Category: Uncategorized

WordPress to Sina Weibo 微博 Automatic Posting

I recently discovered a way to post (automatically) from WordPress to Sina Weibo 微博(China’s version of twitter, which has more than half a billion users!)

The trick is to use IFTTT.com (If this then that).

Steps:

1) Setup up publicize for WordPress to Twitter. (WordPress.com can do this automatically).

2) Go to IFTTT.com, and set up a recipe from Twitter to Weibo. (There is a premade template for that, takes less than 5 minutes to sign up)

Done!

There may be a way for WordPress –> Weibo direct posting, I am still researching on that. (Update: Yes, there is a recipe for direct WordPress –> Weibo too!) It depends on whether you want a short summary, in which case WordPress –> Twitter –> Weibo may suit you better. If you want a full text, then WordPress –> Weibo is great. Or, you can use both!

Hope it is helpful!

weibo

无微不至:微博营销实战指南

《无微不至:微博营销实战指南》内容简介：企业如何利用微博进行营销？如何了解消费者的购买心理？如何把握微博的传播机制，发现用户的行为模式，找到有价 值的客户？如何挖掘数据价值，制定营销方案，实现营销的最佳效果？《无微不至:微博营销实战指南》从如何搭建企业微博营销平台、构建微博体系、塑造企业微 形象、选择微博营销模式，以及微博营销的技能、微博写作技巧等方面详尽地讲述微博营销的方法、技巧，具有实操性强，案例经典，拿来就能用的特点。在《无微 不至:微博营销实战指南》中，读者还会学到以下经典内容：微博营销已不是简单开个账户，发发帖子。微博传播永远是内容为王，无论是重口味，还是小清新，一 定要与草根文化血脉相通。写微博和说相声是一样的，要善于抖包袱，要在140字中写出跌宕起伏。10%的人影响了90%的人的购买行为，微博是影响他人购 买决策的一个有效工具。社交广告即将或者已经成为最主流的社会化营销解决方案。高质量的内容和互动永远是提高粉丝转发率、留住粉丝的不二法宝。中国移动、 中国电信应该如何做微博营销？《独唱团》爆单，快书包如何转危机为商机？如何打造企业官微？1000个真实的粉丝意味着什么？如何用微博编织人脉？微博内 容写作十大技巧是什么……

Chinese Math and Science Books

Just to introduce a few books that can simultaneously improve your child’s Math and Science knowledge, and Chinese at the same time!

The latest news is that China is building the Kra Canal, a news that would mark the beginning of the increased dominance of China in Southeast Asia, hence having a good grasp of Mandarin is no longer optional, but 100% compulsory if you want to have a slice of the pie of the jobs and benefits generated by China.

华文数学/科学书本

1）
可怕的科学•经典数学系列(套装共12册)(三度荣获国际科普图书最高奖)

horrible science

This series of “Horrible Science” Books is translated into Chinese, and is an award winning series of books. Highly recommended!

2)
小学奥数700题详解:3、4、5、6年级

math olympiad

700 Practice Problems for Math Olympiad! These books are very useful for GAT / DSA / GEP Preparation.

3)
走进奇妙的数学世界1-3(套装共3册)

math olympiad world of math

Into the world of Mathematics! 《走进奇妙的数学世界1-3(套装共3册)》内容简介：数学最让人困惑的是为什么这样和有什么用，很多人即使大学毕业也不明白，这套书完美地阐释了数学的 本质，把数学和生活紧密联系在一起。13种基本数学思想，层层深入，完美阐释数学的本质。以两个小矮人贯穿全文，图文并茂，讲故事、出谜题、做游戏，游戏 背后蕴藏数学概念让孩子以最简单、最科学的方式走近数学，爱上数学！不仅仅讲算术，更重在启发从不同角度看待事物、解决问题的思考方式，培养孩子的逻辑思 维能力，提高综合素质。

Finally, for readers of my blog who are new to Chinese, and wish to learn this 5000 year old language, I would recommend some books to learn Chinese for beginners here：

轻松学中文1(课本)(附CD光盘1张)

easy chinese

Learn Chinese in an easy manner! Easy steps to Chinese. (With CD)

Coursera Probability Course and Recommended Probability Book

Just completed the Coursera Probability Course by UPenn (University of Pennsylvania), lectured by Professor Santosh S. Venkatesh who is the author of the highly recommended book: The Theory of Probability: Explorations and Applications.

Coursera Review

The course isn’t very hard, it is very suitable for undergraduates and even high school students should be able to understand majority of the content. It actually overlaps with the A level syllabus in Singapore, and hence I would say that a 17-18 year old student would be able to grasp most of the concepts in this course.

The lecturer is very good at words, and his lectures are full of imagery and vivid descriptions. The homework is a little tricky, and hence would require some thought, even though the concepts tested are elementary (elementary in the sense that it doesn’t require calculus).

A sample of a tricky question is the “Six Saucer Question”: Six cups and saucers come in pairs: there are two cups and saucers that are red, white, and blue. If the cups are placed randomly onto the saucers (one each), find the probability that no cup is upon a saucer of the same color.

It is very tricky and to get it correct on the first try is a major accomplishment.

Overall, this Coursera Course is highly recommended, and students should try to take it the next time it comes out!

WW2 Enigma Machine

How to break 158,962,555,217,826,360,000 codes ?

tomcircle's avatarMath Online Tom Circle

There are 158,962,555,217,826,360,000 possibilities of codes in the German Enigma Machine:

Flaw cracked by the genius Mathematician Alan Turing (Father of Artificial Intelligence) :

“A key can never be itself” — this is ‘the straw that breaks the camel’s back’, a critical clue to break the 158,962,555,217,826,360,000 possible codes !

View original post

Chinese Remainder Theorem History (韩信点兵)

I have written a guest post on https://chinesetuition88.wordpress.com on the very fascinating Chinese Remainder Theorem and its History (韩信点兵). Do check it out, you will be amazed at the genius of Chinese General Han Xin.

