Wednesday, July 15, 2009
Greatness
Tuesday, July 7, 2009
Effectiveness

Tuesday, June 30, 2009
Stay Hungry, Stay Foolish
inspirational-doses.blogspot.com
I hope that you will enjoy the reading and video.
Saturday, August 4, 2007
This Cannot Be It
This cannot be it. Yet it is.For many people, the year ends on the 31st of December. For me, the year ends when a new one begins. For many people, their senior years will seem to be the most significant of their lives up to that point. For me, I just felt like I already had the most significant year of my life up to this point. My junior year was full of ups and downs, and most definitely filled with lots of character building experiences. The first semester of junior year seemed to last longer than all other semesters because of a very special vertically challenged, yet horizontally inclined woman who tried to teach me Statistical Modelling. Plus, I was suffering (I like to think that it was induced by this special woman) from what one of my other professors referred to as "senioritis".
Senioritis: Senioritis is an imaginary syndrome attributed to students nearing the end of high school and college in the United States and Canada. Its symptoms can include laziness, procrastination, apathy toward schoolwork, and truancy.Well, just to clarify, I was most certainly not truant, and definitely not apathetic towards school work. But I was lazy, and I procrastinated. I felt like I needed to get out of college, and do something more practical. But after the long Fall semester ended, I had the great fortune of being able to study abroad in Melbourne. That would probably be the best time of my life, with almost no problems and stress, and also filled with what I reluctantly claim to be, happiness.
However, towards the end of this year, I suffered (not sure if this is the right term, but I will use the word in accordance to what normal people would feel if they had the similar experience) a pretty significant setback. I managed (somehow) to fail my Financial Mathematics final exam which meant that this was my first fail in the history of my life. I am sure many of you feel sorry for me, even those of you who don't know me that well. The trouble with this is, I may have been disappointed for a short while, but for some reason, I can't seem to think of this as a setback. It feels more like an achievement. Mainly because when I keep thinking about why and how I failed the exam, I realized that I have done so much more in terms of my life. I had given my priorities to things that were more important in my life while putting less effort into the exam. I did not expect to fail, don't get me wrong. I did not even give up. But I sure as hell did not study hard enough. I know that for sure because I felt that I needed more time during the exam. This can only happen because of the lack of practice. I know what I lacked. But that was not why I failed, at least not the root of it.
I think I took the path less traveled by. I know many people have read Robert Frost's poem and thought that taking the path less traveled by simply meant choosing the path that is less taken, making an outrageous decision that is contrary to public opinion. But I was later informed that Frost was talking about having two very similar choices, not a choice that fits the norm while another that doesn't. He was talking about making a choice that is less chosen among two very similar and difficult choices. Basically that was what happened before my final exam. I realized that even though doing well in my final exam was very important for my future, I decided that I could afford to not do as well while placing my priorities on where my heart was. I guess Ern's happiness means so much more to me than just a grade on my exam.
That being said, I still feel disappointed about my failure. Many people are shocked, so was I. But in a more positive light, this feels more like an achievement than many of the As that I have throughout college. Not only is this a humbling experience, but it is most definitely eye-opening. Just as Bruce Wayne's father used to ask him when he was a boy,
Bruce, why do we fall? Because we can learn to pick ourselves up.So I cannot say that I actually fell, but in the eyes of many, I probably did. I am not one to dwell on what others think about me. I just know that in light of such events, I realized that by trusting my heart, no matter what happens, even in the face of the darkest hours, I still feel strong and brave and march on.
It is still a black mark in my otherwise clean history. But as they say,
People who have never failed in life have never really succeeded either.Is it as simple as that? The justification of my failure? This cannot be it. Yet it is.
Sunday, September 17, 2006
Evariste Galois (edited)
One of my assignments this week was to write a short paper about a deceased mathematician who contributed in the field of abstract algebra. The mathematician of my choice was Evariste Galois (pronounced "Gal-wa"). Some of you may not have heard of him, but the most famous of his discoveries is to prove using group theory that there is no formula in which polynomials of degree 5 and above can be solved as opposed to quadratic formulas that most of us are familiar with. There are formulas for polynomials of degree 4 and 5 and these can be easily researched in some advanced mathematics book if you decide to explore them. Anyway, here is my short paper on Galois. Hope you enjoy it.
