User talk:Geometry guy: Difference between revisions

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Please leave any comments below. I will reply here (from time to time...)

Welcome!

Hello, Geometry guy, 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 place {{helpme}} on your talk page and ask your question there. Again, welcome! Oleg Alexandrov (talk) 16:17, 7 February 2007 (UTC)[reply]

Thanks Oleg ;)

Math Wikiproject

Just wanted to let you know that the central place for math discussion on Wikipedia is Wikipedia talk:WikiProject Mathematics, in case you ever want to join discussions there or start any. Cheers, Oleg Alexandrov (talk)

Thanks Oleg :) Geometry guy 15:59, 10 February 2007 (UTC)[reply]

Pushforward and pullback

Hello all: I just relinked about fifty pages to pushforward, which has now been disambiguated. If I made a mistake for any of these, my apologies! Geometry guy 22:20, 11 February 2007 (UTC)[reply]

I also relinked a few pullback pages. Same apology applies! Geometry guy 00:12, 12 February 2007 (UTC)[reply]

let me second Oleg's welcome. thanks for your contributions. there was a short note in the vector bundle article about the present discussion being restricted to finite dimensional fibers. it was removed sometime ago. perhaps it is sensible to include the non-finite dimensional case. Mct mht 00:22, 12 February 2007 (UTC)[reply]

It could be worth mentioning. But over a finite dimensional base, or an infinite dimensional base? Geometry guy 00:58, 13 February 2007 (UTC)[reply]

Thanks for all you work on the pullback and pushforward pages! These are in much better shape now then they were. FYI: I've updated the commutative diagram on the pushforward page to match your new notation (you may have to refresh your cache before you see the changes). -- Fropuff 01:15, 12 February 2007 (UTC)[reply]

Thanks - I was hoping you would do that ;) Of course, I don't insist on my choice, but the notation is now at least fairly consistent over the articles tangent space, tangent bundle, pushforward (differential) and pullback (differential geometry), which is surely a desirable feature whatever notation is used. Geometry guy 11:45, 12 February 2007 (UTC)[reply]

Connection (vector bundle)

I've rolled out connection (vector bundle). Have a look. Feel free to butcher it if you want to. We can probably remove a good deal of overlapping material from the connection form page. -- Fropuff 07:13, 16 February 2007 (UTC)[reply]

Looks good! I will make some edits when I get time. So far only one notational issue springs to mind: for the exterior covariant derivative and curvature, I think it's better to superscript the connection, but I don't insist on it. Geometry guy 08:49, 16 February 2007 (UTC)[reply]

Now made some fairly minor edits - hopefully without any butchery - but I did them individually so they can be reverted fairly easily. Geometry guy 21:30, 1 March 2007 (UTC)[reply]

Welcome and suggestion

Hi Geometry guy,

Welcome to Wikipedia! I like what you're doing for the coordinate-system articles, a few of which I started rather hastily when I first joined. But may I offer some advice? Our audience here is not necessarily mathematics graduate students and professors, but rather lay-people who may have little or no training beyond basic calculus. Also, there may some professionals in other fields such as engineering and physics who may use a different nomenclature. Since we're writing encyclopedia articles and not review articles, I'd advise being cautious in using "scary" nomenclature (e.g., "submanifold" and "1-form") early in the article; I've at least tried to warm up the reader a little before hitting them with the most technical language. ;) Please accept this as friendly and kindly meant advice from a fellow lover of geometry, Willow 20:57, 19 February 2007 (UTC) (Geometry girl?)[reply]

Hello and thanks for the welcome and comments. Welcome to my fledgling user page. I agree entirely with your advice: I just wanted to get the terminology clear first. Anyway, I've reordered the article to make it more accessible to lay-people and those from other fields. But perhaps these people shouldn't be hit with D-dimensions either ;) so the rewrite starts in 3 dimensions, and proceeds to other dimensions later. Perhaps the article now needs to be renamed again! Anyway, let me know what you think, either here, or on the talk page for the article, or both. Geometry guy 21:57, 19 February 2007 (UTC)[reply]

Disk

See User talk:Ray gillespie#Disc or disk

Upright d for derivatives and differentials?

