is theoretically possible to slow down light to such a speed, by shining a beam of light through a medium with a refractive index of 100,000.)
It’s a numbers song for children and adults. Count from 0 to 100 and from a hundred to a trillion.
This song was written and performed by A.J. Jenkins. Video by KidsTV123.
A catchy and educational song for kids to count big numbers.
Australian authorities have announced that satellite images taken of a stretch of ocean 1,550 miles southwest of Perth, Australia, are believed to show floating debris that could be part of missing Malaysia Airlines Flight 370. “It is probably the best lead we have right now,” said John Young, a spokesman for the Australian Maritime Safety Authority. Confirmation of the material’s provenance will likely have to wait, however. While a merchant vessel has arrived in the area to help with the search, poor visibility has prevented search aircraft from locating the debris, and the nearest Australian Navy ship is several days’ sail away.
The search for Air France 447 offers a useful template for how investigators can whittle away at the seemingly unsolvable mystery of a midocean airliner disappearance. After the Airbus A330 went missing over the middle of the equatorial Atlantic in 2009, search aircraft took just one day to locate the first pieces of floating wreckage. The recovery of the black box, however, took another painstaking two years, and a full assessment of its implications another year after that.
The first step after determining the debris’ location is to call in the mathematicians. Based on all the data available—the aircraft’s last known position, route of flight, altitude, prevailing winds, sea currents, ocean depth, and so on—a probability is assigned to each variable, and a distribution map of probable locations on the sea floor is generated. Searchers can then deploy their underwater assets to scour the vastness of the deep, working back and forth along grid lines laid out in the areas of maximum probability.
There’s a deep problem inherent in this approach, however, and it’s that the probabilities are themselves only guesses. Searchers are uncertain even as to the extent of their own uncertainty. In the case of Air France 447, the set of base-set assumptions turned out to be wrong, and the first two search seasons scoured thousands of square miles in vain.
What turned the tide for AF447 searchers, in the end, was better math and better undersea technology. A recalculation of the location probabilities using a different mathematical approach led to the redrawing of the search grids much closer to the site of the plane’s disappearance. And a new type of autonomous undersea vehicle—a robot sub, in other words—became available for the first time. Called Remus 6000, these subs were able to navigate on their own along precise grid lines, ascending and diving to match the contours of the undersea terrain. On April 3, 2011, less than a week after the refined search began, one of the three submersibles deployed in the search returned to its mother ship bearing images of a debris field scattered across an abyssal plain. AF447 had been found. A month later another type of unmanned submersible brought the black boxes to the surface.
Given a quadratic equation with roots and , we have:
How do we prove this? It is actually due to the quadratic formula!
Recall that the quadratic formula gives the roots of the quadratic equation as:
Now, we can let
Hence,
In the above proof, we made use of the identity
The above formulas are also known as Vieta’s formulas (for quadratic). There we have it, this is how we prove the formula for the sum and product of roots!
Check out the following interesting comic books explaining Math (Calculus, Linear Algebra, and Statistics) in a fun and enjoyable way.
In The Manga Guide to Calculus, you’ll follow along with Noriko as she learns that calculus is more than just a class designed to weed out would-be science majors. You’ll see that calculus is a useful way to understand the patterns in physics, economics, and the world around us, with help from real-world examples like probability, supply and demand curves, the economics of pollution, and the density of Shochu (a Japanese liquor).
Mr. Seki teaches Noriko how to:
Use differentiation to understand a function’s rate of change
Apply the fundamental theorem of calculus, and grasp the relationship between a function’s derivative and its integral
Integrate and differentiate trigonometric and other complicated functions
Use multivariate calculus and partial differentiation to deal with tricky functions
Use Taylor Expansions to accurately imitate difficult functions with polynomials
Whether you’re struggling through a calculus course for the first time or you just need a painless refresher, you’ll find what you’re looking for in The Manga Guide to Calculus.
Follow along in The Manga Guide to Linear Algebra as Reiji takes Misa from the absolute basics of this tricky subject through mind-bending operations like performing linear transformations, calculating determinants, and finding eigenvectors and eigenvalues. With memorable examples like miniature golf games and karate tournaments, Reiji transforms abstract concepts into something concrete, understandable, and even fun.
