Source: https://class.coursera.org/crypto-013
This free online course on the interesting subject of Cryptography is starting next week, January 5 2015. Do give it a try if you are interested in the subject of Cryptography!
The class duration is 6 weeks, and will cover topics like symmetric key cryptography and public-key cryptography.
The only prerequisite is a bit of Discrete Probability: http://en.wikibooks.org/wiki/High_School_Mathematics_Extensions/Discrete_Probability
The course instructor is Dan Boneh of Stanford University. Hope you find this course interesting!
Wednesday, 31 December 2014
Tuesday, 30 December 2014
The Significance of 8888: MH17+MH370+QZ8501
According to Yahoo, the missing plane QZ8501 may be found at the bottom of the Java Sea. It is not 100% confirmed though. We sincerely hope there are some survivors who may have swum to a nearby island.
“I am absolutely devastated," said AirAsia Group CEO Tony Fernandes. "This is a very difficult moment for all of us at AirAsia as we await further developments of the search and rescue operations but our first priority now is the wellbeing of the family members of those onboard QZ8501."
“I am absolutely devastated," said AirAsia Group CEO Tony Fernandes. "This is a very difficult moment for all of us at AirAsia as we await further developments of the search and rescue operations but our first priority now is the wellbeing of the family members of those onboard QZ8501."
The Significance of 8888
This is a continuation of our earlier analysis on the probability of 3 random numbers (in the range 1-9999) adding up to 8888. (See http://mathtuition88.blogspot.sg/2014/12/math-of-qz8501-sum-of-3-numbers-that.html)
The probability of 3 random numbers adding up to 8888 by chance is merely 0.0039497%, or around 1 in 25,000. This is pretty low, considering it is easier to win the top lottery prize of 4D (around 1 in 10,000 chance).
Other events linked to "8888" or "8" in general
- The "8888 Uprising"
The 8888 Uprising is a series of riots in Myanmar, that occured on 8 August 1988. During this uprising, Aung San Suu Kyi emerged as a national hero.
- Sichuan earthquake (See http://wenda.tianya.cn/question/234aa50da04ba8d4)
The Sichuan earthquake occurred in 2008 May 12 (12/5). 1+2+5=8
It is also known as the Wenchuan earthquake, named after Wenchuan County.
- Blizzard (Snowstorm) in China (See http://baike.baidu.com/view/338422.htm)
In January 25, 2008, a massive snowstorm affected China in cities like Wuhan, Changsha, Nanjing, and many others. The costs to the economy amounted to more than 100 billion yuan. (See also http://en.wikipedia.org/wiki/2008_Chinese_winter_storms)
1+2+5=8
- Tibetan Riots (See http://en.wikipedia.org/wiki/2008_Lhasa_violence)
In March 14, 2008, there was a serious riot in Tibet, where Tibetans targeted Han Chinese, and their businesses, including setting fire and looting.
3+1+4=8
More details (in Chinese) can be found at this website: http://www.renminbao.com/rmb/articles/2008/6/1/47781p.html
Readers should note that it is easy to add up to 8, and hence the news should be taken with a pinch of salt. But as we calculated earlier, adding up to 8888 is not a common event.
Annual Report 2014 for my blog Mathtuition88.com
Source: http://mathtuition88.com/2014/annual-report/
The report for my blog at Mathtuition88.com is out! See: http://mathtuition88.com/2014/annual-report/
WordPress creates a nice annual report, detailing crucial statistics about my blog. My blog received up to 200,000 views in 2014! Hoping to hit a million views soon. :P
Predictably, the most popular post turns out to be Free Exam Papers. Shows how useful doing past year papers is!
Sunday seems to be the day which I post the most. Most of the Sundays, I only teach one student after church, hence I have more time to post.
The O Level Formula List post turns out to be the second most popular post in 2014, beating the post about JC Cut Off Points. 3 of my most popular posts were actually written before 2014! Hence, the report claims that those posts have "staying power", and I should consider writing more about them!
It has been a wonderful year and blogging, originally a means to advertise my Maths tuition service, has turned into a hobby for me. I am now letting my WordPress blog self-run on its own for a moment, while building up my Blogger website, hoping that my Adsense application will be finally approved! My final goal is to be active on WordPress, Blogger, and YouTube, publicizing Mathematics!
Wish all viewers a happy 2015 year of the Goat.
The report for my blog at Mathtuition88.com is out! See: http://mathtuition88.com/2014/annual-report/
WordPress creates a nice annual report, detailing crucial statistics about my blog. My blog received up to 200,000 views in 2014! Hoping to hit a million views soon. :P
Predictably, the most popular post turns out to be Free Exam Papers. Shows how useful doing past year papers is!
