Distance Learning in Mathematics

Back in 2003, I somehow had the desire of taking some distance learning in Mathematics. The idea came about 2 years ago when I was helping my second daughter in her study of 4-unit Mathematics as preparation of the HSC examination (HSC is the joint examination for secondary school students in Australia and is the credential awarded for successful completion of high school study and as basis for entrance to universities). To facilitate the assistance to my daughter, I had to review and refresh my knowledge of my high school mathematics. And in so doing, I came to have rekindled my interest in this subject which was my favourite during my early school days.
I searched the internet for distance learning in university level Mathematics. To my surprise, despite there were lots and lots of distance learning courses everywhere, there were hardly anything in Mathematics. Mathematics is quite a wonderful thing. Everybody learns Mathematics, but few study it. Mathematics is compulsory for everyone in School, but only a handful take it in College. There seemed to be no market for higher level Mathematics. So I searched the universities one by one. Finally I saw in the website of Stanford University, California that they had a program called EPGY (Education Program for Gifted Youths) in which they offered university level Mathematics courses to talented high school students in the form of distance learning. I then wrote to Stanford for possibility of enrollment. I said frankly that I was not sure whether I was gifted, but definitely I was not a youth given my age. Stanford declined insisting their program was aimed for talented high school students only. I expressed that I had gone through the whole world (electronically) and was only able to find this suitable program in Stanford, and that I was very keen to pursue knowledge at this level. After several exchanges of emails, Stanford advised that they could offer the program to teachers of Mathematics. So I suddenly became a teacher and was accepted.
Thence I undertook the program part-time from 2003 to 2006 while I was still working with Qantas. I completed subjects including:

. Multivariable Differential Calculus
. Multivariable Integral Calculus
. Ordinary Differential Equations
. Partial Differential Equations
. Real Analysis
. Complex Analysis
. Logic
. Number Theory
. Linear Algebra
. Modern Algebra

Despite the hard work (it was particularly hard for me being away from school so long), the experience was indeed very enjoyable and satisfying. Although the materials covered were quite involved, some of them are still regarded as 'Introduction' and 'Elementary'. Really there are still so much more lying ahead!

Prisoner's Dilemma

The police had been watching two suspects of bank robbery for some time but they didn't have sufficient evidence for a conviction. One day, these two guys were caught stealing packs of bubble gum in a supermarket. The police put them into separate rooms, visited each of them and offered the same deal: If one testifies (defects from the other) for the prosecution against the other and the other remains silent, the betrayer goes free and the silent suspect receives the full 10-year sentence for bank robbery. If each betrays the other, each receives a 5-year sentence for bank robbery. If both remain silent, both suspects will be sentenced to only a 1-month jail for theft in supermarket. Each suspect was assured that the other would not know about the betrayal before the end of the investigation and each was told that the other was also offered the same deal. Thus, each suspect was facing a dilemma of choosing either to co-operate with the police (betray the other) or not to co-operate with the police (remain silent).
How would the suspect act?
--------------------------------------------------------------------------------
The possible outcomes (pay-off) can be summarized diagrammatically as follows:

	B remains silent	B betrays
A remains silent	A: 1 month B: 1 month	A: 10 years B: goes free
A betrays	A: goes free B: 10 years	A: 5 years B: 5 years

In 'win-lose' terminology, the table looks like this:

	B remains silent	B betrays
A remains silent	win-win	lose much-win much
A betrays	win much-lose much	lose-lose

Clearly from the diagrams above, the best result (for BOTH suspects) could be achieved IF both co-operated with each other and not with the police by remaining silent. Then each would only be sentenced to a 1-month jail for theft. However, since they were shut up separately, they would not be able to negotiate with each other for a co-operation, and they could only guess what the outcomes would be for different scenarios. Without loss of generality, if suspect A remained silent, he had 50% chance for 1-month jail and 50% chance for 10-year jail. His average pay-off was 5 years and a half month. If A betrayed, he had 50% chance to go free and 50% chance for 5-year jail. His average pay-off was 2 and a half years. A might think that, regardless what B chose, he would always receive a higher pay-off (lesser sentence) by betraying. A could actually say, "No matter what B does, I personally am better off betraying than remaining silent. Therefore, for my own sake, I should betray." All things being equal, suspect B would act similarly. Then they both betrayed each other, and both actually got a lesser pay-off (5 years) than they would get by remaining silent (1 month).

This classical prisoner's dilemma illustrates the different strategies that the player (suspect) would take in the game with different perspectives. If the player could look at the broad picture (which only the police could but the suspects could not), he would opt for remaining silent to achieve the best result. If the player looked at the game only from his own perspective (which the suspects were constrained to do), the strategy to remain silent is clearly dominated by that to betray. So the only possible equilibrium for the game is for all players to betray. No matter what the other player does, one player will always gain a greater benefit by playing betrayal. Since in any situation, playing betrayal is more beneficial than playing remaining silent, all rational players will betray. It also shows how a win-win situation (for the suspects) can be turned into a lose-lose situation (as exactly what the police wanted).

