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No topology sub-forum?

  1. Nov 1, 2007 #1
    Why not? Does topics on it go under general maths?
     
  2. jcsd
  3. Nov 1, 2007 #2
    Topology related threads have usually not been moved away from the Calculus & Analysis section, at least.
     
  4. Nov 1, 2007 #3

    JasonRox

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    I think Topology should have a heading somewhere. I never actually know where to post it. General Math? Calculus and Analyis? Or Linear and Abstract Algebra?

    I was thinking that we should rename the headlines as...

    General Math
    Calculus and Differential Equations
    Analysis and Topology
    Linear and Abstract Algebra
    ...and so on...
     
  5. Nov 3, 2007 #4

    Moonbear

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    I hope some other math folks will chime in on this. Basically, you're suggesting we just rearrange two math subforums...instead of having Calculus and Analysis as one subforum, and Differential Equations as another, you're suggesting Analysis be split off from Calculus and combined with Topology, and Diff Eqs be combined with Calculus.

    So, I have a few questions, because I'm not a math person and can't just skim through those forums myself to get a sense of this...
    Are there currently enough Analysis questions in the Calc and Analysis forum to justify moving them off on their own? From previous discussion, we don't get enough topology questions to sustain a forum, so Analysis would have to be a sufficiently popular discussion topic to justify that split.

    Also, does it make sense in terms of the subject matter to combine Analysis and Topology? Or is this more of lumping together two topics for convenience of enough posts to justify a separate forum?

    I can see the logic in combining Calc and Diff Eqs, but from a practical, forum management perspective, are these both subjects with enough questions that it would be overwhelming to have a single forum with them combined?

    Before we start jumping in and rearranging forums, I think these are the questions that need to be considered.

    In the meantime, without having asked Halls or Hurkyl (they'd be the ones to specifically ask), my general impression is that using your best judgement of where a topic that's not specifically listed fits will probably be okay. At worst, they'll move it to a different subforum and you'll know where to put it next time. It would probably be safest to put it in general math, but you could also post it, send them a link to the post by PM and let them know you weren't sure where to place it and if they think it fits better elsewhere, to move it for you.
     
  6. Nov 3, 2007 #5

    morphism

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    Topology & Analysis is a valid combination; so is Topology & Geometry. So a simple renaming of the Geometry subforum would be the easier solution. Although (sadly), there isn't much topology that gets discussed. The Ask A Topologist forum is much more active, although it's plagued with boring homework problems (and the posters do not show any work, so one is less inclined to help them), and it's somewhat of an eyesore.

    Another unrelated question, but one I've wondered about for quite some time, is: why are logic, set theory, statistics and probability all clumped up together? The first two are reasonably detached from the other two. :p
     
  7. Nov 3, 2007 #6

    Chris Hillman

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    Oh, a chance to classify mathematics!

    Due to popular interest in physics, there are too many posts related to differential geometry, so I suggest two headings be "Topology & Analysis", "Manifolds and Geometry", and hope that students with a general topology question will head to the first, while students with a question about de Rham cohomology will head to the second :wink:

    There are existing subject classifications in mathematics, e.g at the arXiv, AMS Subject Classification, etc., but AFAIK no-one is happy with any of them :rolleyes: However, I would stress that good classifications should try to conform to the expected population of submissions. In particular, the topics of PF posts are weighted very different from those of arXiv eprints.

    Coming at the same point from a different direction: "Topology & Analysis" covers a lot of ground, but based upon what I've seen at PF, questions in this area are under-represented wrt the importance and breadth of these areas, so such a heading might be appropriate at PF.

    No matter what headings one comes up with, newbies will be confused since many questions overlap (there are so many interconnections in mathematics!). Still, one can hope by judicious terminology to minimize gross misplacement of threads. I might make some specific recommendations after I've had a chance to think it over. I'd be interested to hear the thoughts of mathwonk and Matt Grime as well!