Students who are interested in Chinese Tuition may check out https://chinesetuition88.wordpress.com for more details.

chinesetuition88's avatarChinese Tuition Singapore

淮安民间传说着一则故事——“韩信点兵”，其次有成语“韩信点兵，多多益善”。韩信带1500名兵士打仗，战死四五百人，站3人一排，多出2人；站5人一排，多出4人；站7人一排，多出6人。韩信马上说出人数：1049。

Translation:

In Ancient China, there was a General named Han Xin, who led an army of 1500 soldiers in a battle. An estimated 400-500 soldiers died in the battle. When the soldiers stood 3 in a row, there were 2 soldiers left over. When they lined up 5 in a row, there were 4 soldiers left over. When they lined up 7 in a row, there were 6 soldiers left over. Han Xin immediately said, “There are 1049 soldiers.”

Amazing! How did Han Xin do that?

Han Xin was not only a brilliant mathematician and general, he was also a very magnanimous guy full of wisdom.

Once, when he was suffering from hunger, he met a woman who provided him with food. He promised to repay her for her kindness after he had made great achievements in life, but it was rebuffed by her…

View original post 342 more words

Quiz: Can You Solve This Sum ?

For more logic puzzles, check out:

Puzzle Baron’s Logic Puzzles

tomcircle's avatarMath Online Tom Circle

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[Hint]: Think out of the box…

Answer below (scroll down)
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Answer:
1 + 13 +…

View original post 57 more words

费马大定理 Fermat’s Last Theorem

Intriguing review (Chinese) of FLT by a non-mathematician. He aims to convey the beauty of Mathematics to students, who unfortunately treat Math as a tool to pass exams from PSLE, O and A level, university math course, then ditch Math upon graduation. Math is the beauty of the universe.

tomcircle's avatarMath Online Tom Circle

费马大定理 Fermat’s Last Theorem (FLT): 17世纪业余数学家法国大法官费马开的一个”玩笑”, 推动350年来现代数学突飞猛进。

FLT 数学长征英雄人物:

1. Fermat (费马 1601@ Toulouse, France)
2. Galois (伽罗瓦): Group Theory (群论)
3. Gauss (高斯)
4. Cauchy (柯西) Lamé (拉梅) Kummer (库马)
5. Solphie Germain
6. Euler (欧拉)
7. Taniyama (谷山丰), Shimura (志村五郎)

集大成:
8. Andrew Wiles (怀尔斯) (证明@1993 -1995)

1.Elliptic Curve (椭圆曲线)
2. Modular Form (模形式)
3. Fermat Last Theorem (费马大定理)

(1) = (2) = (3)

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Math is Forever (Spanish)

With humor and charm, mathematician Eduardo Sáenz de Cabezón answers a question that’s wracked the brains of bored students the world over: What is math for? He shows the beauty of math as the backbone of science — and shows that theorems, not diamonds, are forever. In Spanish, with English subtitles.

Yes, indeed, 1000 years from now, students will still be learning Pythagoras’ Theorem, while other fragments of human knowledge would have faded away.

Check out also this book: Arithmetic and Algebra Again: Leaving Math Anxiety Behind Forever, suitable for students who really need some encouragement and motivation to overcome fear of math! Albert Einstein once said, “You never fail until you stop trying.” Hence, even if you have not done well in math for the past years, there is still hope, don’t give up!

April Fools Video Prank in Math Class

Check out this really funny video on a April Fools Prank during a Math Class!

The teacher played a trick on his math class for April Fool’s Day. In this one, he’s showing a “homework help” video that gets some trigonometry wrong.

Looking for more Math Jokes? Check out the book below!

Math Jokes 4 Mathy Folks

Excellent MITOpenCourseware

tomcircle's avatarMath Online Tom Circle

Strongly recommended free excellent MIT Math for high school, undergrads/grads and any self-study learners.

Thanks Prof. Gilbert Strang for the unselfish sharing.

http://ocw.mit.edu/faculty/gilbert-strang/

I find extremely pleasure when I discovered his brilliant lecture notes in “Generating Function” – a Discrete Math technique for computing sequencing using function, and the application in complex Combinatorics. Download here:

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Example:
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The Math of Shuffling Cards

Previously, the first YouTube video wasn’t working. I have added a new link to the interesting “Looking at Perfect Shuffles” video. 🙂

mathtuition88's avatarMathtuition88

A magic trick based on the “Perfect Shuffle”. Featuring Professor Federico Ardila. I watched his videos on Hopf Algebras while learning the background material for my honours project on Quantum Groups.

Mathemagician Persi Diaconis discusses which is the best way to shuffle: Overhand shuffle, Riffle Shuffle, or “Smoosh” Shuffle? Watch the video to find out!

Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks is an interesting book by Professor Diaconis, featuring Magic Tricks that have a mathematical background! This book is a great idea for a gift for students, teachers, or friends!

View original post

Mathematicians have prevented a world disaster, behind the scenes

Recently, after taking the Coursera course on Cryptography, I had a better appreciation of mathematics and the role of cryptography in our modern society.

I was pleased to read this article Quantum compute this: Mathematicians build code to take on toughest of cyber attacks, and Washington State University mathematicians have designed an encryption code capable of fending off the phenomenal hacking power of a quantum computer.

The quantum computer, though not yet invented, is widely believed to be available soon in the next few years. In the hands of hackers, the quantum computer would be a formidable weapon as current cryptographic methods are extremely vulnerable to the quantum computer as it can factor numbers extremely quickly, leading to number theoretic codes being broken.

What would happen if a Quantum Computer is built

Quantum computers are near

Quantum computers operate on the subatomic level and theoretically provide processing power that is millions, if not billions of times faster than silicon-based computers. Several companies are in the race to develop quantum computers including Google.