Sunday seems to be the day which I post the most. Most of the Sundays, I only teach one student after church, hence I have more time to post.
The O Level Formula List post turns out to be the second most popular post in 2014, beating the post about JC Cut Off Points. 3 of my most popular posts were actually written before 2014! Hence, the report claims that those posts have "staying power", and I should consider writing more about them!
It has been a wonderful year and blogging, originally a means to advertise my Maths tuition service, has turned into a hobby for me. I am now letting my WordPress blog self-run on its own for a moment, while building up my Blogger website, hoping that my Adsense application will be finally approved! My final goal is to be active on WordPress, Blogger, and YouTube, publicizing Mathematics!
Wish all viewers a happy 2015 year of the Goat.
Monday, 29 December 2014
Math Comics
Some of my favorite Math Comics include Spiked Math.
Latest Spiked Math comic (as of 30 Dec 2014):
Their comics are fun, humorous, and include Math!
Latest Spiked Math comic (as of 30 Dec 2014):
Their comics are fun, humorous, and include Math!
More Math Comics
A nice comic about pi(e)!
Includes some classic comics from the famous Peanuts series, featuring Charlie Brown, Snoopy, and friends! There are many comics on the theme of Mathematics there!
Shows how 3D Cartoons for instance those at Pixar are made. Includes a sample video about an old man playing chess with himself!
Includes some fun and quirky Math cartoons, explaining serious Math concepts!
Count Number of Each Letter in a Paragraph
This is a Javascript application that I wrote a long time ago. It can help to count which are the most common letters in any language，even Chinese!
For instance, try typing "四是四，十是十，十四是十四，四十是四十。 莫把四字说成十，休将十字说成四。 若要分清四十和十四，经常练说十和四。" into the textbox, and press "Generate Report". You will see that the word "四" is being mentioned 11 times!
For instance, try typing "四是四，十是十，十四是十四，四十是四十。 莫把四字说成十，休将十字说成四。 若要分清四十和十四，经常练说十和四。" into the textbox, and press "Generate Report". You will see that the word "四" is being mentioned 11 times!
Enter text here:
Singapore Math Questions
Singapore Math Questions
The following are a list of typical questions from the Singapore Math syllabus. Most are taken from my blog at mathtuition88.com.
Singapore Math (Elementary School)
A list of questions on angles, a popular Singapore Math question for grade 6.
An interesting question on circles and fraction!
Need some practice on Chicken and Rabbit questions? Try out these questions generated by a Chicken and Rabbit Question generator.
Singapore Math (High School)
Very useful helpsheet for Singapore Math (High School). Comes in two versions, the more basic Elementary Maths, and the more advance Additional Maths.
A number pattern question that may prove to be quite puzzling...
How to factorize $a^3-b^3$? Comes with a YouTube video!
Check out how to solve this challenging probability question on choosing balls from a bag.
Frequently make careless mistakes for your exams? This article may help you out.
Check out this very challenging logarithm question designed to challenge high school students.
Sunday, 28 December 2014
Math of QZ8501 (Sum of 3 numbers that add up to 8888)
Let's hope the missing plane QZ8501 can be found soon. According to CNN, the plane is most likely at the bottom of the sea. Hopefully there can be some survivors, and our prayers are with them.
Something very mysterious about the recent flight disappearances is that their numbers add up to "8888", a very significant number in Chinese culture. (see our earlier post at: http://mathtuition88.blogspot.sg/2014/12/missing-airasia-flight-qz8501.html)
MH17, MH370, QZ8501
17+370+8501=8888
(total ways) 970299
(ways of adding up to 88) 3741
(probability) 0.3855512579112212
This indeed tallies with our calculations since $$\frac{87 \choose 2}{99^3}]\times 100\%\approx 0.38555$$.
(see WolframAlpha calculation)
Something very mysterious about the recent flight disappearances is that their numbers add up to "8888", a very significant number in Chinese culture. (see our earlier post at: http://mathtuition88.blogspot.sg/2014/12/missing-airasia-flight-qz8501.html)
MH17, MH370, QZ8501
17+370+8501=8888
What are the chances of 3 numbers (taken from the range 1-9999) adding up to 8888?
We will calculate the probability of 3 numbers (between 1 to 9999, since most aeroplane flight numbers are up to four digits) adding up to 8888.
We will first do an analytic theoretical calculation, and then follow up with a numerical simulation to double confirm our calculations.
Theoretical Calculation
Firstly, there are 9999 numbers from 1 to 9999. Hence, in total, there are $9999^3=999700029999$ ways of selecting 3 numbers from the range 1-9999. Repeats are allowed, for example 17, 17, 17, since they could be from different airlines e.g. MH17, QZ17, SQ17, just to illustrate the point.