As you follow Misa through her linear algebra crash course, you’ll learn about:
Basic vector and matrix operations such as addition, subtraction, and multiplication
Linear dependence, independence, and bases
Using Gaussian elimination to calculate inverse matrices
Subspaces, dimension, and linear span
Practical applications of linear algebra in fields like computer graphics, cryptography, and engineering
But Misa’s brother may get more than he bargained for as sparks start to fly between student and tutor. Will Reiji end up with the girl—or just a pummeling from her oversized brother? Real math, real romance, and real action come together like never before in The Manga Guide to Linear Algebra.
The Manga Guide to Statistics
This manga textbook is written for those interested in understanding principles of statistics. Each of the seven chapters is organized into four sections: a cartoon, a text explanation to supplement the cartoon, an exercise that includes the answer, and a summary. Readers can learn much about the subject by just reading the cartoon, but they will gain a more thorough understanding by working through the other three sections in each chapter. Yamamoto provides Rui with easy-to-understand examples and graphic illustrations, making the subject less intimidating.
If you are interested to write for us and submit a guest post, please contact us at mathtuition88@gmail.com, or drop us a message in the comments below! 🙂
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Alexa Internet, Inc. is a California-based subsidiary company of Amazon.com which provides commercial web traffic data. Founded as an independent company in 1996, Alexa was acquired by Amazon in 1999. Its toolbar collects data on browsing behavior and transmits it to the Alexa website, where it is stored and analyzed, forming the basis for the company’s web traffic reporting. As of 2013, Alexa provides traffic data, global rankings and other information on 30 million websites,[3] and its website is visited by over 8.5 million people monthly. (Wikipedia)
This post is a review on Right brain training, and also a list of resources that one can research on regarding to the popular method of Right brain training.
When it comes to New Year’s resolutions, getting your body in shape often tops the list. But what about your brain?
Top Seller on Amazon.com on Right brain training
If your left or right brain is feeling a little flabby, there’s a wide range of books, teaching programs, and even a Nintendo DS game, purporting to train your left and/or right brain. Indeed, if you Google “right brain training”, you’ll score 53,900,000 hits.
These products are based on the belief that the left and right hemispheres are polar opposites. The left brain is often characterised as your intelligent side: rational, logical and analytic. In contrast the right brain is stereotyped as the “touchy-feely” hemisphere, viewed as artistic, creative, and emotive.
Such left and right brain stereotypes have led theorists to suggest that people can be classified according to their “hemisphericity”. If you’re a logical, rational scientist, for instance, you’re left-brained. But creative types, from artists to writers, are right-brained.
Based on my teaching experience, I do find that left-handers (right-brained) students tend to be very creative and usually excel at arts and humanities. However, their math skills can be good too, especially with practice. This shows that the human brain is like a muscle, it gets better with practice and use.
Did you know our Prime Minister Lee Hsien Loong is left-handed too? Barack Obama is also left-handed. Prime Minister Lee Hsien Loong is very good at math, so this should dispel any myths that left-handed students are not good at math.
Understanding the Myth of Left Brain and Right Brain Dominance
The Right Brain
According to the left-brain, right-brain dominance theory, the right side of the brain is best at expressive and creative tasks. Some of the abilities that are popularly associated with the right side of the brain include:
Recognizing faces
Expressing emotions
Music
Reading emotions
Color
Images
Intuition
Creativity
The Left Brain
The left-side of the brain is considered to be adept at tasks that involve logic, language and analytical thinking. The left-brain is often described as being better at:
Language
Logic
Critical thinking
Numbers
Reasoning
Also, check out the above Youtube video to check if you are a right-brained or left-brained person!
The Right Brain vs Left Brain test … do you see the dancer turning clockwise or anti-clockwise?
If clockwise, then you use more of the right side of the brain and vice versa.
Most of us would see the dancer turning anti-clockwise though you can try to focus and change the direction; see if you can do it.
LEFT BRAIN FUNCTIONS
uses logic
detail oriented
facts rule
words and language
present and past
math and science
can comprehend
knowing
acknowledges
order/pattern perception
knows object name
reality based
forms strategies
practical
safe
RIGHT BRAIN FUNCTIONS
uses feeling
“big picture” oriented
imagination rules
symbols and images
present and future
philosophy & religion
can “get it” (i.e. meaning)
believes
appreciates
spatial perception
knows object function
fantasy based
presents possibilities
impetuous
risk taking
Right Brain Training Test
Take the test to see if you are right-brained or left-brained!
Any comments or websites about Right brain training to share? Leave your comments below!
Right Brain Training Video
Watch this free brain training video and follow the instructions to increase your brain power. This is an online “game” that really works to improve brain function. You can actually feel it work!