Internet security is no match for a quantum computer, said Nathan Hamlin, instructor and director of the WSU Math Learning Center. That could spell future trouble for online transactions ranging from buying a book on Amazon to simply sending an email.

Hamlin said quantum computers would have no trouble breaking present security codes, which rely on public key encryption to protect the exchanges.

In a nutshell, public key code uses one public “key” for encryption and a second private “key” for decoding. The system is based on the factoring of impossibly large numbers and, so far, has done a good job keeping computers safe from hackers.

Quantum computers, however, can factor these large numbers very quickly, Hamlin said. But problems like the knapsack code slow them down.

Fortunately, many of the large data breaches in recent years are the result of employee carelessness or bribes and not of cracking the public key encryption code, he said.

Hence, when many people say mathematics is useless, they are actually extremely wrong, as mathematics permeates every aspect of life! Even though maths like calculus is not directly used in everyday life, it is part of our phone, computer, and every part of the modern lifestyle.

Kudos to the mathematicians who have averted a world disaster, before quantum computers are even invented!

If you are interested in what a quantum computer is, and what it can do (it is so powerful that whoever has one would hold the keys to the entire internet), check out this book Schrödinger’s Killer App: Race to Build the World’s First Quantum Computer.

Written by a renowned quantum physicist closely involved in the U.S. government’s development of quantum information science, Schrödinger’s Killer App: Race to Build the World’s First Quantum Computer presents an inside look at the government’s quest to build a quantum computer capable of solving complex mathematical problems and hacking the public-key encryption codes used to secure the Internet. The “killer application” refers to Shor’s quantum factoring algorithm, which would unveil the encrypted communications of the entire Internet if a quantum computer could be built to run the algorithm. Schrödinger’s notion of quantum entanglement—and his infamous cat—is at the heart of it all.

What is a Tensor?

Most people don’t encounter Tensors (the higher level advanced version of Matrices) until they reach senior undergraduate, or even graduate level.

What is a Tensor?

The best explanation I have ever seen, comes from this video by the author of A Student’s Guide to Vectors and Tensors, Daniel A. Fleisch. Using children’s blocks and laymen language, he explains what is a tensor clearly and succinctly in a way that is unbelievably crystal clear.

This YouTube video is watched over 200,000 times, a very commendable achievement for a math video!

Official Definition by Wikipedia

Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples of such relations include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of numerical values. The order (also degree) of a tensor is the dimensionality of the array needed to represent it, or equivalently, the number of indices needed to label a component of that array. For example, a linear map can be represented by a matrix (a 2-dimensional array) and therefore is a 2nd-order tensor. A vector can be represented as a 1-dimensional array and is a 1st-order tensor. Scalars are single numbers and are thus 0th-order tensors. The dimensionality of the array should not be confused with the dimension of the underlying vector space.

Cauchy stress tensor, a second-order tensor.

If you have some programming knowledge, you may view tensors as a type of multidimensional array. A more mathematical abstract way can be achieved by defining tensors in terms of elements of tensor products of vector spaces, which in turn are defined through a universal property.

Cool? The word “tensor” really strikes me as a word that is really sophisticated and complicated!

How to find the distance of a plane to the origin

Given the equation of a plane: ax+by+cz=D, or in vector notation \mathbf{r}\cdot \left( \begin{array}{c} a\\ b\\ c\\ \end{array}\right)=D, how do we find the (shortest) distance of a plane to the origin?

(When a question asks for the distance of a plane to the origin, by definition it means the shortest distance.)

One way to derive the formula is this:

Derivation

Let X be the point on the plane nearest to the origin.

\overrightarrow{OX} must be perpendicular to the plane, i.e. parallel to the normal vector \mathbf{n}=\left(\begin{array}{c}a\\b\\c\\\end{array}\right).

Furthermore, X lies on the plane, hence we have \boxed{\overrightarrow{OX}\cdot\mathbf{n}=D}

Using the formula for dot product, we can get |\overrightarrow{OX}\cdot\mathbf{n}|=|\overrightarrow{OX}||\mathbf{n}|\cos \theta=D

Since \overrightarrow{OX} is parallel to \mathbf{n}, \theta is either 0 or 180 degrees, hence \cos \theta is either 1 or -1.

Thus, we have |\overrightarrow{OX}||\mathbf{n}|=|D|.

The shortest distance from the point X to the origin is then \displaystyle|\overrightarrow{OX}|=\frac{|D|}{|\mathbf{n}|}=\frac{|D|}{\sqrt{a^2+b^2+c^2}}

Ans: Shortest distance from point to plane is \displaystyle\boxed{\frac{|D|}{\sqrt{a^2+b^2+c^2}}}

H2 Maths Condensed Notes and Prelim Papers

If you are looking for a short summarized H2 Maths Notes, with Prelim Papers to practice, do check out our Highly Condensed H2 Maths Notes!

GEP Questions: The Gauss Trick

We will continue our series on GEP Questions. To learn more about Recommended Books for GEP, to practice GEP Questions, visit the link here.

Today, we will discuss the quintessential GEP Question: The Gauss Trick. This GEP question illustrates the fact that giftedness can be trained to a large extent.

Question:

Find the sum of 1+3+5+7+…+95+97+99.

Solution will be below after this text, scroll down after you are ready to see the answer!

If a 9 year child can solve this on his/her first attempt (i.e. see the question for the very first time), then the child is actually at the level of Carl Friedrich Gauss, the legendary mathematician!  When Gauss was a young kid, his teacher set the class a difficult question, 1+2+3+…+99+100, hoping to keep the children quiet and busy while he could have some time to relax. Little did he expect Gauss to come up with the right answer minutes later.

