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Incomplete math classification on this forum

  1. Sep 27, 2016 #1


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    I think that classification of math into subforums on this math forum is highly incomplete.

    For instance, suppose that one wants to discuss number theory or discrete mathematics. Is this supposed to belong to general math? What if one wants to discuss subtleties of the last Fermat theorem or of Ramsey theory, does it really belong to general math?

    Or computation theory, like P=NP conjecture, on which subforum should this be discussed?

    Or discrete dynamical systems? Since they are discrete, the differential equations subforum does not seem appropriate.

    Or algebraic geometry, should it be considered a branch of differential geometry?

    It is also quite unnatural to have logic and set theory in the same subforum with probability and statistics.

    Am I the only one who thinks that math forum should be significantly reorganized?
  2. jcsd
  3. Sep 27, 2016 #2
    You're right. But you should take into account that many topics just don't get many questions. It would be a bit silly to have a forum that only gets 1 question per month. So we need to compromise. That is the rationale behind the current structure.

    But please, if you have a better way of ordering this, I am very willing to discuss this with you and recommending Greg to make the appropriate changes. But keep in mind that you must order it in at most 6 forums that should get a decent amount of traffic and new threads.
  4. Sep 27, 2016 #3


    Staff: Mentor

    I think you're right. However, @greg has to balance things between:
    - too many forums and people will get confused
    - too little and we don't know where to place threads.

    The current scheme seems to parallel math levels of learning.

    Taking a cue from Prof Elwes chapter organization in Math 1001, we could have:

    - Numbers
    - Geometry
    - Algebra
    - Discrete Math
    - Analysis
    - Logic
    - Metamathematics
    - Probability and Statistics
    - Mathematical Physics
    - Games and Recreation


    Alternatively, we could have fewer forums in math and use the post title tagging to define the topic more specifically.
    Last edited by a moderator: May 8, 2017
  5. Sep 27, 2016 #4


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    What about subforums in the math subforums? For example, make a subforum geometry, and there subforums differential geometry, analytic geometry, algebraic geometry, ...
  6. Sep 27, 2016 #5
    Way too complicated. People don't want to navigate through so many subforums.
  7. Sep 27, 2016 #6


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    I suggest we have 10 forums and let @Greg Bernhardt decide on the number base.
    Last edited: Sep 27, 2016
  8. Sep 27, 2016 #7


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    I guess you mean @Greg Bernhardt, not some random greg user :wink:

    I believe we discussed the way math forum is divided not that long ago (well, could be several years) and it is already a compromise between granularity and traffic.
  9. Sep 27, 2016 #8
    It was fairly long ago. I was the one who proposed the current structure. I think it works rather well, but I'm open to suggestions.
  10. Sep 27, 2016 #9


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    In my opinion similar could be said about any forum, esp. for other science or economic questions which are posted from time to time. Sometimes they are related to game theory and end up in the probability section, which is close. And I wonder why there aren't more questions about macro economy which is highly mathematical. Perhaps because there isn't a forum at all?

    But even in physics it's not always clear. Sometimes I find interesting articles on the internet I like to share. They are then are pushed around, because there isn't a unique characterization. E.g. https://www.physicsforums.com/threads/100th-anniversary-of-the-sackurtetrode-equation.885869/

    Is it really classical physics? Or thermodynamics, which would have a right to claim its own section, too? Or quantum mechanics? Or simply something historic for which there is no special thread?

    I think we all have had similar difficulties with some books to put them in an appropriate place on the shelf. I know that one cannot justify one non-optimal situation with another. However, in total its a more complex optimization problem than it looks like at first glance. And as we know, improvement on one goal might lead to a deterioration on another.
    Last edited: Sep 27, 2016
  11. Sep 27, 2016 #10


    Staff: Mentor

  12. Sep 27, 2016 #11
    No doubt forum category structure has its limitations and sacrifices have to be made. We've tried to optimize the structure as much as possible to make browsing as compact and simple as possible while allowing adequate breadth of categories to choose. Sure we could list every science and math topic known to man, but it would be absolute hell to navigate. We're not against possible tweaks, but I think right now the current iteration works very well. Any topics that feel uncategorized should go in the "General" category.

