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Update of my Studies
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Misc
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By Divergence
Posted Thu Aug 03, 2006 at 10:14:11 PM PDT
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After reading through the comments posted on Anonymous Hero's story, I decided I should probably update my previous post.
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After reading through the comments posted on Anonymous Hero's story, I decided I should probably update my previous post. I have not, unfortunately, spent quite as much time at my readings as I would have liked, mostly due to school; the little free time left over was wasted on video games (Halo 2 and Oblivion) unless I went to a friend's house. In any case, I finally ditched the games and decided to start studying again in these last couple of weeks before school, and plan to continue right through the school year (although I won't have much time with two AP classes...) For the next two weeks I will be studying from dawn to dusk, though, so that I can make serious progress. Once school begins, I will probably be able to study around 20 hours a week. My list, partly based off of Anonymous Hero's, is as follows:
- Topology (Munkres)
- Principles of Mathematical Analysis (Rudin)
- Linear Algebra (Lax)
- Abstract Algebra (Dummit)
- Real and Complex Analysis (Rudin)
- Algebra (Lang)
- Differential Topology (Hirsch)
- Algebraic Topology (Spanier)
- Berkeley Problems in Mathematics (Souza)
- A Mathematician's Survival Guide (Krantz)
Of course, I don't plan on until some time in college (I am currently entering my senior year, and hope to be accepted into the University of Chicago for both college and grad school.) From what I have read off of college websites, this will (hopefully) be enough to prepare me for grad school- but if I am missing anything, please post a comment. As to my present progress: I started reading Munkres again a couple days ago, and I'm currently working on section 1.2 problem set, which initially seemed sort of hard but seems almost trivial now. I'm guessing that this is because of the level of abstraction, which I am not used to. In any case, I decided that from now on I'm going to try to work out all proofs mentally; once the mental proof has been checked and refined, I then record it in my notebook. I find it rather amusing that an easy problem can become extremely difficult and time-consuming if I try to work it out mentally- although the main difficulty lies in overcoming my short attention span. Still, I think the ability to solve a problem mentally (and quickly) is worth the effort involved, even if it does occasionally take me a full hour to solve a problem that should take less than 10 minutes. I suppose that this isn't helped by the fact that I am, unfortunately, a perfectionist, esp. when it comes to neatness in writing.
Although I have not been able to keep up with my "formal" readings until now, I have learned quite a bit from various sources such as mathworld, and have gotten some feel for the various fields as well. Even glancing through my books superficially has, I think, given me some indication as to what each subject is about. As a result, I have begun to a major interest in topology (perhaps because I enjoy anything having to do with set and really general theorems) and algebra (ditto.) But I have grow to dislike analysis, at least classical analysis, because, for one thing, being restricted to R^n and C^n is kind of boring, and for another, the proofs always feel so unnatural and formulaic, so unintuitive (at least for me- maybe this is because I am using Rudin as my analysis text?) Should I use another text in place of baby Rudin when I start studying analysis again, and if so, which book? For instance, could I use Royden as a stand alone text for real analysis- without baby Rudin- and complement it with Ahlfors' Complex Analysis? (Speaking of which, a new version of Royden's text is coming out in March 2007.) Or must I study something else (besides baby Rudin) beforehand? I just want to get analysis off my list of worries for grad school ASAP, so that I can focus on topology and analysis. (By the way, any recommendations for either subject are also greatly appreciated.)Thanks for your time and patience- I have no one (not even my high school math teachers, unfortunately) that can give me suggestions for my study plan beyond a basic sketch until I get to college, so I rely on the comments I receive from you.
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