Most 9 year old kids would not be able to solve this on their first try. I wouldn’t be able to solve it correctly even if given an hour when I was a kid! If the children have seen it before and practiced, that is a different story, as it becomes so easy even for a 7 year old kid. Hence, practicing GEP Questions actually leads to an indirect boost of IQ in this manner! The transition from ignorance to knowledge, leading to increased intelligence, can be accomplished by practice! To practice more of these GEP Questions, check out the Math Olympiad Recommended Books page. As a tutor, I know that this Gauss Trick is a “must-know” question for students aiming high for school Math / GEP Selection Test, since almost every kid knows this nowadays, and it is highly popular in tests.

In fact, this technique (Gauss Trick) commonly tested in GEP Questions can be used all the way to JC and beyond! In JC it is covered under the topic of AP/GP (Arithmetic Progression and Geometric Progression).

Solution:

Now, for the solution. This sum is the famous arithmetic progression, where each term differs from the next by a fixed constant. In this case, the constant is 2.

Some solutions use a number pair matching, which can be problematic to explain when the number of terms is odd, but still works nevertheless. We can use another method of writing the sum backwards.

First we note that there are 50 terms in this series. We can know that either by noting that they are the odd numbers from 1 to 100, and half of the numbers are odd, hence there are 100/2=50 terms. Alternatively, we can note that 1=2(1)-1, 3=2(2)-1, 5=2(3)-1, …, 99=2(50)-1, where the number in the brackets acting like a counter.

1+3+5+7+…+95+97+99
99+97+95+…+5+3+1

Note that each pair, 1+99, 3+97, 5+95 actually add up to the same thing, i.e. 100.

Adding up the two expressions above, we get 100×50=5000.

Dividing that by two (since we double counted), we will get 5000/2=2500.

Ans: 2500

Hope you enjoyed solving this question!

Check out this amazing book on Gauss: The Prince of Mathematics: Carl Friedrich Gauss

Gauss is a true Math genius, and you can read more about his life in this interesting biography! This historical narrative will inspire young readers and even curious adults with its touching story of personal achievement.

GEP Screening Test Question Sample: The Tap Question

The Tap Question is another one of those questions that only involve fractions and whole numbers, and hence technically within the grasp of a 9 year old kid sitting for the GEP Screening Test.

However, looks are highly deceiving, and whoever tries the Tap Question for the very first time is highly likely to get stuck. (I was one of them years ago!) The Tap Question is highly popular as a challenging question, due to its psychological nature it is a hard question to grasp. This is a question you wouldn’t want to meet for the first time in the GEP Screening Test. However, if you know how to solve it, it is easy as a piece of cake, and you will be able to solve it during the GEP Screening Test no matter how they twist the question.

GEP Screening Test Sample Math Question (The Tap Question):

A fish tank is connected to three taps.
Tap A can fill the tank in 2 hours.
Tap B can fill the tank in 3 hours.
Tap C can drain the tank in 6 hours.
If all three taps are turned on at the same time, how long would it take to fill the empty fish tank?

Do try out the question before looking at the answer below!

There is a huge difference solving a question for the first time, and solving a question that one has seen before. To familiarize yourself with GEP Screening Test questions that can come out, do check out our Recommended GEP Books. Reading one of those books would increase your child’s repertoire of questions, and hence boost your child’s IQ indirectly. Also, do check out Math Olympiad books, as it is well known that GEP Screening Test Math questions do incorporate some Math Olympiad questions.

A book like The Original Collection of Math Contest Problems: Elementary and Middle School Math Contest problems would be suitable for children training for GEP Screening Test and Math Olympiad simultaneously at the same time.

Solution:

The key insight is to find out what each tap can do in one hour.

Tap A can fill 1/2 of the tank in 1 hour.
Tap B can fill 1/3 of the tank in 1 hour.
Tap C can drain 1/6 of the tank in 1 hour.

Hence, if all of them are turned on simultaneously,
\displaystyle\frac{1}{2}+\frac{1}{3}-\frac{1}{6}=\frac{2}{3} of the tank can be filled in 1 hour.

2/3 of the tank takes 1 hour to fill.
Multiplying this statement by 3,
2 tanks takes 3 hours to fill.
1 tank takes 3/2=1.5 hours to fill.

Ans: 1.5 hours

Hope you had fun solving this!

Also check out the following GEP Screening/Round 2 questions:

By the way, for my foreign readers who are curious what is GEP Screening Test, it is a test conducted in Singapore for entry to the GEP (Gifted Education Programme). The screening and selection tests are conducted at the end of Primary 3, equivalent to Grade 3 or age 9. The official website on GEP Screening Test is available at: http://www.moe.gov.sg/education/programmes/gifted-education-programme/faq/general/

The GEP Screening Math questions can be viewed as the epitome of the Singapore Math system, as it features highly challenging Math questions that are technically in syllabus but few students know how to solve!

Buy H2 Maths Notes / Buy H2 Maths Exam Papers

After a long time, the Highly Condensed H2 Maths Notes is finally ready!

Are you looking for a short, summarized notes for H2 Vectors, H2 Complex Numbers, or even H2 Statistics? Do you remember the formula for the sum of a Geometric Progression?

Purchase this Highly Condensed H2 Maths Notes to quickly review and get ready for your exam!

Free Exam Papers included:
Numerous H2 Maths (Prelim) Free Exam Papers in PDF Format, with Solutions. Schools include ACJC, AJC, HCI, NJC, all the way to YJC, and more.

Note: The set of notes is 9 pages long (2 columns per page, total of 18 columns), i.e. highly condensed and summarized short notes.

Do check it out at our page of Math Resources for Sale!

buy h2 maths exam papers
We specially drew this beautiful graph of a Hyperbola using Geogebra for this Highly Condensed H2 Maths Notes.

 

GEP Sample Question: The Worker Question

Here is a type of a typical GEP Exam Question that can come out. Technically, this question is in syllabus since it only involves Whole Numbers. However, in practice, this is an extremely tough GEP Exam question for students who have not seen the Worker Question before.

