Good Math/Bad Math

Saturday, June 03, 2006

Reader poll about topics; and some site maintenance stuff

I'm going to be doing a bit of work on the site this weekend to try to create a couple of indices for some of the series of posts that I've written. (After three months, I'm starting to realize that the site could use a bit or organization :-) ) So there's going to be a flurry of activity around here that's not terribly interesting, but it will make things easier to find as a result.

I'm also trying to decide what subjects I should write about next. I've got a few possibilities in mind, and I thought I'd ask you folks what you're interested in. Let me know which of the following interest you most; or feel free to "write in" your own suggestions.

  1. Topology. I'm far from an expert on the subject, but it's an interesting one, and I'm willing to study up and write about it, so long as people are patient with me when I inevitably make mistakes.
  2. More group theory. I've got enough time to be able to continue the series of posts on group theory.
  3. Modal logics. In the whole lambda calculus thing, I mentioned the idea of modal logics. There are some really fascinating modal logics (I particularly like temporal and linear logics) that allow you to reason in different ways.
  4. Graph theory. Graph theory is a fascinating area of discrete math that think is a lot of fun.
  5. Category theory. Category theory is similar to group theory; it's one of those fields based on abstracting something down to its bare essentials. In cat theory, it's the concept of a function as a mapping from one thing to another.

22 Comments:

  • Graph theory looks pretty good.

    I am interested in the maths behind good evolution science, as opposed to the crap creationsist have put out. How about touching on population genetics, ecology (eg biodiversity), or cladistics?

    Keep up the good work.

    By Anonymous igor eduardo kupfer, at 12:57 PM  

  • Topology gets my vote. I'd love to see your take on the ideas there. Everyone is familiar with the idea of geometry from high school, topology is the next step.

    Also, "computational topology" is a relatively young field in CS right now. I'm sure the math would be easily relatable to the current work on Morse complexes, geometric modelling and maybe even algorithms in knot theory

    By Anonymous Chris, at 1:32 PM  

  • It's all fun but graph theory and topology would be near the top of my list.

    By Anonymous BMurray, at 1:34 PM  

  • Graph theory gets my vote, just because I find it more fun to "play with on paper."

    By Anonymous allan, at 1:44 PM  

  • My vote goes to graph theory, but topology is very close in the last poll.

    By Anonymous Raimondi, at 4:14 PM  

  • Graph theory or topology.

    By Anonymous Jane, at 4:38 PM  

  • Category theory! I've been trying to get my head round that (in a "so what's the point again?" sense) for some time. Also, can I add Number Theory to your list of things to write about?

    IEK: I'm a complete newbie in the field of population genetics, but I'm really enjoying the book "Population Genetics: a concise guide" (2nd ed.) by John Gillespie. Very well-written, and no background knowledge needed.

    By Blogger Lifewish, at 5:29 PM  

  • What about knot theory? I read Alexei Sossinsky's book on the subject (comments, second from last in the post) but got bogged down in the chapters on Vassiliev invariants...

    By Blogger James, at 5:38 PM  

  • james:

    Unfortunately, I know absolutely nothing about knot theory. It sounds interesting; I'll get a book on it when I get a chance :-), so maybe sometime in the future. But for now, I just don't know enough to be able to do it.

    By Blogger MarkCC, at 7:49 PM  

  • You did not mention statistics or complex nonlinear systems (i.e. chaos) which would be at the top of my list

    By Anonymous steve, at 9:36 PM  

  • steve:

    I deliberately left statistics off the list. I know enough stats to shred most of the trashy ways that people misuse it in bad arguments. But in general, I actually find statistics as a field of mathematical science to be really dull. I'm just not interested enough to be able to write about it in detail.

    Chaos theory is something that's interesting to me, but I don't know enough about it yet to write about it. At some point, I'll get some books and read up. You can expect it to pop up here at some point, but not too soon.

    By Blogger MarkCC, at 9:43 PM  

  • as a reader who enjoys gmbm as a favourite, I'd say topology first of all, and cat theory second of all. both groups are alive, and they seem to be able to 'collide' :)

    By Anonymous Marcus, at 9:57 PM  

  • I'm a bit curious about topology, since you mentioned it had something to do with the idea of "bigger" infinities.

    The good math behind evolution and bad math behind IDiotry is always a draw for me, though I can imagine it getting tiring.

    By Blogger Bronze Dog, at 1:51 PM  

  • James + Mark:

    I don't know what your background is, but here are some recommendations for knot theory books:
    1) Adams - the knot book: very naive introduction assuming very basic math. I don't really like it since I think it's too naive, but I'm working on a Ph.D. in knot theory and therefore the wrong person to ask about basic books.
    2) Lickorish - An introduction to knot theory: good book for people with some knowledge of algebraic topology and topology.
    3) Rolfsen : knots and links. An introduction to algebraic topology via knot theory - can be a bit outdated but great for starters.
    4) Ohtsuki: Quantum invariants: the best source on Vassiliev invariants around. Quite advanced in tone, but doesn't assume too much information (good for beginning graduate students).

    By Anonymous ParanoidMarvin, at 10:40 AM  

  • Modular logic would interest me most, graph theory second - it is mentioned a lot. Topology and group theory I already have some little experience with. Category theory is described a little on Baez web site I think, and he is also a terrific educator. Perhaps the other items have web resources too, but as you do such a nice job, go for it!

    By Anonymous Torbjörn Larsson, at 12:10 PM  

  • Just to let people know how things are looking, here's the current tally, as of 6/5, 3:30pm.

    - Topology: 6
    - Group theory: 0
    - Modal Logic: 1
    - Graph theory: 6
    - Category theory: 1

    By Blogger MarkCC, at 3:33 PM  

  • I'd vote for graph theory. But I'd be even more interested in the applied mathematics of evolutionary theory. Perhaps they can be combined (as in a very recent Nature paper)

    By Anonymous The Reverent Bayes, at 4:53 PM  

  • Duh! _Modal_ logic, yes.

    By Anonymous Torbjörn Larsson, at 5:02 PM  

  • Does fuzzy logic fit into any of those? (I don't know, I'm a math-challenged physiologist). If not, then cat theory, group theory, and topology.

    By Blogger gonesavage, at 8:51 PM  

  • If you don't write about category theory, then by Gum I will. It's one of the topics which I am studying this summer in an effort to formalize my understanding of things I have only used or seen select aspects of.

    By Blogger Blake Stacey, at 9:08 PM  

  • Graph theory, please--it seems relevant to a lot of important social and techological ideas today.

    Thanks, and keep up the good work,

    ecv

    By Blogger e, at 1:19 AM  

  • 1) Category theory

    2) Graph theory

    When I was studying topology, it was taught in a way that didn't work for me. So I have some familiarity but also some annoyance about it. For group theory, I'm good. Modal logics is the least interesting to me of the bunch, but if you post it, I'll at least skim. :)

    By Blogger Julia, at 9:45 AM  

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