ayushkhaitan

Oh. and I forgot to add one thing.

I recently took part in the Senior and Open Sections of the Singapore Math Olympiad.
I got a bronze for one, and a special mention for the other.

In my school cohort, out of the 40 best Math students who took part in the event, I got the highest in one section and the second highest in the other.
I think that's probably because our school is just two years old, and we received little and inappropriate training [ I really don't intend to sound like a pathetic wheener here ]
We don't have any facility for 'olympiad training', and my Math teacher just gave the cohort a couple of questions to do a week before the contest, and called it a day.....

Moreover, I'm pretty sure that I'll be getting the 'Best Math student' award at the end of the year, which will be given to the student who has performed the best in Math over the past two years of the IB Diploma course.

As you can see, I'm pretty much a Math maniac

frankchn

You are going to compete with other Singaporeans with international Olympiad medals so you will have quite a tough time getting in.

With regards to your papers in Mathematics and all that, I think you will need a better grounding in your fundamentals of mathematics - your multivariate calculus, differential equations (ordinary, partial), linear algebra+functional analysis and discrete mathematics before really trying to embark on any sort of research. I've met some of the most brilliant individuals in my and my junior batch w.r.t. Mathematics (i.e. SMO Open Champion, IMO Silver) and I don't they are ready to do any sort of serious research in Math either.

ayushkhaitan

Oh. Thanks for the reply

As I've stated earlier, my dismal performance in the olympiads when compared with national standards was mainly because I had no freaking idea what to expect. This was my first experience at any olympiad. However, I do understand that that offers very little in way of justification.

I don't think I'll be competing with the Singaporean cohort though because I'm an Indian national studying in Singapore on scholarship.

My research in Math is simple: we all know that when we graph functions, we plot the y-value vertically, and the x-value horizontally, which gives us a coordinate.
Now let's take a coordinate plane, and divide the x-axis in tiny bits. Now construct isoceles triangles on these lines- take the two ends of the small lines on the x-axis, and connect these two ends to any point in the graph. These lines connecting the line to the points should be equal in length. These lines will make an angle at any point on the graph One should notice that the higher the graph [i.e. the larger the y-value], the smaller the angle that will be made.
Hence, instead of constructing a graph by graphing the value of the range against the value of the domain, one can plot the same graph by considering various value on the x-axis, and then the angles that these value will make with the graph.
This turns the whole of analysis [as far as my knowledge goes] on its head.

Moreover, I've also developed a sort of calculus for this [differentiation, not integration].
Some of the patterns displayed in such functions are quite neat......

frankchn

You will be competing with the Singaporean cohort because you will graduate from a Singaporean-based JC or other high school.

Well yeah. They need proof that you are indeed good in what you say you are good in - and usually olympiads and other sort of science fairs are the best bet this will happen.

Have you tried submitting your research to SSEF or any of the other science fairs?

frankchn

If you divide the x-axis into tiny but finite bits, you will end up with a series of points and not a continuous function. If you divide the x-axis into infinitely tiny bits, then I think you will lose the concept of "triangle".

Anyway, to turn a standard one-one y=f(x) function into your concept, I think it is just "angle of triangle with base at location x-dx to x+dx" = tan^-1(f(x)/dx) where dx is of course the "tiny bit".

ayushkhaitan

I do have some achievements in the field of Math, but I'll elaborate on that in my application form rather than brag about them here

The nearest thing that I've come to winning an olympiad is that I was captain of the Math team that won the Geeta Memorial Math Cup in 2004, which is like an all-State Math competition based on the unexplored recesses of Math [mostly miscellaneous].

However, you're right in saying that my dismal performance in the olympiad does not explicitly show my skill at math.
However, I'll try and demonstrate that through my paper. The school award should also count for something.

As for submitting my paper to SSEF, I was made aware of them earlier this year, only to know that the registration deadline had passed.
Moreover, because my school is only 2 years old, there was no backing from the authorities. The school is only focused on the curriculum at the moment.
That is perhaps the reason for the non-existent math olympiad training, which I'm told is an elaborate procedure in other Singaporean schools.