GEP Test Question Sample (Worker Question):

6 men working 8 hours a day can paint a house in 2 days. In how many more days will 4 men, working 3 hours a day at the same rate, complete the same job?

Before you scroll down to check the answer, do give it a try! From personal experience as a tutor, even a 16 year old typical Secondary 4 student cannot solve this question if it is the first time they see it. However, once I explain the solution to them, it is extremely easy and students will get it immediately, even for primary school kids. Someone who has seen these types of questions before can solve it under a minute!

This shows the immense advantage one has if he/she has been exposed to certain types of questions. This is same for the GEP General Ability Test (GAT), a type of “IQ test”, which is basically pattern recognition. If a child has been exposed to books like Match Wits With Mensa: The Complete Quiz Book, words cannot describe the huge advantage he/she has over someone who has not seen a logic pattern puzzle before.

Solution to GEP Sample Question (Worker Question):

There are many types of solutions to this question, but my favorite is using the man-days concept. Man-days is a unit for the amount of work that is needed for something. E.g. If building a house needs 10 man-days, it can be accomplished by either 1 man x 10 days = 10 man-days, or 5 men x 2 days = 10 man-days, etc.

For this question, we will use the unit of man-hours instead.

6x8x2=96 man-hours are needed to paint the entire house.

4 men working 3 hours a day would lead to 12 man-hours a day. Hence 96/12=8 days are needed.

Warning: This is where they trap the careless students! The question asks for how many more days. Hence, the answer is 8-2=6 more days.

Ans: 6 days

Do also check out the Chicken and Rabbit GEP Math Question, which is another type of popular GEP Selection Test and Screening Test question, and can be practiced beforehand as a GEP Mock Test.

 

Xinmin Secondary 2010 Prelim Paper I Q24 Solution (Challenging/Difficult Probability O Level Question)

Just to reblog this earlier post on a really challenging Probability O Level Question.

Also, do check out my other related posts on Probability:

Probability is becoming a really important branch of mathematics. One of the most famous Singaporean mathematicians is Professor Louis Chen Hsiao Yun who has a theorem named after him! (Stein-Chen method of Poisson approximation) Professor Chen researches on Probability.

To begin your journey in Probabilty, Introduction to Probability, 2nd Edition is a good book to start learning from. An intuitive, yet precise introduction to probability theory, stochastic processes, and probabilistic models used in science, engineering, economics, and related fields. You may also wish to refer to our comprehensive list of Recommended Undergraduate Books.

(One of the best books to begin your journey in studying the mysterious topic of Probability)

 

mathtuition88's avatarMathtuition88

A bag A contains 9 black balls, 6 white balls and 3 red balls. A bag B contains 6 black balls, 2 white balls and 4 green balls. Ali takes out 1 ball from each bag randomly. When Ali takes out 1 ball from one bag, he will put it into the other bag and then takes out one ball from that bag. Find the probability that

(a) the ball is black from bag A, followed by white from bag B,
(b) both the balls are white in colour,
(c) the ball is black or white from bag B, followed by red from bag A,
(d) both the balls are of different colours,
(e) both the balls are not black or white in colours.

probability maths tuition

Solution:

(a) $latex displaystylefrac{9}{18}timesfrac{2}{13}=frac{1}{13}$

(b) Probability of white ball from bag A, followed by white ball from bag B=$latex displaystyle=frac{1}{2}timesfrac{6}{18}timesfrac{3}{13}=frac{1}{26}$

Probability of white from B, followed…

View original post 105 more words

GEP Exam Paper / GEP Questions

Firstly, do check out our GEP Recommended Books if you are interested in books that will help boost your chances of entering GEP.

A typical sample GEP Exam Paper Question (Math) is the Chicken and Rabbit Question. This test is highly popular in the GEP Screening / GEP Selection Test, Round 1 or even extremely difficult Round 2.

A sample question would go like this:

A farmer has 36 chickens and rabbits in total.
He counted 124 legs altogether.
How many chickens and how many rabbits are there?

(By the way, this question is generated from my Chicken and Rabbit Question Generator!)

This is a highly typical GEP Exam paper question that may come out in the GEP test.

How do we solve it? One way is the trial and error or Guess and Check method. However, this method may not work for high numbers. What if the farmer had 10000 sheep?

The GEP Exam Paper has limited time, hence, we would need to solve it in an efficient way.

There is one method called the Assumption method, where students can remember the acronym ASSD!

Steps of ASSD to solve GEP Exam Paper “Chicken and Rabbit” Question:

Step 1 (A): Assume) Let’s assume all the 36 animals are chickens.

Then, there would be 36×2=72 legs in total.

Step 2 (S): Subtract) Clearly, 72 legs is too few.

In reality, there are 124-72=52 legs more.

Step 3 (S): Subtract) 4-2=2

Each rabbit has 2 more legs than a chicken.

Step 4 (D): Divide)

The extra 52 legs must be due to the rabbits, and each rabbit contributes 2 more legs.

Hence, there are 52/2=26 rabbits!

There must be 36-26=10 chickens then.

Check

During the GEP Exam Paper, checking is essential to avoid careless mistakes. 26×4+10×2=124, which tallies! Hence, we are right!

To practice more Chicken and Rabbit questions, which is highly likely to come out in the GEP Exam Papers, check out our Chicken and Rabbit Worksheet Generator.

Lastly, do check out our GEP Recommended Books which may be the most useful books on the market (not found in Singapore since most major bookstores like Borders have closed down).

Scientists have proven that IQ can be increased, and hence reading a book like Match Wits With Mensa: The Complete Quiz Book would increase your score in the GEP Exam Paper (Logic) section during the GEP Screening / Selection Test.

Coursera Cryptography I Review

I have just completed the Coursera Cryptography I course by Dan Boneh successfully, and received the statement of accomplishment!

Review of the Course

Difficulty: 4.9/5

This course is really difficult for those with no computer science background. Although there is a section on number theory, most of the sections are new to me as my background is mostly undergraduate mathematics. (Though I did take a course IT1002 (from NUS) called Introduction to Programming, which is mostly on Java Programming.)

