Today is the first lecture of CS3216, and I was very excited to attend the class.
Still, things will be lecture will be commented/blogged later, I'm very tired now, attending lecture for the whole afternoon and night, and not having yet. I'm here now cos there're some important things I have to do as soon as possible.
Today is the first lecture of CS3216, and one of the most special things in this lecture is the show-and-tell session. Still, I think of this session before, but I ended up finding myself have no particular talents or something like that to show off. Thus, at first I just intended that I would be only introduce about myself. However, to me, I'm not the only one in this situation. There's at least another one in the class, and fortunately, his turn was before mine. He was just talking about his blog. This gave me the idea of just introducing my articles in inequalities, which is just normal, but is my pride, representing for a long time learning Maths of mine, and also, one of the most wonderful and also craziest thing I've done so far, in my opinion. As it happened on the go, the inequality articles of mine wasn't post in my blog. So firstly, posting it is an important thing for me to do.
Secondly, there're some another thoughts about the show-and-tell session. People there were awesome, indeed. But those issues will be left to my later post. The thing I just want to mention here, is me :-). Actually, a bit disappointed about myself. My performance today was rather lame, I must admit. Truly, at first, maybe I was strongly impressed by the 'Wii ...' show-and-tell of the previous CS3216 in the past, that I thought that if I had to show something in the show-and-tell session, I must show something related to my role in the course, and even more, something really fantastic. And I could find nothing like that about myself, which is regretful to say. However, after the session today, I think that I was quite wrong. It's not a must for me to show something related to my role in the class, and even not something fantastic. I just have to show something, anything at all, tell anything I feel like, I think, but I have to truly show something. Truly, now when I'm thinking back, I think I could probably do some skating trick, or just playing the harmonica,..., even though I'm not good at them :-P. Still, it's better than doing nothing :-). Today was not good as my performance was rather poor, but still, it was good that I realized something. The next time, I will become better :).
A little off topic about inequalities. Back then, when I was in high school, grade 10, I went crazy and learnt almost no stuff at all in the curriculum (in Mathematics) (I didn't want to learn, I was a little bored). Instead, I chose what I want to learn, what I learnt myself, and I found inequalities interesting and decided to study a little deeply about it back then. It was not long before I had to come back to the school's curriculum, but the time I learnt inequalities was one of the most memorable moments of mine, and it was very fun and very happy. I was able to do something that is not a must for me to do, I learnt something that no one forced me to learn, but it is what I really, really wanted to learn. Why I mention it here? Because I think CS3216 is something partly like that, and now I really can't wait to learn CS3216 more and more.
Here comes my (and some friends, we worked together) articles. Actually, some of them hasn't been finished yet, I had some other ideas long after I finished them, but I was a little busy and haven't been able to manage time to update yet, and also, I am lazy :-P. Another interesting thing about these articles it that they are non-copied from any source. The idea was self-created :-). Actually, the idea for the first one is inspired, i.e. generalized, by a smart solution to one problem. But the point is that, if you learn Mathematics a little bit deeply, you will see that there's smart solution for many problems, which is short, and very clever; however, whether that solution can be generalized to become method is a different problem, and even if it can, how to generalize it might also become a problem. In addition, I also added some more techniques to the generalized method :-). Anyway, regretfully, now all my articles are kind of outdated already.
Here comes my articles.
Oh, LaTeX sucks here. I used PcTeX for typing my articles, and it's not well displayed here, so I think it's better to give link to download.
First article, the SOS-Schur method (now I think it's just a technique :-P )
http://www.mediafire.com/?izmuqtyylzl
Secone article, a useful technique in SOS and SOS-Schur method (sorry, this one is in Vietnamese, I didn't write an English version of this).
http://www.mediafire.com/?jyhymvndmmy
Final article, a method of solving 3-variable inequalities. Truthfully, this method can be done by hand, but actually it's computer-based, so normally the solution is ugly. But this one is quite strong.
http://www.mediafire.com/?1ntkx2mnzzm
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I did not, for one, think you are lame. There are certain talents that you just can't put on display, in public - your passion for math is one of those talents.
ReplyDeleteI am quite frankly in awe of your passion for the field. I've downloaded the pdfs, and, I must say, nice work. =)
Cedric
really:-). It's very nice to hear so :-).
ReplyDeleteSo maybe I was a little too strict about myself. Truthfully speaking, when seeing all of you, I hoped I could show some 'visible' things as well.
PS: I must admit that I barely understood even half of what the articles were saying. I'm too tired, I think, the equations were swimming before my eyes. Will take a second stab tomorrow.
ReplyDeleteOn a related note, CS3216 is all about inequalities (if you know what I mean) :)
ReplyDelete@ Dienasty: Of course you can understand lah, I was just grade 10 when writing them.
ReplyDelete@ Adhiraj: Frankly, I don't quite understand. But back then when I was in grade 10, one of the key things that made me like inequalities was that I thought inequalities were everywhere in life, in some sense.
Cong: it's amazing that you are proving these inequalities at such a young age. It took me more than 30 minutes to understand the "very simple example" (which you solved at grade 10 ) mentioned in page 1 of SOS_Schur.pdf
ReplyDeleteDon't worry about not having a talent to show. The 3 pdfs that you have attached shows that you are BEYOND talented.
Cheers,
Ji Wei
Ji Wei: The truth is that, you are overestimating me. The reason why it took you that long to understand is because I wrote too short. The idea is simple, it's just that I skipped some parts of the solution. If you see the detailed solution, you will know that things are very simple.
ReplyDeleteAnd one thing I must clarify, example 1.1 and 2.1 weren't solved by me. Example 2.1 appeared in some IMO, and the solution shown in the pdf was the shortest solution in that contest, earning its owner a special prize (if I'm not mistaken) (note that the very solution I know is as follows: 'the inequality is equivalent to c(a+b-c)(a-b)^2 + a(a+c-b)(a-c)(b-c) > 0'). Example 1.1 was in some inequality book. And they were the sources which gave me the idea to write the first article.