    OTH, why wait? Here are my initial suggestions, based upon very little thought (!):
    • rename "Linear & Abstract Algebra" as "Linear and Modern Algebra" (the latter embraces groups, rings, fields, group actions, and many other topics which are rarely the subject of PF posts--- such as tensor algebra; questions about the latter would probably be misplaced in the next but they are rare so this would be tolerable),
    • rename "Tensor Analysis & Differential Geometry" as "Manifolds and Geometry" (theory of manifolds is usually taken to embrace calculus on manifolds, aka exterior calculus, and differential geometry is founded in part upon tensor calculus),
    • keep "Differential Equations" (well-defined area which gets a lot of traffic), or rename it "Differential Equations and Dynamical Systems" (this might induce newbies with a question about ergodic theory to put their post here instead of in "Topology and Analysis", but that might be acceptable and even more or less valid),
    • rename "Set Theory, Logic, Probability, Statistics" as "Probability Theory and Statistics",
    • rename "Number Theory" as "Combinatorics, Graphs, and Number Theory" (number theory gets too much traffic; there are two few questions about graphs and combinatorics, but combinatorics and graph theory are often taught as one course and often with some number theory tossed into the mix),
    • rename "General Math" as "Foundations" (embraces mathematical logic, set theory and some category theory),
    • split "Calculus and Analysis" into "Topology and Analysis" and, wince wince, "Calculus and All Other Math" (many questions in calculus should probably go to "Homework Help" but that notice could be a sticky).
    Some kind of "grab bag" seems neccessary, and since Calculus probably attracts the greatest number of frantic newbies...

    COI notice: I have an obvious interest in promoting dynamical systems, but I resisted the urge to propose a new forum just for that subject, since I acknowlege that despite its importance it attracts few questions at PF. I can't help predicting that if we renamed "Differential Equations" as "Differential Equations and Dynamical Systems", questions about dynamical systems might in fact appear more often, which would probably be a good thing! IOW, I predict that to some extent changing forum names at PF might actually noticeably change the nature of the traffic!

    As a random test, suppose someone hears that the Szemeredi Lemma is the most important result in all of mathematics; where would he inquire about that? Depending upon the context in which he has encountered it, his post could go to "Combinatorics, Graphs, and Number Theory" or "Probability Theory and Statistics" or "Topology and Analysis". Which illustrates the near impossibility of creating any entirely satisfactory classification. Still, my initial feeling is that the categories I tenatively proposed above correspond fairly well to PF traffic over the past year.
     
    Last edited: Nov 3, 2007
  8. Nov 5, 2007 #7

    Integral

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    Chris,
    Thanks for your input. I like your suggestions and would support the changes you propose, inculding the addition of "dynamical systems" to the DE forum title.
     
  9. Nov 5, 2007 #8

    Chris Hillman

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    Thanks, Integral! :smile:

    I think it's possible that some newbies who are confused about where to place their question may wind up not posting at all :frown: That's what I was getting at when I suggested that improving the index might improve traffic.

    Another thought occurs: I suspect that the lurkers least likely to post are the cautious thoughtful types who know their own limitations and who don't like to say anything which might prove wrong or even foolish. I sometimes get the impression that the n00bs most likely to delurk are too young/inexperienced/manic to read good responses with sufficient care (given that quite a few simple questions turn out to involve subtle mathematical issues.) If so, I doubt there is any cure for this "self-selection phenomenon".
     
  10. Nov 5, 2007 #9

    JasonRox

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    I like Chris's layout too although I think "General" Math should remain and not changed to "Foundations".
     
  11. Nov 15, 2007 #10

    Chris Hillman

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    Jason and I had some further pertinent comments in another thread; see [post=1503282]this post[/post] and my reply.

    Moonbear, I have been too lazy to PM mathwonk or Matt Grime but I recommend seeking there input too. I think renaming/reorganizing is probably a good idea, but only after input from these knowledgeable and experienced (at PF) mathematicians.
     
  12. Nov 16, 2007 #11
    Eventhough Topology and Analysis are similar I consider them seperate. I would put Topology under Geometry section.
     
  13. Nov 17, 2007 #12

    Chris Hillman

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    Your honors, I object!
    • Most students first encounter topology in a general topology course, which typically focus on constructions whcih are useful in analysis. This is the most likely source of questions from newbies on topology.
    • Topological issues are very important in analysis.
    • Topological issues are also very important in geometry (which is currently usually understood to encompass the theory of manifolds, differential geometry, vector bundles, and related constructions), but students who know enough to have questions about de Rham cohomology will, I hope, see that their post should go in the proposed "Geometry" forum.
    But as Kummer's comment shows, mathematics is far too varied and interconnected to succumb gracefully to any attempt to categorize its body parts.
     
  14. Nov 19, 2007 #13

    Chris Hillman

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    Another PF user independently (?) suggests reorganizing math forums at PF

    Ehrenfest has posted some new comments which I think should be moved to this thread [post=1510174]here[/post] (see also subsequent discussion).
     
  15. Nov 19, 2007 #14

    JasonRox

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    But Topology needs to be put somewhere. The topic is a very large topic.

    It's still surprising that Topology isn't listed anywhere yet.
     