Especially the programming exercises are very tough for people with limited programming knowledge! However, note that the programming assignments are entirely optional.

Course Content

This course covers the theory and practice of cryptographic systems. Topics included symmetric encryption, data integrity, public-key encryption, and key exchange. The course emphasized the correct use of these primitives.

Interesting Things about this Course

It is interesting to note how complex the field of cryptography is, and how smart hackers have become. It is possible to do a timing attack where even the time taken to respond to say a login, can be used by hackers to guess your password. Every logical operation in a computer takes time to execute, and the time can differ based on the input; with precise measurements of the time for each operation, an attacker can work backwards to the input. – Wikipedia

Needless to say, as our world becomes increasingly digital, cryptography becomes increasingly important.

I wrote two JavaScript applications to help solve some of the programming challenges in this course:

Sadly, WordPress doesn’t support JavaScript, so I have to write them on my sister blog: http://www.mathtuition88.blogspot.com

If you are interesting in programming, particularly app programming, why not check out this book Learning iOS Game Programming: A Hands-On Guide to Building Your First iPhone Game. You may be the creator of the next “Flappy Bird” which reportedly earned its creator $50,000 a day! Wow!

Read this to be the next Flappy Bird creator! Michael Daley walks you through every step as you build a killer 2D game for the iPhone.

Solution to HP A4 Printer Paper Mysterious Question

A while ago, I posted the HP A4 Paper Mysterious Question which goes like this:

Problem of the Week

Suppose f is a function from positive integers to positive integers satisfying f(1)=1, f(2n)=f(n), and f(2n+1)=f(2n)+1, for all positive integers n.

Find the maximum of f(n) when n is greater than or equal to 1 and less than or equal to 1994.

So far no one seems to have solved the question on the internet yet!

I have given it a try, and will post the solution below!

If you are interested in Math Olympiad, it is a good idea to invest in a good book to learn more tips and tricks about Math Olympiad. One excellent Math Olympiad author is Titu Andreescu, trainer of the USA IMO team. His book 104 Number Theory Problems: From the Training of the USA IMO Team is highly recommended for training specifically on Number Theory Olympiad questions, one of the most arcane and mysterious fields of mathematics. He does write on other Math Olympiad subjects too, like Combinatorics, so do check it out by clicking the link above, and looking at the Amazon suggested books.

Now, to the solution of the Mysterious HP A4 Paper Question:

We will solve the problem in a few steps.

Step 1

First, we will prove that \boxed{f(2^n-1)=n}. We will do this by induction. When n=1, f(2^1-1)=f(1)=1. Suppose f(2^k-1)=k. Then,

\begin{aligned} f(2^{k+1}-1)&=f(2(2^k)-1)\\ &=f(2(2^k-1)+1)\\ &=f(2(2^k-1))+1\\ &=f(2^k-1)+1\\ &=k+1 \end{aligned}

Thus, we have proved that f(2^n-1)=n for all integers n.

Step 2

Next, we will prove a little lemma. Let g(x)=2x+1. We will prove, again by induction, that \boxed{g^n (1)=2^{n+1}-1}. Note that g^n(x) means the composition of the function g with itself n times.

Firstly, for the base case, g^1(1)=2+1=3=2^2-1 is true. Suppose g^k (1)=2^{k+1}-1 is true. Then, g^{k+1}(1)=2(2^{k+1}-1)+1=2^{k+2}-1. Thus, the statement is true.

Step 3

Next, we will prove that if y<2^n-1, then f(y)<n. We will write y=2^{\alpha_1}x_1, where x_1 is odd. We have that x_1<2^{n-\alpha_1}.

\begin{aligned} f(y)&=f(2^{\alpha_1} x_1)\\ &=f(x_1) \end{aligned}

Since x_1 is odd, we have x_1=2k_1+1, where k_1<2^{n-\alpha_1-1}.

Continuing, we have

\begin{aligned} f(x_1)&=f(2k_1+1)\\ &=f(2k_1)+1\\ &=f(k_1)+1 \end{aligned}

We will write k_1=2^{\alpha_2}x_2, where x_2 is odd. We have x_2<2^{n-\alpha_1-\alpha_2-1}.

\begin{aligned} f(k_1)+1&=f(2^{\alpha_2}x_2)+1\\ &=f(x_2)+1 \end{aligned}

where x_2=2k_2+1, and k_2<2^{n-\alpha_1-\alpha_2-2}.

\begin{aligned} f(x_2)+1&=f(2k_2)+1+1\\ &=f(k_2)+2\\ &=\cdots\\ &=f(k_j)+j \end{aligned}

where k_j=1, 1=k_j<2^{n-\alpha_1-\alpha_2-\cdots-\alpha_j-j}.

Case 1: All the \alpha_i are 0, then y=2(\cdots 2(k_j)+1=g^j(1)=2^{j+1}-1. Then, j+1<n, i.e. j<n-1.

Thus, f(y)=f(k_j)+j<1+n-1=n.

Case 2: Not all the \alpha_1 are 0, then, 1=k_j<2^{n-\alpha_1-\alpha_2-\cdots-\alpha_j-j}\leq 2^{n-j-1}. We have 2^0=1<2^{n-j-1}, thus, 0<n-j-1, which means that j<n-1. Thus, f(y)=f(k_j)+j<1+n-1=n.

Step 4 (Conclusion)

Using Step 1, we have f(1023)=f(2^{10}-1)=10, f(2047)=f(2^{11}-1)=11. Using Step 3, we guarantee that if y<2047, then f(y)<11. Thus, the maximum value of f(n) is 10.

