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Take a proof based math class in college. They will likely start at a low enough level to make you happy. Once you get to the point where the subjects start d

by thefool 16y ago

Take a proof based math class in college. They will likely start at a low enough level to make you happy. Once you get to the point where the subjects start dividing, you'll see that the real skill that math teaches you is to look at a problem, and create a set of definitions which frame all the properties of the problem and make them make sense in that framework. You get this skill by both playing with problems and trying to define frameworks (theorems, lemma's, axioms, ect) and by reading about the techniques that others have developed. It isn't about rote memorization, its about playing with abstract concepts till you have a way of understanding them. One thing that playing will teach you is that it will show you that the path you take to understanding something is not the same as the simplest path for explaining something once you understand it. In contrast, in things like physics you are generally given the frameworks (by the mathematicians) and the cleverness comes from understanding how particular situations can be described by the existing (pretty abstract) frameworks (like newtons laws). If you are bothered by how some of the ideas seem to appear from nowhere, notice that there is a lot of math out there that you don't know, and even basic statements about open and closed sets build on a lot of more basic set theory and group theory.

todayiamme 16y ago
Thanks a lot for commenting. Your comment was pretty insightful to me and validated a few of the assumptions I had made. Although, it is highly unlikely that I will end up at a college which offers such a class (indian education pretty much sucks) I'll search OCW and iTunes U until I find something like that. I want to play with abstract concepts like you've said, but I have internal problems which I need to overcome before reaching that goal. I can't sit down at stuff at any lengths of time like that until I am really engrossed stuff from my past comes up and I tend to get emotionally strained whenever this happens. I remember stuff that shouldn't be there in my mind in the first place and it is a constant battle to get stuff done. So, is there any structure you use to get stuff done?
- pmb 16y ago
  Don't sell Indian universities short. It is very hard to get a job in mathematics, which means that even at "bad" universities the mathematics faculty can be quite good.
  - todayiamme 16y ago
    That's the problem you see. No one takes a job in mathematics, down here the trend is to do engineering get a MBA and work in Goldman Sachs. I wish this wasn't so, but it's quite true. There are precious few souls who try to buck the norm, but they are far and few in between. Most mathematicians end up in coaching institutions which exist for one thing; to "crack" the IIT-JEE for the aforementioned rat race. I really wish I could sell them short, but outside the IISc and TIFR along with a few other research organizations there is hardly any innovation taking place. Most universities are intellectually dead and students study only to get "placements" in some company so that they can prepare for their MBA later on. I know that this sounds like an excessive generalization, but I live near one of those prestigious IITs and I've worked with a PhD student as well as solicited the advice of a few professors. You know what shocked me? One of them, who is one of the original brilliant researchers and an ex-dean, told me point blank to get the hell out of this country and that my future isn't over here. I really want to change things, but since I am in this system I simply can't do it. However, at least I can speak the truth. Please try to understand that I am not judging anyone in this context. It isn't anybody's fault. It's just a reflection of how the majority of this society thinks.
    - pmb 16y ago
      You misunderstand me. I am not saying that Indian Universities properly prepare you for a lifetime of success. I am saying that it is certain you can get the mathematical knowledge you want from them. As to whether that is the career you want or whether you want to be a mathematician - I have no idea. But if you want to learn and understand proof-based math, Indian universities are as good as everyone else's, and the good ones are quite good.
- thefool 16y ago
  Get this book: http://matrixeditions.com/UnifiedApproach4th.html http://matrixeditions.com/UnifiedApproach4th.html and work through it if you want a rigorous treatment of MV calc and intro analysis. Or this book: http://www.amazon.com/gp/product/0914098918/ref=pd_lpo_k2_dp_sr_1?pf_rd_p=486539851&pf_rd_s=lpo-top-stripe-1&pf_rd_t=201&pf_rd_i=0914098896&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=0RS8QS2PE53QBP4B74C6 http://www.amazon.com/gp/product/0914098918/ref=pd_lpo_k2_dp... for regular calculus. Read them, work through the problems, get an answer key, email your solutions to professors asking them to look at them. You will get a good introduction to analysis (and exposure to many other parts of math) from those two books.

by thefool 16y ago

todayiamme 16y ago

Thanks a lot for commenting. Your comment was pretty insightful to me and validated a few of the assumptions I had made. Although, it is highly unlikely that I will end up at a college which offers such a class (indian education pretty much sucks) I'll search OCW and iTunes U until I find something like that. I want to play with abstract concepts like you've said, but I have internal problems which I need to overcome before reaching that goal. I can't sit down at stuff at any lengths of time like that until I am really engrossed stuff from my past comes up and I tend to get emotionally strained whenever this happens. I remember stuff that shouldn't be there in my mind in the first place and it is a constant battle to get stuff done. So, is there any structure you use to get stuff done?

pmb 16y ago
Don't sell Indian universities short. It is very hard to get a job in mathematics, which means that even at "bad" universities the mathematics faculty can be quite good.
- todayiamme 16y ago
  That's the problem you see. No one takes a job in mathematics, down here the trend is to do engineering get a MBA and work in Goldman Sachs. I wish this wasn't so, but it's quite true. There are precious few souls who try to buck the norm, but they are far and few in between. Most mathematicians end up in coaching institutions which exist for one thing; to "crack" the IIT-JEE for the aforementioned rat race. I really wish I could sell them short, but outside the IISc and TIFR along with a few other research organizations there is hardly any innovation taking place. Most universities are intellectually dead and students study only to get "placements" in some company so that they can prepare for their MBA later on. I know that this sounds like an excessive generalization, but I live near one of those prestigious IITs and I've worked with a PhD student as well as solicited the advice of a few professors. You know what shocked me? One of them, who is one of the original brilliant researchers and an ex-dean, told me point blank to get the hell out of this country and that my future isn't over here. I really want to change things, but since I am in this system I simply can't do it. However, at least I can speak the truth. Please try to understand that I am not judging anyone in this context. It isn't anybody's fault. It's just a reflection of how the majority of this society thinks.
  - pmb 16y ago
    You misunderstand me. I am not saying that Indian Universities properly prepare you for a lifetime of success. I am saying that it is certain you can get the mathematical knowledge you want from them. As to whether that is the career you want or whether you want to be a mathematician - I have no idea. But if you want to learn and understand proof-based math, Indian universities are as good as everyone else's, and the good ones are quite good.
thefool 16y ago
Get this book: http://matrixeditions.com/UnifiedApproach4th.html http://matrixeditions.com/UnifiedApproach4th.html and work through it if you want a rigorous treatment of MV calc and intro analysis. Or this book: http://www.amazon.com/gp/product/0914098918/ref=pd_lpo_k2_dp_sr_1?pf_rd_p=486539851&pf_rd_s=lpo-top-stripe-1&pf_rd_t=201&pf_rd_i=0914098896&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=0RS8QS2PE53QBP4B74C6 http://www.amazon.com/gp/product/0914098918/ref=pd_lpo_k2_dp... for regular calculus. Read them, work through the problems, get an answer key, email your solutions to professors asking them to look at them. You will get a good introduction to analysis (and exposure to many other parts of math) from those two books.