Brain Training can increase your brain power just like weight training can increase your strength. Use this exercise to work out your brain. Bookmark this video and come back and practice with variations on the basics as discussed in the video.
Recently, I added the Maths Blog to the Teach100 website. Glad to know that the blog has been approved!
“Thank you for submitting Singapore Maths Tuition to the Teach100! Your blog has been approved and is currently ranked at #427 of 601 blogs. Congratulations! We recently reached our 500th blog, and are excited to add your blog to our growing community!”
National Pi Day is actually a U.S. holiday. The House of Representatives passed House Resolution 224 in 2009, designating March 14 as National Pi Day. The resolution “encourages schools and educators to observe the day with appropriate activities that teach students about Pi and engage them about the study of mathematics.” (Source: http://www.usatoday.com/story/tech/2014/03/13/pi-day-friday-31415/6369483/)
Do you wish Pi day was a national holiday in your country? I sure do! Leave your comments below!
There are many academic institutions in the world and rankings on certain faculties help determine the best ones in certain fields. Students who are extremely in mathematics will automatically want to enroll and join universities that are highly ranked as far as mathematics is concerned. Year by year, the rankings are released and can be accessed through the internet and various academic public publications. In addition to stellar performance, there are other factors that are considered during the rankings. This article will mention a few of the top mathematics institutions around the world.
The University of Cambridge
This is not only one of the oldest universities in the United Kingdom but also in the world. Its scholarly achievements have made it popular and famous the world over. Its high performance in mathematics and other fields is accredited to research and well trained and knowledgeable faculty tutors. External examiners and bodies such as the Quality Assurance Agency have all endorsed the performance of the university time and again. The University of Cambridge has vast studying resources such as museums, libraries and other collections. Teaching is done by lecturers who are experts and authorities in their field through seminars and lectures making this university the very top of this list.
The University of Toronto
The University of Toronto is one of the best in the world not only in mathematics but when it comes to research. Its research capabilities in all fields are rivaled only by the prestigious Harvard Universities. One thing that makes this institution great in mathematics is its system of graduate supervision and teaching strengths. The university attracts and enrolls professionals, graduates and undergraduates in the mathematical field and they are all taught by the best researchers. It has both on campus and off campus students. International students get to enjoy learning mathematics and visiting come of Canada’s most breathtaking scenic sites.
The Australian National University
This top ranked university was established back in 1946 and has risen over the years to be the top university in Australia and one of the best in the world. Mathematically speaking, the university’s teaching methods and perfectly teacher to student ratio ensure that the mathematical faculty is of international standards. Campus students do not even have to venture outside as the campus has all the social amenities needed. To make it even better, the university is well networked with some of the world’s leading academic institutions and this means that it has access to the latest information in research.
National University of Singapore
Asia is not left behind as far as mathematical prowess is concerned as the National university of Singapore puts it on the global map. One of the things that make it a top institution is its well-structured exchange programs with other universities that are mathematical giants. For this reason, the university’s best students apply for ESTA VISA in order to join other brilliant mathematical minds in other universities. The university also offers joint degree programs with other leading universities. Due to the university’s strength in research, it is affiliated with global research bodies such as International Alliance of Research Universities.
A Maths Paper 2:
29/10/2014 (Wednesday)
08:00-10:30
The schedule for the first few weeks seems to be quite tight, for instance on 28/10/2014 students would have to handle A Maths Paper 1, and Chemistry Paper 2. (A Maths Paper 1 would be quite exhausting for students on its own)
After the major papers are over, students will have plenty of time to study for their Science Paper 1 (MCQ), with Biology Paper 1 being one of the last papers on 13/11/2014.
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.
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)
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):
From this, we have
Similarly,
But since , we have . Dividing throughout by gives Bayes’ Formula:
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.)
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:
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 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.
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…
“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 =
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 =
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 =
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!
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)
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)
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/)
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
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
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.
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.
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.
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.”
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.
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.
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.
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…
“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.
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.
(Pic from, appropriately, digyourowngrave.com)
The 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…
For O Levels, we need to be proficient in both Calculus (Differentiation and Integration), AND Trigonometry! Students need to revise early to avoid being like Mr Bean!
“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…
Diameter d=2r 
with roots 
and 
, we have:
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, you have entered the mysterious world of complex numbers.
is a real number! Let us explain it here:
. This has been voted as the most beautiful equation in mathematics by many people.
, we have 
. Dividing throughout by 
gives Bayes’ Formula: 
, 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.
Mathtuition88 