Ans: 10

ST Yao丘成桐

Yao Sheng Tong (丘成桐) is the first Chinese (China – HK) who won the Fields Medal, he later also won the Wolf Prize after his PhD-thesis mentor SS. Chern (陈省身)。He is the first Chinese to head Harvard Math Faculty.

tomcircle's avatarMath Online Tom Circle

丘成桐 (ST Yao 1949~) Fields Medal @1982 [33岁] proved Calabi Conjecture

1. 读私立 培正中学, 高中遇 好数学老师. @香港中文大学, 发觉 Math Beauty, ‘豁然开朗’.
2. Best Math student not necessary Mathematician, only sufficient!
3. 一名数学科学家 都应对 文学,哲学 这类 学科有基本的涉猎. 好的数学 使你体验到庄子讲的
“天地与我并生, 万物与我为一” 的境界
4. 成功 = 要有数学热情.
Strategy:
a. 深入思考
b. 在心中或纸上仔细研究
c. Find clues from book, till get answer.
d. 出题目给自己

View original post

庖丁解牛数学方法

tomcircle's avatarMath Online Tom Circle

“庖丁解牛”数学方法
庄子讲庖丁(butcher)解牛有三个功夫階段：
1st Level: 看见一只全牛 (Whole Cow)

2nd Level: 三年后，不见全牛，只见牛的生理结構(Anatomy) ：骨骼，肌肉，筋腱。

3rd Level: 不以目视而是神视，＂与桑林之舞合拍，与经首之会同律。＂达到了”物我”两忘的境界。Intuition.

数学的方法也如此。

1st Level: Whole Math (Primary school to High School)

2nd Level: Component Structure – (Undergraduate Math)：
Macro- structure (Algebra : Group, Ring, Field, Vector Space… );
Micro-structure (Analysis : Calculus, Topology, etc)

3rd Level: 无处不数 Ubiquitous Math – (Graduate Math)
eg. Fermat’s Last Theorem used all Math theories available today to prove.

View original post

Math Duality

Singapore still follows the outdated UK Math pedagogy, using the old term “Advanced Calculus” (高等微积分) for the huge discipline of “Analysis” (分析) — the ‘Micro’ view of Math.

tomcircle's avatarMath Online Tom Circle

Mathematics is roughly divided into 2 categories:

‘Macro’ Math: Algebra

‘Micro’ Math: Analysis (or the outdated name Calculus)

Algebra has been transformed rapidly from 19th century after Galois’s invention of Group Theory, and expanded by David Hilbert and his students E. Noether, Artin, etc in Axiomatic Algebra, takes a very macro view of Mathematical structures in abstract thinking.

Analysis, also after 19th century Cauchy and Wierestrass’s invention of ‘epsilon-delta’ micro view of Calculus, transformed the Newton Calculus into rigourous Math.

The old school of division of Pure and Applied Math is no longer valid. Take for example, the Applied Math used in Google Search Algorithm uses abstract Vector Space of Matrices in Linear Algebra (Pure Math).

View original post

Singaporean’s Plan for the Long Weekend (Aug 7-Aug 10)

As every Singaporean should know by now, August 7 is going to be a public holiday this year, due to SG 50, i.e. Singapore’s 50th anniversary as a nation.

A quick check using the mental calculation of dates (Doomsday Algorithm), we can know that August 8 is Saturday, hence August 7 is a Friday. Thus, August 7 to August 10 is indeed a long weekend!

What are Singaporeans doing during the long weekend? Hint: It has something to do with studying. This is a really funny cartoon by Singaporean cartoonist “Chew on it”

chew on it math

Math and Motivation

Like many human endeavors, Math is one subject that requires motivation to excel.

There is this inspirational story that I found on https://schoolbag.sg/story/from-rock-bottom-to-top-of-the-class

With no interest in studying and thoroughly convinced he will never do well, M Thirukkumaran was on a downward spiral in secondary school and was almost retained in Secondary One and Two.

Fast forward nearly 10 years, Thiru, 23, is now studying Business Analytics at the National University of Singapore (NUS) under NEA and PUB’s National Environment and Water (NEW) Scholarship.

What turned Thiru a full 180 degrees around? It was the first taste of success, through the efforts of a teacher, Mr Tan Thiam Boon.

In Secondary Three at Monfort Secondary School, Thiru felt that he had hit rock bottom. During a rudimentary algebra test, he scored one mark out of a total score of 50. Instead of shaking his head in disbelief and despair, his mathematics teacher, Mr Tan, went out of his way to coach Thiru after school. But his efforts were in vain.

“Mentally, I had already accepted that I would not be able to do it,” said Thiru.

Undeterred, Mr Tan encouraged Thiru to pay full attention for the next topic, Trigonometry. Dejected and with little left to lose, Thiru came early to sit at the front of the class and followed the lesson attentively. About a week later, Mr Tan distributed the results of a test starting from the lowest to the highest scorers.

Thiru recalled the incident with great clarity.

“Naturally, I had expected my name to be the first to be called. But it was not and I was afraid my paper was lost. But instead, it was the last name called! I still remember the smile on Mr Tan’s face, and the confusion on everyone else’s that day. I sat dumbfounded. Mr Tan had managed to do what nobody else had. In one fell swoop, he eliminated the negative labels that society and I had placed on myself, and reinstated my confidence.  More importantly, he showed me that I was capable, that I wasn’t a “delinquent” or a failure. It was akin to recovering from blindness.”

That initial spark ignited a passion, drive and desire to test his potential and accomplish what he did not even dare to imagine before. Thiru topped his class in mathematics and did well at the N-level and O-level examinations. At Tampines Junior College, his teachers gave him the opportunity to take H2 physics and mathematics, even though he did not take the prescribed secondary school subjects. Thiru’s hard work and determination paid off, often in the top 5% of the cohort for the regular examinations, and emerging as one of the college’s top students at the A-level examinations.

As a tutor, I know this is not easy. I have coached students from Fail to A grade. However,  1/50 is a really bad fail, and to achieve A in a matter of months requires extreme effort short of a miracle. For Thiru to overcome his challenges and extremely weak Math foundation to achieve his amazing accomplishments, required a motivational figure in the form of his Math teacher.

