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!
Wednesday, May 26, 2010
Monday, May 17, 2010
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:
In 'win-lose' terminology, the table looks like this:
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).
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).
Tuesday, May 11, 2010
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.
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.
Monday, May 3, 2010
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!
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!
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