Help! Degradation in System Performance

I read this story from one of my friends, and I relay here for sharing in this blog.

A woman writes to the IT Technical Support.
Dear Tech Support,
Last year I upgraded from Boyfriend 5.0 to Husband 1.0, and I noticed a distinct slowdown in the overall system performance, particularly in the flower and jewellery applications, which operated flawlessly under Boyfriend 5.0.
In addition, Husband 1.0 uninstalled many other valuable programs such as Romance 9.5 and Personal Attention 6.5, and then installed undesirable programs such as News 5.0, Money 3.0 and Golf 4.1.
Conversation 8.0 no longer runs, and House Cleaning 2.6 simply crashes the system.
Please note that I have tried running Nagging 5.3 to fix these problems, but to no avail.
What can I do?
SIGNED,
-----------------------------------------------------------------------------
Reply

Dear Madam,
First, keep in mind, Boyfriend 5.0 is an Entertainment Package, while Husband 1.0 is an Operating System.
Please enter command: ithoughtyoulovedme.html and try to download Tears 6.2 and do not forget to install Guilt 3.0 update.
If that application works as designed, Husband 1.0 should then automatically run the applications Jewellery 2.0 and Flower3.5.
However, remember, overuse of the above applications can cause Husband 1.0 to default to Silence 2.5 or Beer 6.1.
Please note that Beer 6.1 is a very bad program that will download the Snoring Loudly Beta.
Whatever you do, DO NOT under any circumstances install Mother-In-Law 1.0 (it runs a virus in the background that will eventually seize control of all your system resources.).
In addition, please do not attempt to reinstall the Boyfriend 5.0 program. These are unsupported applications and will crash with Husband 1.0.
In summary, Husband 1.0 is a great program, but it does have limited memory and cannot learn new applications quickly.
You might consider buying additional software to improve memory and performance. We recommend: Cooking 3.0 and Hot Look 7.7.
Good luck Madam.
IT SUPPORT DESK.

Why I Blog

People asked me why I wrote these blogs.

Firstly, as mentioned in my first blog (My New Blog on 10/10/09), I was trying to learn to use the contemporary internet tools like Facebook, Blogging etc with my son in order to catch up with the latest technology, despite I was once a 36-year IT professional. As time went along, I just got into the practice of writing, and came to enjoy writing in its own right.
Secondly, as people knows me, I'm a man of few words. I don't like to talk much as I'm not good in talking. I have difficulty communicating with machines (witness my blog - Voice Recognition System on 11/10/09) as well as communicating with humans (witness my blog - Different Wave-lengths on 2/12/09). But I can do much better in writing than in talking (witness all my blogs!). Given in my retirement now, I believe I could have the time to communicate more with everyone, and communicate more effectively using these spaces.
Lastly, but not the least, I think life is beautiful (if we look at the bright side). There are always interesting and funny stories either we heard or read, or we came across in our everyday lives. We'd feel happier ourselves by sharing these happiness with people around us. If we take time to look more closely, we may even be able to pick up some good advices or lessons useful for everyone. I call these my StoryBlogs. I hope they would provide opportunities for having some fun, and occasionally (hopefully) some good advices to my readers.

Happy blogging!

First Encounter of 3-D TV

Samsung launched the new 3-D TV in Australia in April, 2010. We went to Harvey Norman in Gordon Centre on Monday to view the demonstration. Harvey Norman is now offering a promotional package including a 46" LED High Definition 3-D TV, a 3-D Blu-Ray player and 2 pairs of 3-D glasses at the price of $3699 Australian dollars. This set was being displayed at the site, and we viewed a demonstration of a soccer match and formula car racing with these equipment.
With the 3-D glasses on, the colours on the screen were bright and beautiful. The images were sharp and clear, with objects popping out in front of the eyes as real. The feelings were similar to those as experienced with 3-D movies, but with much more comfort to view casually by yourself. It was really amazing, a bit pricey at this stage though.
After about 10 minutes of viewing, I felt dizzy and had to leave the demonstration. I walked wobbly down the escalator and had to sit on a bench in front of Woolworths to rest for a while to recover. We subsequently canceled our plan for afternoon tea in Chatswood as result.

That was my first experience (and impression) of the 3-D TV. Gosh!