However, my Math teachers has always encouraged me to pursue my interest much beyond curriculum, in stark and covert violation of the 'stick to text' policy enforced by our crappy Head of Staff. I think he has some good things to say about me in his letter of recommendation.

ayushkhaitan

You can take the lengths of the bases of the triangle to be as long as you like.

Have you heard of sampling in data processing? What basically happens is that at regular intervals of time [like 0.2 seconds say], information is retrieved from analog data, and stored as digital data.

In the same way, if we take the lengths of the bases to be, say 2 cm, we will retrieve only certain values of the function....at regular intervals.
However, as the lengths of the triangles grow smaller, and 'approach' a point, a more accurate representation of the function can be approached.
Moreover, this gives rise to the idea of calculus. The lengths of the bases only approach the dimensions of a point. Hence, the concept of a triangle and hence an angle still exists.
In fact, it is this sentiment of 'limits' that gave rise to calculus.

Say, for example, I want to graph f(x)= sinx, as per my definition of function.

Then my graph will extend from infinity to a height in which an isoceles triangle will make an angle of 1 radian/degree. This is because the range of sin x is -1 to 1. Hence, as the value of sin x approaches 0 at x=0, the value of the angle which the triangles make will also approach 0. Hence, the graph will approach infnity. Hope this helps.

lizzardfire

heh. In the same post, even.

ayushkhaitan

lol.
I was just referring to my 'olympiad' experience......although this was not an olympiad, it was still a math competition.
I have some other achievements in math too, which I'm sure you'll object to if I list them here.

ayushkhaitan

bump.........?

Hriundeli

Seriously dude? I thought by now you'd realize we can't give you a number. Your SATs are fine. Is there anything else in particular you'd like to hear from us? Is there a reason you can't wait until you get your decision back, like the rest?

Sorry for sounding rude, but bumping a 4 month-old thread to show off your math achievements and to be patted on the head with "you have a decent chance of getting in" is just not cool...

ayushkhaitan

Oh. Thanks for replying.
I didn't exactly wish to 'show off', and apologize if this has come across the wrong way.
It's just that there have been some developments over the past few months, and I wished to ascertain if they significantly affected my chances.
Btw, I haven't applied yet, as I believe international applicants can only apply RD.

As for my SAT score, I was going through the scores of some accepted candidates, and I thought my score was lower than the accepted norm [although I understand international applicants may get some benefit of doubt in CR and writing].

Thanks anyway.

lizzardfire

Your SAT scores are all within our 25-75% ranges. I don't see how your continual expressions of your own accomplishments in mathematics can be construed as anything other than "showing off".

You understand that all the posters who are even Caltech students have already replied to your thread. We don't do "chances". All you're getting at this point is random other high schoolers who are giving you misguided ego boosts.

I have no idea if admissions has seen this thread. Odds are that they have, but if you keep bumping this thread I'm going to make sure that they do. Last time I checked, admissions wasn't a huge fan of undeserved arrogance.

Techy233

"developing my own branch of analysis"

w.t.f. - have you ever taken an actual course in analysis?

ayushkhaitan

Techy233
No. I haven't. However, the IB Diploma Math course gives one a nice introduction to functions and relations. I followed that up by reading some undergraduate texts on analysis- topics like limits, integration inequalities, etc.
I came across various different definitions of functions and limits, and I thought of an original idea to develop my own alternative definition. You can read the subsequent posts to get the rough idea.

lizzardfire
My main question in my previous posts was that will my less than impressive performance in the Singapore Math Olympiad have a detrimental effect on my application. This is in light of the fact that only SMO winners generally get accepted in reputed tech schools. With all due respect, I hardly call this 'showing off'.
Anyway, this will be my last post, so that I get loads of free time to deflate my bloated ego.
Adieu