  16. Nov 19, 2007 #15

    Chris Hillman

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    I asked the moderators to combine the three threads to no avail, but to repeat what I wrote above and in one of the other threads:

    So I tentatively proposed "Topology and Analysis". See also my comments in the other threads, where I argued against "Topology and Geometry". And sorry for the three threads but it's not my fault--- I tried! Note that, as it happens, my proposal would also address the issue raised by Ehrenfest.
     
  17. Nov 19, 2007 #16
    Weyl said the angel of topology and the devil of algebra fights for the heart and soul of every branch of mathematics. So topology must be big to say the least.
     
  18. Nov 19, 2007 #17

    JasonRox

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    Where do you get all these little fun facts?
     
  19. Nov 19, 2007 #18

    Chris Hillman

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  20. Nov 19, 2007 #19

    mathwonk

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    i don't really mind if forums are organized based on frequency of posting, but logially it is nonsense. i.e. a separate topic should logically remain mathematically separate even if it is unpopular. i.e. this is aNOTHER INSTANCE OF BUREAUCRacy dictating scientific reality.

    but i can live with it. we are dependent on the existence of the forum and someone has to do the grunt work.
     
  21. Nov 19, 2007 #20
    The opening quote to Micheal Artin's 'Algebra' book.
     
  22. Nov 20, 2007 #21

    matt grime

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    Thanks to Chris for pointing me here.

    I don't have any useful suggestions at this stage, since I've only just thought about it. But here are some observations on current posting issues that need to be eradicated.

    1. Posting of point-set topology questions in the set theory forum, or general math, when if anything it should be analysis.

    2. The dubious position of measure theory posts (general, analysis, probability)

    3. Algebraic questions not getting posted in algebra.

    My only constructive comment right now is that we should not label the subforums according to the American university undergraduate's expectation of mathematics as a subsidiary subject to engineering.

    If you were to force me to make a pie in the sky suggestion right away (and I should be something positive, I suppose), then here's a whacky idea, based upon a 'bigger picture' of mathematics:

    1. Introductory mathematics (What currently passes for "analysis")
    2. Algebraic Topology and Geometry
    3. Differential Equations and Dynamical Systems
    4. Measure Theory and Probability
    5. Foundations of Mathematics (Logic, sets, categories)
    6. Number Theory (if we must - this seems to be the least used forum, and the one with the highest crackpot hit rate).

    And possibly a thread called "How do I do this integral, differentiate this, or find the limit as (x,y) tends to (0,0)", which take up a disproportianate amount of space.
     
  23. Nov 20, 2007 #22
    Matt, where would differential topology go?

    More importantly, where would algebra go?
     
  24. Nov 20, 2007 #23

    matt grime

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    Oh for pity's sake, it wasn't supposed to be exhaustive. If we include representation theory with Alg. geom and Topology that will do. Moreover, any mathematical question on 'differential geometry' can be considered part of alg top or alg geom, and anything on general relativity and tensors can be shipped off to physics instead, where it will have a much better group of people to answer questions on it.


    I would also propose a ban on pointless debates like which subject is better, whilst we're at it.
     
  25. Nov 20, 2007 #24

    Evo

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    Those seem good. I don't understand why the math forums lack the descriptions that you see, for instance, with forum headings in physics and engineering. If we did this, it would certainly help students decide which forum might be best to start with.
     
    Last edited: Nov 20, 2007
  26. Nov 20, 2007 #25

    Chris Hillman

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    Yes, I've been arguing that something like this would be an essential component of making the proposed reorganization work better than the current organization.

    Let me try to reconcile my proposal with Matt's:

    • Calculus and Miscellaneous
    • Combinatorics, Graphs, and Number Theory
    • Differential Equations and Dynamical Systems
    • Linear and Modern Algebra
    • Foundations (Logic, Sets, Categories)
    • Manifolds and Geometry
    • Measure Theory, Probability, Information Theory, Statistics
    • Topology and Analysis

    The biggest different between our proposals appear to be that my title "Manifolds and Geometry" would mostly subsume his "Algebraic Topology and Geometry", plus as discussed previously I advocate broadening "Number Theory" to include some other topics (combinatorics, graph theory) which are often taught in the same UG courses alongside number theory. Also, as discussed above, I propose to broaden "Measure Theory and Probability" to include information theory and statistics.

    As per the discussion above, "Linear and Modern Algebra" and some of the other titles will look a bit odd to working mathematicians; they are compromises intended to head off anticipated misunderstandings by mathematical newbies who barely know what is a "matrix" is probably will not know that groups, rings, fields, modules and vector spaces are all of a piece.

    Matt, can you live with this? Mathwonk?
     
    Last edited: Nov 20, 2007
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