Next, we need to consider how many positive integer solutions there are to $x_1+x_2+x_3=8888$. One of them would be 17, 370, 8501; but there are many more like 1, 1, 8886.
The technique to solve this type of question is to use a Stars and bars (combinatorics) method.
We can write 8888 stars, and to separate them into 3 "bins" we need 2 bars. Hence, out of 8887 possible gaps, we need to choose two gaps to put the bars. Hence, the total number of ways is ${8887 \choose 2}=39484941$.
Hence, the final probability, the chance of 3 random numbers adding up to 8888 is $$\frac{39484941}{999700029999}=0.0039497\%$$, or around 1 in 25,000.
(WolframAlpha Calculation)
For comparison, this is rarer than winning the top prize in 4D (a popular guess the correct 4 digit number lottery in Singapore), which has a probability of 0.01%, or 1 in 10,000.
It is more common than winning the Jackpot in Lottery, which has a probability of 1 in 14 million.
The technique to solve this type of question is to use a Stars and bars (combinatorics) method.
We can write 8888 stars, and to separate them into 3 "bins" we need 2 bars. Hence, out of 8887 possible gaps, we need to choose two gaps to put the bars. Hence, the total number of ways is ${8887 \choose 2}=39484941$.
Hence, the final probability, the chance of 3 random numbers adding up to 8888 is $$\frac{39484941}{999700029999}=0.0039497\%$$, or around 1 in 25,000.
(WolframAlpha Calculation)
For comparison, this is rarer than winning the top prize in 4D (a popular guess the correct 4 digit number lottery in Singapore), which has a probability of 0.01%, or 1 in 10,000.
It is more common than winning the Jackpot in Lottery, which has a probability of 1 in 14 million.
Computer Verification
We write a simple Python code to verify our calculations. (We verify a simpler case: probability of 3 numbers (range 1-99) adding up to 88.
total=0
counter=0
for x in range(1,100):
for y in range (1,100):
for z in range (1,100):
total+=1
if x+y+z==88:
counter+=1
print (total)
print (counter)
print (counter/total*100.0) (total ways) 970299
(ways of adding up to 88) 3741
(probability) 0.3855512579112212
This indeed tallies with our calculations since $$\frac{87 \choose 2}{99^3}]\times 100\%\approx 0.38555$$.
(see WolframAlpha calculation)
Missing AirAsia flight QZ8501
My sincerest condolences to all the passengers and families of those taking QZ8501. It is really a tragedy, to have so many air disasters in a short time. As I also travel yearly, I can empathize with all the passengers, the crew, and finally the family and friends of those who took the flight. God bless them, and may they rest in peace.
Eerie Coincidence of Missing Flight Numbers (Math)
Source: Hardwarezone
Someone from Hardwarezone did a calculation of the flight numbers of the missing flights recently (MH17 + MH370 + QZ8501)
17+370+8501=8888 !!
For Westerners who may not know the significance of 8888, it is one of the most auspicious 4 dight numbers for Chinese, because "8" rhymes with 发 ("fa", "huat", which means prosper). Any car license plate "8888" must have cost a bomb for the owner.
But why does the flight numbers add up to "8888", such an eerie coincidence. Nobody knows...
Math equation could help find missing Malaysian plane
Math, specifically Bayesian Search Theory, could help find the missing Malaysian plane. Hopefully it can be applied with success like in the case of Air France Flight 447.
Saturday, 27 December 2014
IB HL Math
IB HL Math Resources
Here are some useful websites on IB HL Maths syllabus:
This site by ACS(I) offers an introductory guide to the syllabus of the IB HL Maths course.
This wiki page describes a summary of IB SL and HL Maths
A recent (2014) detailed syllabus of the IB HL Math
A very brief and concise summary of what the IB HL Math is about.
The official site of the IB describing the IB HL Math
Hope it helps!
New Job Opening for Mathematician
Source: Spiked Math
North Pole: Career Opportunities (Mathematician)
Qualifications:
- Knowledge and ability to implement heuristics solutions of a dynamic travelling salesman problem. (subtle math joke here: Travelling Salesman Problem is a problem in Graph Theory)
- A cheerful demeanor and ability to excel in a team oriented environment (need to work well with reindeer)
- Must be able to meet strict deadlines (deliver presents before Christmas)
- Working knowledge of regulatory compliance
- Trustworthy and be able to work with sensitive data
- Point ears is a plus (LOL)
Do you get the joke? Any idea who is the employer?? :P
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