Commonly Seen Good Chinese Couplets

--------------------------------------------------------------------------------

三十功名塵與土
八千里路雲和月

--------------------------------------------------------------------------------

落霞與孤霧齊飛
秋水共長天一色

--------------------------------------------------------------------------------

春蠶到死絲方盡
蠟炬成灰淚始乾

--------------------------------------------------------------------------------

慈母手中線
遊子身上衣

--------------------------------------------------------------------------------

福如東海
壽比南山

--------------------------------------------------------------------------------

福無重至
禍不單行

--------------------------------------------------------------------------------

福無重至今天至
禍不單行昨日行

--------------------------------------------------------------------------------

Recent Life in Retirement

People asked me how I was doing in retirement lately.
Well. Apart from the daily chores like taking my son to school, picking him up from school and helping him with school activities and homework etc, I recently enjoyed quite a bit with poetry.

閒來吟詩作對, 感懷身世, 不亦樂乎!
正所謂:

器官皆下垂
唯有血壓高

三更不睡何時了
夜尿知多少

白髮 mung 不盡
春風吹又生

心臟血壓藥
粒粒皆辛苦

高纖麵包淡如水
餓看雪糕紅豆冰

How to Become Happier

We cannot always be happy,
but
we can always be happier.

Like sunshine and rain, it is natural that we have ups and downs in our lives. We all have happy and unhappy moments. While we cannot always be happy, we can always work to make ourselves becoming happier.
Here are some ways to help doing so:

1. Keep healthy. Happiness starts with good health.
2. Care and love the people around you, and make them happy.
3. Greet with a smile from the bottom of your heart. You will receive the same in return.
4. Look for interesting and funny stories, and share with everyone.
5. Pursue a couple of new interests, but don't force into becoming new routines.
6. Remember there is always a bright side of everything.
7. Forget the unhappy experiences. Forgive those who made you unhappy.
8. Devote to the work you love, but don't become a slave of it.
9. Don't be overcritical in life. Appreciate the good fortune when in good fortune.
10. Accept occasional bad encounters. Release unhappy feelings with peaceful means.
11. Don't compare, don't bother.
12. Enjoy life, and don't waste time on unnecessary worries.
13. Make wishes which are easy to come true.
14. Recall your favorite things.
15. Grasp instantaneous inspirations. Make good use of them and don't let go easily.
16. Have a cup of tea with a few good friends. Chat freely with whatever comes to mind.
17. Take a vacation with people who can make you happy.
18. Watch a comedy and have a big laugh.
19. Give yourself a present.
20. Give your beloved one a surprise.

Wish you happier!

The Three Words

The easiest words - A B C
When we feel the thing is easy, we say "It's as easy as A B C".

The most beautiful sounds - Do Re Me
You are probably already aware if you have seen the movie 'The Sound of Music'.

The basic foundation of everything - One Two Three
Numbers are the building blocks of Mathematics. Mathematics is the mother of all sciences. Science is the mother of all inventions. Invention produces everything we have today.

The first words when meeting a friend - How Are You
This is the most common, simplest and yet warm and polite greeting when meeting friends whom you know or not.

The most friendly words of appreciation - Thank You Mate
This is a bit Aussie, but it is the most friendly appreciation expression here down under.

The easiest way to get away doing something - I Don't Know
Don't use this too much. Try to be more positive and helpful next time.

The most difficult words to say - I Love You
Usually things are easier said than done. For this, it's easier done than said. We may be doing this already to people around us. But to most, it is difficult to say the words out from the mouth.

The mostly heard words everyday around us - O My God
We hear these words everywhere, at any time and almost in every occasions. We hear them when people are overjoyed, happy, surprised, shocked, frightened, sad, distressed, depressed, hurt, angry, furious, disappointed, annoyed, regretful, ......... , you name it. True, God is everywhere!

The Two Swallows

This is a translation of the Chinese poem - 'Swallows' (燕詩) from Po Chu-i (白居易) , (772 - 846) :

Under the beam live two swallows,
a happy, joyous and blissful couple.
Together a love nest that they build,
and give birth to four sweet little fellows.
Days and nights the four babies grow,
chirping to beg for food to swallow.
Worms are hard to catch and find,
but young mouths seem never satisfied.
Though torn and worn the bodies are,
willing and capable still in parent's minds.
Despite dozen times flying to and fro,
yet fear kids in nest still with hunger and in trouble.
So tirelessly they work, and work, and work,
and unknowingly a month's already come and go.
The children slowly get taller and stronger,
while thinner and weaker becomes the couple.
Muttering to teach the kids to speak,
the two brush their young feathers each by each.
Once the wings get into full strengths,
the two lead them flying in court bit by bit.
Now freely they fly higher and farther,
without looking back to their father and mother.
With the wind they're finally gone,
scattering everywhere and everywhere.
The couple shouts loud and hard to the skies,
calling each by their names but no one replies.
Nothing can they do but back to their empty nest,
sobbing into the whole night in sorrow and in tears.
Birdie. Birdie. Don't you cry.
You should reflect and come to realize.
When once you were kids, you did fly,
leaving parents behind with their broken minds.
What your parents saw the other day,
was exactly and truly what you are seeing in front of your eyes.

To all the children of the world!