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May 12th, 2009, 11:40 PM   #1
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Mathematics and me

Hello everyone,

Just wanted to share my story with you. This is my first post.

I never had any particular talent or inclination for mathematics. I attended a prestigious private school. There, I enjoyed grasping new mathematical ideas, but hated routinely solving textbook problems, which I found tedious and boring. Consequently, my mathematical skills remained underdeveloped. At the age of 14, I couldn't even perform basic algebraic manipulations confidently. For example, I often wrote: a / (b + c) = (a / b) + (a / c). However, I developed an early interest (aged around 10) in computer programming. At the same age of 14, I could develop algorithms for extraordinarily complicated problems, could implement them in 4 languages, and was considered a programming prodigy.

In high school, along came calculus. I never really broke even with the subject, and almost failed my maths courses. The Rouse Ball Professor of Mathematics at Cambridge University, Timothy Gowers, writes: "Because mathematics continually builds upon itself, it is important to keep up when learning it... Every so often, a new idea is introduced which is very important and markedly more sophisticated than those that have come before, and each one provides an opportunity to fall behind... Those who are not ready to make the necessary conceptual leap when they meet one of these ideas will feel insecure about all the mathematics that builds on it." That's exactly what happened. I wasn't ready for calculus. My early enthusiasm soon turned to despair, and I never developed even elementary calculus skills. My stomach churned whenever I saw a d/dx or an integral sign in an examination paper - I knew it was a dead end.

However, my high school grades were very good overall, and I topped my class in Computer Science and English. I was admitted to a reputed college and, believe it or not, it was decided that I should major with Honours in Physics. Unsuprisingly, my mathematical inability crippled my Physics education. Emotionally also, I was caught in a downward spiral at the time. I failed to rescue my maths. After a couple of nightmarish years, I graduated near the bottom of my class. Without meaningful prospects of employment or further education, I enrolled in a 3-year vocational course in 'computer applications' at an unknown institution, upon completion of which I was promised a menial position in the software industry. I had given up on the academic life, and decided that it was not for me.

That was two years ago. Today, I live for mathematics. And a few other things also, I suppose, but that's beside the point. I'm presently involved in a research project on cellular neural networks, and I'll be applying to grad school next year. I've been self-studying for close to a year now, trying to fill in the craters in my mathematical education. There's still a long way to go, on the long road to mathematical maturity. But I'm 23 years old now. One question haunts me: Is it too late?

Thoughts? You don't have to answer the above question; I'll be grateful for any comments, personal experiences, opinions and ideas that you may like to share with me. Thanks for reading!

P.S. No one forced you to read this, and no one is forcing you to reply. Thus, if you do reply, kindly refrain from statements such as: "Go to hell, I'm not f****** interested in your f****** life-history."
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May 13th, 2009, 05:21 AM   #2
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Re: Mathematics and me

Quote:
Originally Posted by velvet_ghost
But I'm 23 years old now. One question haunts me: Is it too late?
Not nearly. If you work (e.g.) toward a Ph.D, you could still have one before the average age (well, median; it's around 30 or early 30s).
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May 14th, 2009, 02:22 AM   #3
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Re: Mathematics and me

It is absolutely not too late. You will certainly be challenged, but it seems you're capable of the precise thinking required by mathematics, you were just turned off by tedious calculation (it happened to me, too, to a much lesser extent).

Anyway, what math have you picked up since you've started studying again?
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May 14th, 2009, 07:05 AM   #4
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Re: Mathematics and me

Thanks for replying.

Well, I started out with linear algebra. Today, I've reached the standard expected of an advanced undergrad (majoring in maths). For those of you interested in linear algebra, you should check out Prof. Gilbert Strang's video lectures on MIT OpenCourseWare. I tacked some discrete maths simultaneously, and studied logic and set theory, modern algebraic structures, basic Galois theory, order relations, graphs and trees. Then I moved on to elementary number theory, discrete probability, generating functions, combinatorics, asymptotics and recurrence problems. I also learnt basic algorithmics and computation theory.