From User talk:86.11.118.108

Please do not do mass changes in Wikipedia articles replacing italic d with roman d in math notation. This was discussed before, and italic d is preferred. If you want to raise this topic again, please do so at Wikipedia talk:WikiProject Mathematics. Thanks. Oleg Alexandrov (talk) 03:36, 23 March 2007 (UTC)[reply]

I think Oleg is being a bit hard on you here: your edits were clearly in good faith and it takes a while to get into the spirit of wikipedia. Why not get an account and join the discussion? Geometry guy 11:16, 23 March 2007 (UTC)[reply]

Thank you!

Hi - no, he was right, because I am new and I didn't read up on policy. I have posted my thoughts on the discussion page, and I do take responsibility for the unsolicited edits; after all, I'd be quite annoyed if someone modified to their liking something I had worked hard on without even an explanation!

Thanks for the the support though; do see my explanation on the talk:Integral page - I think on Wikipedia in the mathematics markup there is a lot to be gained from the Roman d. I never knew I would be so passionate about formatting as I have become!!! I will create an account, and I hope to be more constructive in future.

Thank you very much for the support!

Simon

And here I am with the account, and I shall hereby stop spamming your talk page. Thanks once again. Psymun 19:37, 24 March 2007 (UTC)[reply]

Welcome to wikipedia and congratulations on getting an account! Talk is not spam, but is encouraged: it helps us users work together rather than against each other. I've copied your talk from the anonymous page over here too. Wikipedia, especially in maths, is generally a nice and friendly place, but you sometimes have to take the rough with the smooth, even in calculus! Geometry guy 20:05, 24 March 2007 (UTC)[reply]

Plücker (and Grassmann) coordinates

Hello again, and thank you for providing a voice of reason in a chicken-or-egg type discussion. It was very frustrating to run into someone who denies the facts and twists the meanings to promote a pet point of view. Plücker embedding should definitely be written, but given the sensibilities, I won't do it myself. Arcfrk 21:08, 27 March 2007 (UTC)[reply]

You are very welcome. I share your frustration that a fundamental article like Plücker coordinates is overwhelmed by details coming from a computer graphics perspective, but these things sort themselves out in the long run, through forks and subarticles. (Let me remind you of Derivative, where I hope some progress is being made - the article is no longer at least, one third devoted to notation.) But, as I am fond of saying (especially to myself, as a reminder when I stray), wikipedia is an encyclopedia, not a math textbook, and I guess from what you have said before that you like to emphasise the same thing. Anyway, please don't underestimate KSmrq, who is an experienced editor with (in my view, from what I have seen) a nice mixture of mathematical expertise and a good idea of what an encyclopedic math article should be about. The comments on your page, even if they were written in a frustrated moment, contain some good advice. I actually prefer to post my area of expertise on my user page, as it helps me resist the temptation to argue from authority, rather than demonstrate my expertise through my knowledge of the facts (anyone can check my user page if they want to - in any case it proves nothing, which is one reason I like to stay anonymous, so my contribs are judged at face value). I hope you continue to have fun - it's an interesting place! Geometry guy 22:43, 27 March 2007 (UTC)[reply]

I saw that you've started an article on Plücker embedding, which was long overdue, and hope that it will develop smoothly! I actually looked at Category:Differential calculus per your suggestion, the two main articles there were indeed in messy state(s), and more than I could handle at the moment, so I didn't do anything about them. Thanks for your tip concerning posting the area of expertise on the user page, I haven't thought about it in those terms. My rationale had been not to post any identifying information, especially, since it's unnecessary for Wikipedia project; but I see how it could have its advantages. As for the experienced editor that you've mentioned, I had been quite impressed by his contributions, but after his conduct in Plücker coordinates discussion, he is off my list of reasonable people (as in: exercising one's reason in a proper manner; those with whom it makes sense to employ reasoning or argument). By the way, if you have time, can you, please, take a look at Abstract algebra#History and examples that I've written and tell me your opinion? Best, Arcfrk 01:30, 28 March 2007 (UTC)[reply]

