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May 13th, 2009, 05:21 AM   #2
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Re: Mathematics and me

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 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).

 May 14th, 2009, 02:22 AM #3 Senior Member   Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3 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?
 May 14th, 2009, 07:05 AM #4 Newbie   Joined: May 2009 Posts: 13 Thanks: 0 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.
May 15th, 2009, 08:00 AM   #5
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Re: Mathematics and me

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 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.

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.

May 15th, 2009, 05:22 PM   #7
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Re: Mathematics and me

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 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.

 May 15th, 2009, 05:27 PM #8 Senior Member   Joined: Nov 2008 Posts: 199 Thanks: 0 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.
 May 15th, 2009, 07:43 PM #9 Newbie   Joined: May 2009 Posts: 13 Thanks: 0 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.
 May 16th, 2009, 08:59 PM #10 Newbie   Joined: May 2009 Posts: 13 Thanks: 0 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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