The Life and Death of Evariste Galois
We know that Abel’s death was caused by poverty, but Galois’ death was a consequence of the stupidity of others. “Galois’ short life serves as a great example of the triumph of crass stupidity over untamable genius. Throughout his life, his magnificent powers were shattered before the mass stupidity aligned against him, and he was beaten by one unconquerable fool after another.” [1]
Galois was born on October 25, 1811 and lived a happy life until he was twelve. The only teacher he had until then was his mother. She taught him Greek, Latin and religion where she imparted her own skepticism about religion to her son. Galois' father was an important man in the community and in 1815 he was elected mayor of Bourg-la-Reine. [2]
At the age of twelve, Galois started formal schooling at the Louis-le-Grand in
Even though Galois’ school experiences were tumultuous, it was his first exposure to mathematics. February 1827 was a turning point in Galois' life. He discovered the splendid geometry of Legendre and was greatly inspired. Later on, he read Abel’s works and absorbed the masterpieces of algebraic analysis at the mere age of fifteen [1]. He quickly became absorbed in mathematics and his director of studies wrote
It is the passion for mathematics which dominates him. I think it would be best for him if his parents would allow him to study nothing but this. He is wasting his time here and does nothing but torment his teachers and overwhelm himself with punishments.
Galois' school reports began to describe him as singular, bizarre, original and closed. It is interesting that perhaps the most original mathematician who ever lived should be criticized for being original. [2]
In 1828 Galois took the examination of the École Polytechnique but failed because he did not know some basic mathematics [3]. Commenting on his failure, Terquem (editor of the Nouvelles Annales de Mathematiques) remarks
A candidate of superior intelligence is lost with an examiner of inferior intelligence. Because they don’t understand me, I am barbarian [1].
In 1828, at seventeen, Galois met a man who could understand his genius, Louis Richard. Richard recognized Galois’ talents and proclaimed that Galois should be admitted to the Polytechnique without examination. Richard also said that “This pupil has a marked superiority above all his fellow students; he works only at the most advanced parts of mathematics.”
At eighteen, Galois wrote his important research on the theory of equations and submitted it to the
He failed the École Polytechnique examination again in 1829 shortly after his father’s suicide. The priest of Bourg-la-Reine forged Mayor Galois' name on malicious forged epigrams directed at Galois' own relatives. Galois' father was a good natured man and the scandal that ensued was more than he could stand. He hanged himself in his
His disturbed mental state after his father’s death was part of the reason of his failure. He also did mathematics almost entirely in his head and this annoyed his examiners [3]. This examination has become a legend. During the oral part of the examination, one of the inquisitors ventured to argue a mathematical difficulty with Galois. The man was both wrong and obstinate. Galois lost his patience. He knew he had officially failed. In his rage, he hurled the eraser at his tormentor’s face and hit him.
Galois sent Cauchy further work on the theory of equations, but then learned from Bulletin de Férussac of a posthumous article by Abel which overlapped with a part of his work. Galois then took Cauchy's advice and submitted a new article On the condition that an equation is soluble by radicals in February 1830. The paper was sent to Fourier, the secretary of the Paris Academy, to be considered for the Grand Prize in mathematics. Fourier died in April 1830 and Galois' paper was never subsequently found and so never considered for the prize [2]. After these series of misfortunes, Galois exclaimed, “Genius is condemned by a malicious social organization to an eternal denial of justice in favor of fawning mediocrity” [1].
Galois then spent most of the last year and a half of his life in prison for revolutionary political offenses. To make matters worse, he received a rejection of his memoir in prison. Poisson had reported that “His argument is neither sufficiently clear nor sufficiently developed to allow us to judge its rigor”. In March 1832 a cholera epidemic swept
Galois fought a duel with Perscheux d'Herbinville on 30 May because of his political beliefs [1]. The night before the duel, Galois spent the fleeting hours feverishly dashing off his scientific last will and testament, writing against time to glean a few of the great things in his mind before his death. He wrote in desperation and time and again his thoughts broke off and he wrote in the margin:
There is something to complete in this demonstration. I do not have the time.
Galois was wounded in the duel and was abandoned by d'Herbinville and his own seconds and found by a peasant. He died in
Significance of his work:
During the Middle Ages, mathematicians believed that unlike the quadratic equations, the algebraic formula for solving cubic equations was not possible. In the sixteenth century, Cardano, an Italian mathematician demonstrated that both cubic and quartic equations were solvable by radicals. With Cardano’s publications, mathematicians began in search for algebraic solutions for quintic polynomials. Abel built upon Lagranges’ work and managed to prove that for the general polynomial equation of degree 5 and above is not solvable by radicals. We know this from our ERES reading for Problem Set 4.