Well it is a start. Thanks for looking at the calculus stuff: my main problem is that I have entered a strange world in which calculus is done either in one variable or in Banach spaces - a serious reality check is needed here! Anyway. please try not to rush to judgement with fellow editors: your comments can be quite provocative, generally in a positive way, but this doesn't always bring out the best in other editors. Meanwhile, I hope I will have a chance to look at the abstract algebra stuff soon. Geometry guy 01:49, 28 March 2007 (UTC)[reply]

Abstract algebra

(From above) ... By the way, if you have time, can you, please, take a look at Abstract algebra#History and examples that I've written and tell me your opinion? Best, Arcfrk 01:30, 28 March 2007 (UTC)[reply]

I had a quick click on your link. You've added an impressive amount of detailed content: possibly a case for a subarticle, but have a look at History of algebra, which is rather disconnected from the rest of wikipedia right now, and let me know what you think. Also, to be pedantic, footnotes go at the end of the page - I'll fix it for now. Geometry guy 02:13, 28 March 2007 (UTC)[reply]

I read History of algebra, it's an impressive piece of work. In fact, a secondary goal of mine was to fill the void it left concerning abstract algebra. But the primary question is, does the section that I added help to understand what abstract algebra is about? My concern is how to keep a balance between merely providing a list of topics and overwhelming the reader with explanations for which (s)he may be unprepared; in other words, is this section useful to non-algebraists? Arcfrk 05:20, 28 March 2007 (UTC)[reply]

I've read this in more detail now. You've added a lot of nice content here. I especially like the introductory paragraphs. As for your question, well the honest answer is "probably not". The intro does to some extent, but the group theory archetype rather overwhelms the reader with names of people and mathematical concepts, and might leave a non-algebraist wondering "if abstract groups are all permutation groups then what was the point of the abstraction?" However, the problem may be that this section is trying to do too much (another platitude of mine): it is hard to cover history, motivation and examples all at once as these themes get in the way of each other. Perhaps there should be a separate section on motivation? Alternatively, this article could defer to History of abstract algebra for all the names and dates, and concentrate instead on the themes. Also I wonder whether the example of attempts to prove Fermat's last theorem leading to rings, ideals and the ideal class group would be a good way in for the general reader?

Anyway, this is great start! Geometry guy 17:10, 28 March 2007 (UTC)[reply]

Thank you for looking at it! Yes, I was rightly worried that it's a bit too much too fast, but cowardly tried to silence my inner editor nonetheless. Some of the group theory related stuff can go into (non-existent) history of abstract algebra, but at the moment I don't have necessary time and resources to write a decent overview of the rest of the history. Probably, you are right that Fermat's last theorem is a better model for exposition of genesis of abstract algebra for more general audience. I'll get around to it in a while, and, please, let me know if you have any more ideas. Arcfrk 03:45, 29 March 2007 (UTC)[reply]

Math class

I added a few maths classifications to some articles I've been involved with. Rather than leave them as unclassified, I made an attempt to rate them myself. Please have a look (anyone) and change them if you want (I may not have been objective). The comment I have left is very bland in most cases, so please replace it with some more concrete suggestions for improvements. Geometry guy 09:35, 30 March 2007 (UTC)[reply]

Disambiguation for Mathieu group numbers

I saw your edits to M22, M23, and M24. I think your descriptions were the best anyone had come up with yet. I only made some stylistic changes to the entries (I removed periods and parentheses), but I otherwise left them unchanged. Thank you for the assistance. Dr. Submillimeter 15:00, 30 March 2007 (UTC)[reply]

Thanks, and sorry about the misplaced period! I also edited M11 and M12. The final form of the dab is not so important, but could you make sure it stays consistent across the five articles? Thanks. Geometry guy 15:05, 30 March 2007 (UTC)[reply]

I will do that. I am currently cruising through all disambiguation links between M1 and M110 to clean them up. Many of the pages violated multiple guidelines at MoS:DAB. Again, thank you for the explanation on the disambiguation pages.

