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I would read it because I've always got the impression that you're a really smart guy but I wouldnt understand anything.  Math has always frightened me.
But best of luck with your dissertation though. :D:D:D
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Haha, I'm taking the honors introduction to analysis course here at Berkeley, and we covered filters a month or so ago. Tomorrow is our final >_<
http://math.berkeley.edu/~wodzicki/H104.F10/Topology.pdf
Filters start on page 4, but you already know all of this stuff.
Good luck with your dissertation!
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Aotearoa39261 Posts
Ah gl for your final! You must have covered nets as well  I fortunately got to skip all of that haha
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Very interesting. I wish I understood it. I don't know very much about topology, so most of this feels way over my head, even as a math major myself. The LaTeX looks fine though, from what I can tell.
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Wish I could understand this, but I haven't gotten into topology at all yet, but it sounds pretty interesting. (2nd year math/compsci major)
Best of luck Plexa!
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Looks interesting although i don't really understand much of it. But good luck anyway on your future work.
Oh, and making that look good in Latex must have been a pain in the ass with all those special characters and math expressions
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United States24756 Posts
I'm not exactly sure what an Honours in Mathematics is equivalent to in the systems I'm familiar with. After you finish your dissertation, what will that make you?
I'd give you feedback but I'm too unfamiliar with this type of math to be much help.
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Now i may be an english major, but i've got to tell you there apparently is an error in the first sentence:
It quickly becomes apparent that sequences are not adequet in a general topo-
logical setting and that new more general concepts need to be introduced.
Adaquate is spelled wrong, and the latter half: "and that new more general concepts need to be introduced." should either have the e in new changed to now, or have a comma after new.
"and that new, more general concepts need to be introduced".
But all of the math gibberish seems very intelligent. :D i noticed a few more errors that may or may not be errors depending on gibberish context. are you in the proofreading stage yet?
EDIT: and also this is a rather dull and confusing beginning for the paper anyway. perhaps explain what makes it apparent, something like "Upon using some gibberish with another thing, it becomes apparent..." ect.
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I thought it was adequate, not adaquate.
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On December 17 2010 07:55 Pokebunny wrote:
I thought it was adequate, not adaquate.
it is. epic fail by me. my bad.
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Muphry's Law is inerrant.
And wow, nice job, Plexa. I don't even begin to understand what you are writing about, but I am impressed! It is like some sort of mysterious, majestic poetry written by Martians.
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I was able to understand it (with my inferior math knowledge) until the basic concepts part, so I'd say that you did a good job writing your draft. =)
Though I have to say, if that first part is really that long, I can only imagine how long the rest of the dissertation is going to be. ^^
well good luck Plexa, I'm sure you'll do fine. =P
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United States10328 Posts
Hmm, about math writing:
Please end your sentences with periods! Even statements of "remarks"/"lemmas" etc.. (and equations are sentences (or parts thereof) too, so if they end a sentence, use a period!" (You end sentences with periods like... half the time.) [E.g. Lemma 1.44 should have a period after the (IV). -L(f,P) = U(-f,P). And perhaps commas after the other equations.]
You could also try to use the \begin{eqnarray} environment for that, though I suppose that's been deprecated... rather, use the \begin{align} environment. This gives you equation numbers on each line (after the equation, though... so if you want the number to go before the equation, just stick with this. And maybe use \textrm to make it non-math-mode.) Automatically numbered equations
can be annoying to keep up with, but you can do like \label and \ref and funny things like that to keep track of it dynamically (it requires compiling twice though.)
Try not to form run-on sentences. Use commas or semicolons (or even periods) as necessary. (As a general rule, if the sentence has more than one clause, it should have a comma or semicolon!) Also, fix typos. For example, Remark 1.49: "havenn't." Also in Remark 1.49, "implicitly" would be better than "silently," I feel.
Too bad I don't understand all the math itself though ... maybe I'll take topology in a year or two though, so yay
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Aotearoa39261 Posts
Thanks very much for all of that ]343[, I'm not going to touch this thing today since it would be terrible for my sanity, but when I get to reviewing it tomorrow or next week I'll incorporate the things you suggest.
On December 17 2010 05:47 micronesia wrote:
I'm not exactly sure what an Honours in Mathematics is equivalent to in the systems I'm familiar with. After you finish your dissertation, what will that make you? At the moment I have a Bsc in Maths, after I'm done with this year I'll have a Bsc (hons) in Maths. The honours year comprises of 6 papers and 1 year long dissertation. It's not expected to be groundbreaking or revolutionary in anyway, it's purely for the research experience. After this I will most likely begin my Masters (that would be in july next year) and then go from there.
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United States24756 Posts
Okay that makes a bit more sense. I was looking through and this document is pretty dense but not substantive enough to be the type of dissertation that would get you a doctorate :p
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Aotearoa39261 Posts
Yeah this is the baby stuff anyway, all background information haha
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Putting off studying for my analysis final as well and saw this haha. Latex makes everything look so pretty. Great job so far!
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F.3 is wrong, it should be "then" and not "and".
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Is this written for a "layman" with some experience in mathematics but not convergence spaces in particular? Presumably it is, since in your own words it's all the baby stuff - background information. If so then perhaps you could motivate the definition of a filter a bit more, maybe by first looking at an example where sequences aren't sufficient to define continuity, or by defining a net first. It's just a suggestion, since after reading the first few pages I still have no idea why on earth you'd ever want a filter.
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Aotearoa39261 Posts
On December 17 2010 12:59 Klockan3 wrote:
F.3 is wrong, it should be "then" and not "and".
Thanks
On December 17 2010 15:33 Wonders wrote:
Is this written for a "layman" with some experience in mathematics but not convergence spaces in particular? Presumably it is, since in your own words it's all the baby stuff - background information. If so then perhaps you could motivate the definition of a filter a bit more, maybe by first looking at an example where sequences aren't sufficient to define continuity, or by defining a net first. It's just a suggestion, since after reading the first few pages I still have no idea why on earth you'd ever want a filter.
Either nets or filters suffice as a generalisation (and indeed, they're equivalent). I think including a motivating example at the beginning would be a good idea though (although imo the rewards for dealing with compactness using filters is justification enough :D!).
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My understanding was that filters are even more general than nets though. Nets seem to be easily motivated by the need to define topological properties in terms of sequences. An analogous motivation for filters would be very useful to someone who's never heard of them before.
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EPT