Galois extended the question of solvability by radicals in his Memoir on the Conditions for Solvability of Equations by Radicals. The memoir not only provided a theoretical framework for answering the solvability question, but also developed a framework for mathematical theory with far-reaching applications. He translated the problem of solvability into the language of field theory using a primitive form of the idea of an extension field [5]. Galois introduced the idea of what we refer to today as the Galois group. Using the Galois group, Galois was able to analyze a particular splitting field for a given polynomial. His results completely characterized the situation: a polynomial is solvable by radicals precisely when its Galois group admits a certain sequence of normal subgroups.
In solving this problem, Galois founded abstract algebra and group theory, which are fundamental to computer science, physics, coding theory and cryptography. Today, a "Galois connection" is a way of solving challenging mathematical problems by translating them into different mathematical domains, making the original problem amenable to a number of new solution techniques.
*Note to reader: For an example of a quintic polynomial that is not solvable by radicals, refer to page 559 in our textbook [3].
Conclusion:
Like Abel, Evariste Galois did not have a chance to live a full life and to witness the success of his works. Through a series of unfortunate events and wild coincidences, his talent was not duly noted. Cauchy had lost Galois’ abstract while Fourier passed away before he could judge his paper for a prestigious award. Today, Galois is not only remembered by his works, but also by the legends that were created about him. One can hardly forget the image a young talented mathematician throwing a chalkboard eraser at an examiner because of the examiner’s stubbornness and stupidity. Another legend about Galois was that he tried to write down everything he knew about group theory during the night before his duel which caused his tragic passing. To sum his misfortunes accurately, I repeat the quote from Galois:
“Genius is condemned by a malicious social organization to an eternal denial of justice in favor of fawning mediocrity” [1].
Bibliography
[1]
[2] The MacTutor History of Mathematics archive,
http://turnbull.mcs.st-and.ac.uk/~history/Biographies/Galois.html
[3] Gallian, Joseph A., Contemporary Abstract Algebra, Houghton Mifflin Company, 2002
[4] Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Galois
[5] Gellasch, Amy and Jardine, Dick, From Calculus to Computers, the Mathematical Association of
Thursday, August 10, 2006
Our Deepest Fear
“Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure. It is our light, not our darkness, that frightens us most. We ask ourselves, 'Who am I to be brilliant, gorgeous, talented, and famous?' Actually, who are you not to be? You are a child of God. Your playing small does not serve the world. There is nothing enlightened about shrinking so that people won't feel insecure around you. We were born to make manifest the glory of God that is within us. It's not just in some of us; it's in all of us. And when we let our own light shine, we unconsciously give other people permission to do the same. As we are liberated from our own fear, our presence automatically liberates others.”
- Marrianne Williamson -
Tuesday, May 30, 2006
About Teaching How to Fish...
Last year, I gave a lecture on "How to plan?". I used Stephen Covey's idea of "Begin with the end in mind" to help the students think of plans during their games. I do not believe in teaching students about where to move, and where you should put your pieces, etc. In short, I do not believe in giving the fish to people. I believe in teaching them how to fish. Hence, by teaching them how to plan, in a way teaches them how to think in chess. Now, instead of just having moves to follow from chess books, the students will be able to formulate plans for themselves. Give a man a fish and you will feed him for a day, teach a man how to fish, and he is fed for life.
So this year, in accordance to my believes in improving as a chess player, I decided to talk about "How not to lose a losing game?" What a fascinating topic. One can almost believe that I can perform miracles. I just used a catchy title but my most important point is that even though it is frustrating to play in a losing position, we can try to make it very difficult for the opponent to win. It is more frustrating not being able to win a won game than to play a losing game.
In addition, I also believe that there is more to my teachings than just about chess. I believe that my lessons can also be applied in life. Stephen Covey's idea clearly functions as one of the seven habits of highly successful people. Also, the idea about making it difficult for your opponent to win is a way of overcoming tough situations. Even though we might face tremendous odds, we should still perservere. Even when frustration kicks in, patience will give us a chance to overcome the odds.
So, if you are reading this, you have just learnt 2 important lessons about life. Pay it forward!
