User talk:Shellgirl

Welcome to my talk page!

Welcome

Hello, Shellgirl, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are some pages that you might find helpful:

I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes (~~~~); this will automatically produce your name and the date. If you need help, check out Wikipedia:Questions, ask me on my talk page, or ask your question and then place {{helpme}} after the question on your talk page. Again, welcome!

And don't forget, the edit summary is your friend. :) – Oleg Alexandrov (talk) 16:34, 4 April 2007 (UTC)[reply]

Jessica responds

Hi Oleg! I put your welcome notice at the bottom of my discussion page, mainly because you referred to me as basepagename and therefore I assumed I was getting an automatic message. Since it now appears at the top again, I am entertaining the thought that this could be a personal welcome. I like the pictures you have on the amoeba page, by the way. If you happen to read this, what do you think of exercises in wikipedia, or alternatively developing supporting exercises at wikiversity? If you don't read this, I'll probably come ask you this question at some point ... —The preceding unsigned comment was added by Shellgirl (talk • contribs).

Yeah, this is a personal welcome (well, I welcome a lot of people, so the welcome process is kind of semi-automated in my head, but still, it was me and not a bot). The basename thing, well, let's say it's a long story why it is there.

I did not move my welcome back up, I guess that's Geometry guy's doing. :)

I am glad you liked the amoeba pictures.

I don't quite agree with exercises in Wikipedia articles, that's encyclopedic I think. Perhaps they could be reworded as properties (that is, without telling the reader to solve them). But I leave it up to you.

Cheers, Oleg Alexandrov (talk) 04:43, 5 April 2007 (UTC)[reply]

Guilty as charged ;) I was just following the (strange-at-first) WP convention to put the newest threads at the bottom. Anyway, you can always check the history, where, as Oleg says, "the edit summary is your friend", even on talk pages! Geometry guy 10:56, 5 April 2007 (UTC)[reply]

Best linear approximation

And a warm welcome from me too! I see you have already made some useful edits to several pages. Concerning Derivative, although I am a big fan of the "best linear approximation" point of view, I wasn't convinced when Innerproduct added this paragraph recently, as the first section is already rather overloaded, and linear approximation is discussed in a later paragraph. I would be inclined to delete it, or use it to elaborate the final paragraph of the "Jacobian and differential" section. Let me know what you think, either here, or we can take the discussion over to Talk:derivative.

My other reservation about this is (as you have probably seen for yourself) that Big O notation is something of a mess from a mathematical point of view, since it is heavily geared towards the computer science perspective: if you feel the impulse to improve it at some point, I encourage you to be bold! I hope you have fun here, anyway. Geometry guy 17:22, 4 April 2007 (UTC)[reply]

Jessica replies Hi geometry guy, and thanks for the welcome!

I like the linear approximation definition, since it is a geometric intuition that persists through all levels of sophistication and at the same time is accessible to novices. For the same reason, I don't like the use of little o notation in this paragraph, since this is likely to pull a novice mathematician out of context -- especially because this notation isn't used in most calculus classes, as far as I am aware. I preserved it from an earlier edition, but now I think I'll go back and take it out.

It seems like the best place to make edits is at the edge of my understanding. That is, when I first understand something clearly and well -- perhaps with the help of wikipedia -- and there is some change that I think would have helped out my process of comprehension. But of course, this takes a little more nerve.

I am hesitant to do a lot of editing on big O notation, precisely because I am a mathematician and not a computer scientist. Although I guess there are certainly times when I use big O notation (for example when examining asymptotic behavior of stastical physics models).

David Mumford has an interesting discussion about presenting calculus where he quotes Lancelot Hogben's introduction to the derivative from Mathematics for the Millions, and where he writes that "virtually no sentence in English not written in mathematical jargon has an unambiguous interpretation not depending on the use of common sense by the listener." He also points out that once a precise definition is given, "most students become convinced something very complicated must be going on," and that this belief can even be exacerbated by also presenting a simple description of the meaning (i.e., they don't get the precise statement and now additionally they don't get the connection between the precise statement and the intuitive description). His article is at

http://www.dam.brown.edu/people/mumford/Papers/CalcReform.pdf.