Presently, I'm battling my old enemy - analysis, who seems to be putting up an exceptional fight. But I have a firm grasp on basic real analysis now, something I owe entirely to Spivak's 'Calculus', a fantastic book if I ever read one. I also learnt vector calculus, and even a little calculus on manifolds. Presently, I'm struggling with differential geometry and complex analysis. I have Rudin's 'Real and Complex Analysis' open at my desk right now.
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May 15th, 2009, 08:00 AM   #5
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Re: Mathematics and me

Quote:
Originally Posted by velvet_ghost
Presently, I'm battling my old enemy - analysis, who seems to be putting up an exceptional fight. But I have a firm grasp on basic real analysis now, something I owe entirely to Spivak's 'Calculus', a fantastic book if I ever read one. I also learnt vector calculus, and even a little calculus on manifolds. Presently, I'm struggling with differential geometry and complex analysis. I have Rudin's 'Real and Complex Analysis' open at my desk right now.
I thinks I already mentioned this elsewhere but if you are only studying mathematics to applies it in computer programming at the extreme level then studying small books like 50 problems in propability or X # of puzzles for something or interesting logics exercises. Most of modern mathematics books are highly abstract, look like they are totally useless, if you don't believe me go ask one of it author to use it to build a spaceship, a spacestation or a anti-gravity vechile. I don't think they can. I studied some of Steward book on Calculus I and II, and it is filled with flaws, it like eating something that is half-way cooked. The other stuffs, it is totally uncooked and some of it is not even editable, unless you can eat rock and survive I don't suggest you waste your time. If I was not a mathematician, I would not even study something that is not clear to me, that is not my job, unless you wants to be a mathematician. Stuffs that are clear that I noticed as a student:

Calculus (partial-differential-integral equations, its flux version as in path, surfaces,...) [good enough to build a working warp drive,...]
Algebra (analytical algebra,...) [good enough to over take the "digital age" whatever that mean,...]
Probability [good for alot of things]

Unless you also want to be an anthopologist and start studying languages, natures,... You could go crazy if you are like have no good family that don't really care or a bad surrounding envoriment. The people here are jerks, and some of them outright loser.
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May 15th, 2009, 08:07 AM   #6
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Re: Mathematics and me

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Originally Posted by MyNameIsVu
Most of modern mathematics books are highly abstract, look like they are totally useless, if you don't believe me go ask one of it author to use it to build a spaceship, a spacestation or a anti-gravity vechile.
Somehow I don't see it as a flaw that most textbook authors couldn't build an anti-gravity vehicle.
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May 15th, 2009, 05:22 PM   #7
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Re: Mathematics and me

Quote:
Originally Posted by CRGreathouse
Somehow I don't see it as a flaw that most textbook authors couldn't build an anti-gravity vehicle.
This is surely because you don't have the benefit of MyNameIsVu's towering genius. If only his communication skills matched his powers of analysis then we could all have a taste of his colossal insight.
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May 15th, 2009, 05:27 PM   #8
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Re: Mathematics and me

More related to the original point, it's definitely not too late. Keep up the good work!

p.s. When you are self studying do you have a means of checking your proofs for errors? I ask because in my experience their are some subtle reasoning flaws that can become rooted without a teacher of some kind pointing them out.
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May 15th, 2009, 07:43 PM   #9
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Re: Mathematics and me

@ pseudonym: You're absolutely right. I was also making several subtle logical errors initially, especially in analysis. I don't have a formal 'teacher', but luckily I have friends in maths grad school; I ask them to go through some representative proofs from time to time.

@MyNameIsVu: You raise an important point: the practical value of mathematical abstraction. To my mind, its value is indisputable. For example, you can't quite 'imagine' imaginary numbers (or complex numbers), can you? And yet their immense utility in physics and engineering is well known. Similarly, you can't 'visualize' n-dimensional geometry. And yet, there would be no string theory without it. And please refrain from statements like: 'The people here are jerks, and some of them outright loser.' Firstly, it's wrong grammar. Secondly, if you don't like this forum, don't post in it.

Any other opinions (argued rationally) on the topic of mathematical abstraction will be welcome.
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May 16th, 2009, 08:59 PM   #10
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Re: Mathematics and me

@MyNameIsVu: I've never claimed to be 'good' at mathematics. On the contrary, I've always been mathematically inept. Even today, I'm constantly reminded (during the course of my studies) that this remains the case. However, I don't understand what you mean by: "you have chose to focus yours time differently".

I don't study abstract algebra and analysis to improve my programming skills. For that, I study algorithmics and computation theory. Pure mathematics is only a hobby of mine. I study it because I enjoy doing so, no matter how impotent it makes me feel.

Please do not post statements such as: "The stupid American probabily think they all smart with all theirs "hidden" reserve technologies" in this thread. I have reported your post for racism. Further, few would call abstract mathematics a 'technology'. It is not even a science, but a beautiful and riveting art-form.

Also, just so that you know, I am not American, and I do not presently live in America. Neither is English my native language.
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