Thursday, May 25, 2006
Decisions
If a man cannot choose, he ceases to be a man - Anthony Burgess, "A Clockwork Orange"
Although every man believes that his decisions and resolutions involve the most multifarious factors, in reality they are a mere oscillation between flight and longing - Herman Broch
One day Alice came to a fork in the road and saw a Cheshire cat in a tree. "Which road do I take?" she asked. "Where do you want to go?" was his response. "I don't know," Alice answered. "Then," said the cat, "it doesn't matter." - Lewis Carroll
When choosing between two evils, always choose the one you haven't tried yet - Mae West
Decisions usually aren't between good and bad, they are between bad and worse, and it's often not clear which choice is worse - Mark Stosberg
May all your decisions be swift and deadly - Shihong :)
There is always more than one way to get to where we want to be. If we miss a turn, just take the next. See you at the top, buddy!
Sunday, April 23, 2006
Jeeez... Am I that good??
So how do you solve the abovementioned question? Think mols. I mean someone who asked that question should at least know what a mole is. So guess what, I asked her what a mole is, and she gave me all that crap definition about the Avogadro number and all that crap. Perhaps I didn't make myself clear. What is your idea of a mole? Most people's mind just jump to, Avogadro number... Avogadro number... NO, YOU FREAKING ZOMBIES!! A mole is THE AMOUNT OF SUBSTANCE... gosh... My dad always told me that the most important part of the definition of something is always after the word "IS". So there you go, AMOUNT OF SUBSTANCE. So in order to solve that previous question, you figure out the amount of moles of CaSO4 you have, and that's precisely the amount of crystallized CaSO4 you have. Why? Because the amount of CaSO4 in CaSO4 did not change, since of course, we assume there is sufficient water to crystallize all of the calcium sulphate. So by figuring out the amount of moles of CaSO4.xH20, we can easily figure out what x is via the ever famous ratio of mass and molecular mass. Despite not doing chemistry for 5 years, I was still able to solve this problem, all through deduction, that the amount of moles of CaSO4 cannot change.
My critical thinking skills amaze myself sometimes... If you want to survive in this world, stop depending on your textbooks, coz you ain't getting any help in the real world.
Sunday, April 16, 2006
Quotable Quotes Part 2
Effort is not about how much you speak for your work, it's how much your work speaks for you
These are actually 2 original quotes from me. I give you people full rights to quote me. Cheers!
Saturday, April 15, 2006
Quotable Quotes
The trouble with trouble is that it always starts out as fun
You can't lose what you never put on the table, but you can't win a lot either
Against overwhelming odds, you will lose
Never test depth of water with both feet
These are just a few of my life's principles. Something that I thought would be interesting for you chuckers to ponder about. I know barely anyone reads my blog, but at least I get shit off my mind. Someday, this (my blog) could be worth a lot of money. The insights to MY mind.
Friday, April 14, 2006
Perseverance
Definition:
determined continuation with something: steady and continued action or belief, usually over a long period and especially despite difficulties or setbacks
Brooksbank (my Math 311 (Number Theory) professor, who happens to be British; all the engineering girls think he's cute, no idea why I gave that information but get on with it!) just returned our Number Theory exam today and I got a B- on that. I am resigned to getting a B- at the end of the semester, and in fact, I would be very surprised if I got anything higher. Am I disappointed? Not really. I thought I would end up doing worse. It was an insanely hard exam and to be honest, I think he was rather lenient with the marking already. I would have been killed if he had picked on my proofs very strictly. For example, I claimed that the GCD (10, n) = 1 (for you math noobs, GCD (10, n) is the greatest commond divider of 10 and n) just so that I could use Euler's Theorem to make my proof neat. But then, GCD (10,n) was not necessarily 1 and that I could have done the proof through the methods of reduced residue sets, which is one of my weakest areas. My understanding of reduced residues and primitive roots are very shakey. But after the exam, I felt like I understood them more. I had to study them, work on them, over and over again, just trying to prove the stuff that was required of me.
Upon hindsight, I saw myself giving up. The exam was due on Wednesday and on Wednesday morning itself, I woke up at 9 a.m. just to work on it. My classes start at 12 p.m. so I had 3 hours. I turned off my computer, and just sat there and focused really hard. But at 10.45 a.m. I resigned to my fate. I gave up working, turned on my computer, and started procrastinating. I played some computer games, even though I told myself that I already quit. But the essence of the situation was that, I gave up.
