The French method of drawing curves is very systematic:
“Pratique de l’etude d’une fonction”
Let f be the function represented by the curve C
Steps:
1. Simplify f(x). Determine the Domain of definition (D) of f;
2. Determine the sub-domain E of D, taking into account of the periodicity (eg. cos, sin, etc) and symmetry of f;
3. Study the Continuity of f;
4. Study the derivative of fand determine f'(x);
5. Find the limits of fwithin the boundary of the intervals in E;
6. Construct the Table of Variation;
7. Study the infinite branches;
8. Study the remarkable points: point of inflection, intersection points with the X and Y axes;
9. Draw the representative curve C.
Example:
$latex displaystyletext{f: } x mapsto frac{2x^{3}+27}{2x^2}$ Step 1: Determine the Domain of Definition D D = R* = R –…
Donald Knuth (Great Computer Mathematician, Stanford University, LaTex inventor) noted the Bible uses a phrase like:
“as my Father is to me, I am to you”
=> F= Father = line AB
I (or me) = AC
U = You = CB
=> F/I = I/U = Φ
Note: Φ = 1.61803 = – 2 sin 666°
Related Links: Find sites that are similar to the site you are visiting.
Wayback: See how a site looked in the past.
Hot Pages & Searches: See what’s popular on the web right now.
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.
$Latex i^{i } = 0.207879576…$
$latex i = sqrt{-1}$
If a is algebraic and b is algebraic but irrational then $latex a^b $ is transcendental. (Gelfond-Schneider Theorem)
Since i is algebraic but irrational, the theorem applies.
1. We know
$latex e^{ix}= cos x + i sin x$
Let $latex x = pi/2 $
2. $latex e^{i pi/2} = cos pi/2 + i sin pi/2 $
$latex cos pi/2 = cos 90^circ = 0 $
$latex sin 90^circ = 1 $
$latex i sin 90^circ = (i)*(1) = i $
3. Therefore
$latex e^{ipi/2} = i$
4. Take the ith power of both sides, the right side being $latex i^i $ and the left side =
$latex (e^{ipi/2})^{i}= e^{-pi/2} $
5. Therefore
$latex i^{i} = e^{-pi/2} = .207879576…$
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.
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.
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…
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.
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…
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.
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.”
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!
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.
“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…
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
Know any other funny Math Jokes? Post it in the comments below! 🙂
Top 5 Math Jokes:
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!”
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.”
There are three kinds of people in the world; those who can count and those who can’t.
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.
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 .”
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
Pure mathematics is, in its way, the poetry of logical ideas. ~Albert Einstein
A mathematician is a device for turning coffee into theorems. ~Paul Erdos
Give me a place to stand, and I will move the earth. ~ Archimedes
Mathematics is the door and key to the sciences. ~ Roger Bacon
The essence of mathematics is its freedom. ~ Cantor
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
Mathematics is the queen of the sciences and number theory is the queen of mathematics. ~ Gauss
Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country. ~ Hilbert
When you can measure what you are talking about and express it in numbers, you know something about it. ~ Kelvin
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.
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.
Example:
Einstein had the Erdős Number 2 , through his assistant who co-wrote a paper with Paul Erdős.
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)
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…
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?
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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: 