Such motivational teachers are rare, and I am glad that Thiru has found his mentor.

Helen Exley — ‘Books can be dangerous. The best ones should be labeled This could change your life.’ Books are another source of motivation. For those who have not yet found their motivational figure, do not wait as true motivational teachers are few and far between. To encounter one like Thiru requires luck and good fortune. However, good motivational books are there and available if you look for it. I have compiled a list of Motivational Books for the Student, which is available by clicking on the link.

In Math, you must always believe that you can solve the answer, in order to solve it. Just like Thiru, if you believe in yourself, you can do it! A nice book to read about Math and Motivation is Math Doesn’t Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail. Ideal for teenagers, this book features an award winning actress who struggled with math, but later overcame her fears to be one of the top in UCLA Math faculty. Even Terence Tao praised her.

Book by Truly Gifted Kid (GEP Book)

This is the book written by a truly gifted kid, the book of all gifted books. If you are looking for GEP books, this is the GEP book to rule all GEP books, written by the gifted kid himself.

The book is titled: We Can Do

I was reading the online news, and discovered this story about Moshe Kai Cavalin.

The one thing 14-year-old Moshe Kai Cavalin dislikes is being called a genius.

All he did, after all, was enroll in college at age 8 and earn his first of two Associate of Arts degrees from East Los Angeles Community College in 2009 at age 11, graduating with a perfect 4.0 grade point average.

Now, at 14, he’s poised to graduate from UCLA this year. He’s also just published an English edition of his first book, “We Can Do.”

Not only is he focused on academics (he researches on Wormhole Theory), he is also proficient in Chinese martial arts, scuba diving, and also writing books. He is also a math major!

Personally, I think the title “We Can Do” is a clever word play on Jeet Kune Do, a style of martial arts invented by Bruce Lee!

If you want to read the Chinese version, it is also available: （Go to College At 8-year-old!） 八歲進大學

More books on giftedness, GEP at: GEP Books Compendium

Also, thanks to one of my readers who bought this book via my website: The Stanford Mathematics Problem Book: With Hints and Solutions (Dover Books on Mathematics)
This volume features a complete set of problems, hints, and solutions based on Stanford University’s well-known competitive examination in mathematics.

Video on Moshe Kai Cavalin, of half Jewish, half Chinese descent:

Indian bride walks out of wedding when groom fails math test

Source: https://sg.news.yahoo.com/groom-fails-math-test-indian-bride-walks-wedding-065433753.html

Here’s one more reason to learn math!

NEW DELHI (AP) — An Indian bride walked out of her wedding ceremony after the groom failed to solve a simple math problem, police said Friday.

The bride tested the groom on his math skills and when he got the sum wrong, she walked out.

The question she asked: How much is 15 plus six?

His reply: 17.

The news may seem like a joke, but on a more serious note, the usage of calculators in Primary 5 & Primary 6 has led to a drop in the mental arithmetic standards of children in Singapore! As a tutor, I have clearly observed the difference before and after the calculator usage was introduced. Many a times, students need a calculator to calculate what is 18+15, for example. Also, 8 times 8 (mental calculation) would pose a challenge nowadays to some students ages 9-12, whereas in the past students would know it is 64 in less than a second.

What is happening is that students are getting a bit too reliant on the calculator, and hence their human calculator (a.k.a brain) has lack of training in this aspect. How to remedy it is to practice and train in more multiplication questions.

 

 

 

Happy Pi Day!

Tomorrow (March 14) is an important day for math lovers! It is the famous Pi Day! Pi is approximately 3.14 which corresponds to the date March 14.

Check out our post last year on Pi Day:

Here are some other previous posts on Pi:

If you are looking for a Pi Day T Shirt, Pi Day Once in a Century March 14, 2015 T-Shirt Large Black is definitely what you are looking for. By the way, this year’s Pi Day is a league above the other Pi Days, as you can see from the image below. (click the image for a larger picture) This year’s Pi Day date culminates in the lengthy decimal expansion of Pi: 3.141592653! The year 2015 (i.e this year) is needed for the “15” in the decimal.

pi day t shirt
Click to view larger zoomed in picture on Amazon

 

 

6 Common Misconceptions About Mathematics Degrees

Some interesting info on studying mathematics in university.

ACEI Global's avatarACEI-Global

March 12th, 2015

[Note: This blog, written by Samantha Woodcock, was originally posted on http://www.topuniversities.com, and reposted here on Academic Exchange by permission from the author.]

math

Considering studying mathematics at university but not sure you fit the right mold? Think it’ll be too difficult, too nerdy, or won’t provide enough career options? Get ready to re-think your idea of the “typical” math student, and what’s involved in a mathematics degree…

1.  Maths students are giant geeks.

mathstudent

Now there are the students out there that would remind you of the Sheldon Coopers of the world, but for the most part maths students are just normal people who have a passion for numbers. Not all of them wear glasses; they all don’t carry a calculator everywhere and they also don’t insist on wearing white shirts and plaid. Mathematics is also easy to combine with another subject, including art, all sciences…

View original post 497 more words

Buy Math Notes with Exam Papers

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

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

Currently, we have 4 products:

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

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

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

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

 

 

20% Discount on the following Math Resources!

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

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

10% Discount Code: ilovemath

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

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

Do check out the Math Resources for Sale page!

 

GR0568 Q2 Solution (Tangent to Graph)

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

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

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

Solution:

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

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

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

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

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

Answer: (E)

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

GR0568 GRE Math Test Solutions

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

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

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

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

Solution:

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

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

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

 

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

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

Welcome message from the Probability team:

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

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

Best wishes,
The Probability Course Team

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

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

Cédric Villani

 

 

The Useless Number

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

Also, check out these related posts on complex numbers:

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