On a subject up your alley. Suppose you have a connection on the tangent bundle of a smooth complex manifold, not inherited a priori from a metric but just a bundle whose direct sum with the vertical sub-bundle gives the whole tangent bundle of the tangent bundle. If parallel transport by this connection gives complex linear maps on the tangent spaces of the manifold, does it follow that the connection induces a Riemannian metric?

Cheers,

Shellgirl 21:55, 4 April 2007 (UTC)[reply]

Hi Jessica. Yes, if you take out the little o notation, I am sure it will be less likely to be deleted by another editor (e.g. me ;) ). Your attitude to making new edits at the edge of your understanding is great. It should take less nerve, because you will be less "emotionally committed" to your edit (forgive the phrase). Go for it, I say: this is what WP:BB is all about. The worst that can happen is a revert.

As for big O, this article really needs a mathematician's point of view: after all, mathematics has been using this notation long before computers existed. I will back up any mathematician who tries to improve this article, and encourage others to join in likewise.

Finally your question. No, complex linear connections do not generally induce Riemannian metrics. For one thing, the holonomy group had better be compact. Geometry guy 22:26, 4 April 2007 (UTC)[reply]

PS. Hope you don't mind me wikifying a bit your answer. I've been here since January, and it took me a while to get familiar...

Jessica writes

Hi geometry guy --

Wow. I just read the discussion on the derivative. I don't mind at all if you take the section out. What a tricky thing to write! I got all tongue-twisted trying to figure out what would to write in a way that was precise and also clear to the novice. I don't think I succeeded. Since teaching calculus is not one of my favorite activities, I think I'll switch over to other topics.

Regarding connections: this is what I thought; it came up on the Kahler_manifold page, where I've now added a small clarifying edit.

Jessica

Well spotted! As for derivative, yes this stuff is hard to write - fortunately we are writing an encyclopedia, not a textbook, so the key is to be accessible rather than pedagogical, which is a bit less onerous. Anyway, I am currently trying to resist the feeling of ownership of the article, since I did quite a lot of work on it recently, so I will leave your edits for a bit longer. If no one else takes it up, I will try and find a way to weave the linear approximation point of view into the main definition or the Jacobian section. Geometry guy 11:08, 5 April 2007 (UTC)[reply]

I've now reworked the definition section to incorporate the linear approximation point of view. I also took the opportunity afforded by the mention of Taylor series to expand the higher derivatives section, which was a weak-point in the article in my view. Your comments would be very welcome. Geometry guy 14:50, 6 April 2007 (UTC)[reply]

Inclusion of exercises

Jessica writes In my edit on circle inversions I added two exercises, which I am guessing are not really in the encyclopedic spirit of wikipedia. On the other hand, I think embedded exercises would make the pages even more useful. Maybe the exercises could be stated on wikipedia, and then linked to wikiversity (which seems like an interesting idea, although not well populated yet) where further explanations, hints, solutions, and connections to other exercises could be available.

Shellgirl 22:07, 4 April 2007 (UTC)[reply]

Model theory

Hi Shellgirl,

I have some concerns about your recent edits at model theory. I will elaborate on the talk page of that article. --Trovatore 00:06, 6 April 2007 (UTC)[reply]

Re: Redirect

I replied on my talk page. Oleg Alexandrov (talk) 03:07, 6 April 2007 (UTC)[reply]

Boustrophedon transform

Hi Jessica. Welcome here. For some reason, I wrote an article here on the Boustrophedon transform with a lot of help from a certain paper by M, S & W. Would you mind having a look and making sure I didn't write anything stupid? I can already see that I used a different spelling of the b-word. Feel free to rip the article apart. -- Jitse Niesen (talk) 07:13, 10 April 2007 (UTC)[reply]