As for Mathieu group, it at least looks like an effort to explain this concept in layman's terms. It's an improvement over the previous version of the article, although it is still tough to follow. Thank you for working on it. (If it makes you feel any better, I see the same problems with physics articles.) I leave it to you to decide on whether to remove the "technical" template. Dr. Submillimeter 19:37, 30 March 2007 (UTC)[reply]

Unfortunately, some articles are just inherently technical, so the best we can hope to do is provide the links to more basic articles in as coherent a way as possible. Anyway, I am not an expert on group theory. I expect an expert will remove the "technical" template at some point, but hopefully after improving the article further ;) Meanwhile your efforts on the M-article dabs are surely very worthwhile. Although to be really pedantic about MoS:DAB#Order of entries, it does give guidelines for ordering articles other than order of appearance in Google searches. Even as a UK guy, I'm not sure that UK motorways are particularly important encyclopaedic entries. I (for one) would certainly be happy if the Messier objects appeared high on the list! Geometry guy 19:51, 30 March 2007 (UTC)[reply]

PS. Don't forget MoS:DAB#Break rules - where appropriate of course...

Help with EB?

Hi Geometry guy,

Could I ask a favor of you? ... I'd appreciate it muchly! :) Geometry girl 21:07, 30 March 2007 (UTC)[reply]

Thank you Geometry girl, especially for your efforts to ask so nicely :). I am quite sad that I had to reply so harshly, but I was very honoured by your invitation, and felt I could only do this honour true justice by answering very honestly. Anyway, I have copied this talk over to your page, as it really belongs in your impressively broad domain, rather than my limited one. Geometry guy 23:52, 30 March 2007 (UTC)[reply]

Hmmm... I just read some of the discussions about EB (I deliberately made my review without reading them) and can see how the POV has arisen from a clamour to point out the failings and criticisms of EB. There is certainly space for an article on these criticisms, but they are given too much weight in the main article, particularly if (as some editors suggest) making EB into a Featured Article is intended demonstrate the neutrality of WP. Geometry guy 01:13, 31 March 2007 (UTC)[reply]

FYI

Hi Geometry guy, in case you didn't see it, I've directed a comment to you here. Regards, Paul August ☎ 21:07, 31 March 2007 (UTC)[reply]

Derivative

OK, thx. I actually had pretty good luck in the end with Edits in the end, though not at first. Similar to some of your experience, possibly. Best wishes. --Thomasmeeks 21:29, 1 April 2007 (UTC)[reply]

Linear Algebra intro

Here's what I think might make a better introduction to the linear algebra article. I've tried to give some more idea what the field is about (in my own view), to explain the key words a little bit (so hopefully it won't scare off all laymen), and to provide some idea of applications. Use it (with or without modifications) or disregard as you please. Good luck. GV, 1 april 2007.

"Linear algebra is the branch of mathematics concerned with the study of vector spaces (also called linear spaces) and linear maps (also called linear transformations). Like other algebraic structures, vector spaces are defined as sets of elements, with operations that yield elements of the same set - just like adding or multiplying numbers yield another number. For such a set to be called a vector space (and its elements, vectors) the operations have to obey certain rules, or axioms. From these axioms and further definitions many useful and interesting properties of vector spaces can be proved.

In particular, vector spaces can be mapped onto other vector spaces or themselves; meaning that there are functions that take one vector as argument, and that when applied to all vectors in a vector space yield a new set that once again obeys the axioms of a vector space. Such functions are called linear transformations and are computationally represented by matrices.

Vector spaces are a central theme in modern mathematics because many objects of mathematical study exhibit the structure of a vector space, e.g. Euclidean space, sets of functions, and n-tuples of (rational, real or complex) numbers. This explains the use of vectors in analytic geometry (readily generalizable to more than 3 dimensions), in solving systems of linear equations (and hence of partial differential equations), and in statistics. In the natural sciences and the social sciences nonlinear models are often approximated by linear ones in order to make use of the computational methods of linear algebra."