BUT, here comes the big BUT, as I reflect upon it, right here, right now, did I regret not working harder? I don't. I think I did my best, and that's the best a man can do. That was my vow to Ern, and I think I should stand true to it. When I looked at the solutions of those problems, there was no way I would have figured those out to that detail. I could never have escaped my fate. I had no regrets. But when I think about it right now, even though I gave up, I persevered. I tried and tried.
per·se·ver·ance (noun)
Definition:
determined continuation with something: steady and continued action or belief, usually over a long period and especially despite difficulties or setbacks
DESPITE DIFFICULTIES AND SETBACKS...
Friday, April 7, 2006
Anger Management
I tell other people and myself that I do not get angry easily. In fact, I don't appear angry at all. No matter how bad things happen to me, it seems that I always remain calm. But in actual fact, when I think about it, I am an angry person. What triggered this self-reflection? This morning, the morning I was looking forward to for the past week, I was supposed to wake up at 8 a.m. and call Ern, and after calling her for 4 times, she finally picked up. To my utter disappointment, she forgot that I was going to call her and she was out for supper with her friends. I was pretty sad about the whole thing and I told her to message me when she got back to the room. At 10 a.m., which was 12 a.m. where she was, I called her again and this time, she only picked up after 15 times. I know, I know, I am desperate. It's past midnight and I was afraid she wasn't OK, since she didn't message me.
Anyways, our conversation wasn't really pretty. She was still out and she was only heading back. What can I say? She will definitely be tired when she reaches back to her apartment and she refuses to wake up early the next day. So she told me to wait till she gets back to Penang and we will talk on Sunday. Well, this seems like a minor issue, but when she hung up, I got so angry that I chucked the phone. I did not vent my anger on her. I was just pissed about the whole thing. Is it even possible for you to forget that your boyfriend/girlfriend is going to call you? Man, this pisses me off. Since I have no other avenue of venting my anger, other than almost breaking my phone, I decided to blog my piss out.
Man... I just realized I am an angry person. I need help.
Thursday, March 2, 2006
Inspire me... Inspire me not...
Well, one way we often get inspired is through the experiences of others. It could be as simple as watching a movie, where you see how someone had to go through hardships to achieve the extraodinary, the feel good kind of movie where the ending is always happy. For example, a movie like "Miracle", where the US Olympic Ice Hockey team defeated the Soviet Union in the 1982 winter olympics when it was thought to be impossible. Anyways, watch it and you will understand. Another such movie would be "Remember the Titans". That is about American Football but the idea is similar.
But what I am trying to point out today is that, recently, I have been inspired by numerous people just by what they have said to me. As mentioned, I am not talking about mere motivation here. But the professors at Bucknell, make an effort to know your work and try their best to inspire you to do the best you can. That's what makes Bucknell different. A lot of people never spent the time to get to know their professors in universities. We tend to regard our professors as just mentors who are there only to impart knowledge upon us. However, at BU, the professors are more than just teachers. They are your friends. I will not go too far as to explain what exactly did some of my professors say to me that inspired me. But when I think about it further, I realize that it is not just the things that they say, but the way they say it. It is kind of gesture, the kind of sincerity and the kind of expression in their face that shows you that not only do they want to help you succeed, but it is their pleasure to see that you actually get where you want to go.
In other words, the professors at BU help you realize your dream. By realize, I do not mean help you find your path, but actually guide you along it. I have not been to any other university besides Bucknell. Hence, I cannot claim that Bucknell has this edge over other universities. However, having such great professors at Bucknell makes me honored to be here. In addition, in the Spring of 2007, I am hoping to study abroad at Melbourne University, one of the top universities in the world. I look forward to the difference in experience, and enrichment that I will get over there.
Saturday, February 25, 2006
Ain't No Mountain Low Enough
But I had to take Number Theory (Math 311) which is hard as heck. There's like so much crap that I don't even know and I thought I was done with proofs after Real Analysis (Math 308), but NO NO NO... I was far from done. Now instead of proving stuff about real numbers, I have to prove stuff about positive integers. How fun is that?
Another disappointment is Mathematical Statistics (Math 304). What the hell is this insanely difficult assignments. There are more proofs in that class too! Why, why, why me? Dammit... who in the world needs to know the maximum likelihood estimator of the sample distribution parameter? Do you even know what I am talking about? Gosh... Save Our Souls!!