    Some forums do have prefixes to narrow topics better. However I still think they should be secondary because the forum category structure is still very good for random browsing.
  13. Sep 27, 2016 #12


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    Maybe you can provide a sticky thread somewhere that explains where people should ask their equations about subjects that are less clear to which category they belong.
  14. Sep 27, 2016 #13
    The few that are unclear are pretty unlikely to read the sticky. Easier to just move them if needed. Just the way the world works :)
  15. Sep 27, 2016 #14


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    Could you write an Insight about this once?
  16. Sep 27, 2016 #15
    It would fill a book :D
  17. Sep 27, 2016 #16


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    Staff: Mentor

    Or just 2:44

    (I know it's not the original, but I loved her hair ... and the memories.)
  18. Sep 28, 2016 #17


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    Here is my proposal of the structure, which takes into account both the current number of pages in existing subforums and the natural division of mathematics into branches.

    1. General Math
    2. Calculus
    3. Algebra (linear and abstract)
    4. Analysis and Math Modelling (including differential equations, dynamical systems, game theory, etc.)
    5. Geometry and Topology
    6. Probability, Statistics, Discrete Math and Number Theory
    7. Computation and Math Software (including LaTeX)
    8. Foundations (logic, set theory, category theory, philosophy)
    Last edited: Sep 28, 2016
  19. Sep 28, 2016 #18


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    I don't like it. With such a strategy, some advanced topics may easily remain unnoticed by experts in the field who do not regularly read "general math". General math should be reserved for non-advanced stuff like elementary math, popular math, recreational math or history of math.

    What do you think about my proposed structure in the post above? Note that the number of subforums is the same as before, and yet, as far as I can see, no major branch of mathematics is missing.
    Last edited: Sep 28, 2016
  20. Sep 28, 2016 #19


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    I have several objections to this particular classification:

    - Elementary math is missing.

    - Topology is missing.

    - Computation is missing.

    - Logic and Metamathematics naturally fit together.

    - Number theory (if this is what one means by "Numbers") and Discrete Math can also fit together.

    - I am a theoretical physicist, but there is no need for "Mathematical Physics" because each mathematical aspect of physics naturally fits to some "pure" branch of mathematics such as analysis (e.g. special functions, advanced calculus, differential equations, or functional analysis), algebra (especially group theory), geometry or topology.

    - If by "Games" one means game theory, this is a very serious branch of mathematics which has nothing to do with popular computer games and does not fit well with Recreation.
    Last edited: Sep 28, 2016
  21. Sep 28, 2016 #20


    Staff: Mentor

    Okay so here's the further chapter breakdown from MAth 1001 by Prof Elwes:
    Code (Text):

    - basics
    - arithmetic
    - number systems
    - rational numbers
    - factors and multiples
    - induction
    - representation of numbers
    - transcendental numbers
    - ruler and compass
    - constructions
    - diophantine equations
    - prime numbers

    - euclidean geometry
    - triangles
    - circles
    - polygons and polyhedra
    - transformations
    - tessellations
    - curves and surfaces
    - polar coordinates
    - discrete geometry
    - differential geometry
    - topology
    - knot theory
    - non-euclidean geometry
    - algebraic topology
    - algebraic geometry
    - diophantine geometry

    - letters for numbers
    - equations
    - vectors and matrices
    - group theory
    - abstract algebra

    - combinatorics
    - graph theory
    - ramsey theory

    - continuity
    - differential calculus
    - integral calculus
    - complex analysis
    - power series
    - exponentiation
    - fractals
    - dynamical systems
    - differential equations
    - fourier analysis

    - basic logic
    - science of deduction
    - set theory
    - hilberts program
    - complexity theory
    - computability theory
    - model theory
    - uncertainty and paradoxes

    - what mathematicians do
    - mathematics and technology
    - philosophies of mathematics

    - statistics
    - probability
    - probability distributions
    - stochastic processes
    - cryptography

    - newtonian mechanics
    - waves
    - fields and flows
    - special relativity
    - gravity
    - quantum mechanics
    - quantum field theory

    - game theory
    - fibonacci
    - puzzles and perplexities
    Anyway, this is one mathematicians (Prof Elwes) take on organizing the various topics of mathematics.

    However right away you can see that is can get very broad and very deep and in the PF case most questions will be what students encounter in high school and undergraduate math for the STEM courses and we hit only a couple of the topics in a big way.
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