Wikipedia talk:WikiProject Mathematics

For older discussion, see /Archive1, /Archive2, /Archive3, /Archive4(TeX), /Archive5, /spoof edits alert (past hoaxes), /Archive6

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Nominated article

• I nominate Lebesgue integral. Charles Matthews 08:17, 19 Feb 2004 (UTC)
  • Hello Charles. I do like the Lebesgue integral article, although it gets bogged down toward the end -- it seems like the discussion sections can be tightened up quite a bit. Comments? Wile E. Heresiarch 02:33, 8 Apr 2004 (UTC)
    • Always room for improvement. I chose it mainly because it touches all the major bases (motivation, some history, towards applications, picture, real content), so is quite a good template. Charles Matthews 06:31, 8 Apr 2004 (UTC)
• I second the nomination for Lebesgue integral. I'll also nominate Bayes' theorem. Wile E. Heresiarch 02:33, 8 Apr 2004 (UTC)

Other articles I think are good in their ways are Boy's surface (graphics) and Nicholas Bourbaki (perspective and NPOV - I have worked on this one). Charles Matthews 09:19, 15 Jul 2004 (UTC)

Begging the question

I'd like to point people to the mathematical remark in the article Begging the question. See also my comment on the talk page which has thus far generated no responses. There's gotta be a better example than either of these two. - dcljr 06:01, 9 Feb 2005 (UTC)

New Mathematics Wikiportal

I know I've posted this on most of your user talkpages, but I felt it was important to add to the project page as well.

I wanted to point out to you the new Mathematics Wikiportal- more specifically, to the Mathematics Collaboration of the Week page. I'm looking for any math-related stubs or non-existant articles that you would like to see on Wikipedia. Additionally, I wondered if you'd be willing to help out on some of the Collaboration of the Week pages.

I encourage you to vote on the current Collaboration of the Week, because I'm very interested in which articles you think need to be written or added to, and because I understand that I cannot do the enormous amount of work required on some of the Math stubs alone. I'm asking for your help, and also your critiques on the way the portal is set up.

Please direct all comments to my user-talk page, the Math Wikiportal talk page, or the Math Collaboration of the Week talk page. Thanks a lot for your support! ral315 02:54, Feb 11, 2005 (UTC)

ral315: This is a better way to communicate to the Wikipedian mathematics community, rather than posting on everybody's talk pages — some people consider that to be spamming. Your portal looks interesting. I'll put in on my watchlist and lend a hand as time and interest permits. As for mathematics articles needing attention check out Wikipedia:Pages needing attention/Mathematics. Paul August ☎ 06:27, Feb 11, 2005 (UTC)

As I said on User talk:Ral315#Wikiportal, personally, I really appreciated the note you left on my talk page. It might have been months before I'd have found the portal without it, as I'm much more active in other areas right now. And over the years, whenever I've taken the trouble to identify the people I thought would be interested in something and give them each a personal heads-up on it, I've only ever had thanks. But within Wikipedia there are many sub-communities, and this one seems not to like it. I've noted that now, and I'm sure you have too. I'm not convinced it's representative of the whole of Wikipedia, or even the Maths community, but certainly take it as applying to the more active members of this Wikiproject. Andrewa 13:05, 11 Feb 2005 (UTC)

Tex rendering -- help!

Can someone sort out my TeX rendering at effective population size please? I have most of it, but I'm not sure how to group subscripts/superscripts together e.g. p [sub] 1 + q [/sub] sort of idea. Dunc|☺ 15:03, 25 Feb 2005 (UTC)

Oh, I sorted that one myself. But I'm still stuck on having a fhat [sub]foo[/sub] because they won't go together, which leaves a gap and {} don't seem to work ?!? Dunc|☺ 15:26, 25 Feb 2005 (UTC)

Fixed. dbenbenn | talk 20:38, 25 Feb 2005 (UTC)

binomial expansion of (p_1 + ... + p_n)^c

I've asked this on Wikipedia:Reference_desk#.5B.5Bbinomial_expansion.5D.5D too, but, what is the binomial expansion of $(p_{1}+...+p_{n})^{c}$? I don't think this is covered in the articles that are there at the moment. (I want to derive the fully general Hardy-Weinberg law). Dunc|☺ 19:22, 2 Mar 2005 (UTC)

Assuming c is an integer > 2, refer to the multinomial theorem. Charles Matthews 20:52, 2 Mar 2005 (UTC)

\phi or \varphi

It seems to be the norm on wikipedia to use $\phi$ for writing one of the angle coordinates in spherical coordinates. I think that it is usually the norm to use $\varphi$ in mathematics and physics. I'd be willing to go through and change a bunch of the pages that use \phi to use \varphi instead. But I don't want to go against established policy. It just seems to me that the 'pedia should use the conventions that are common in mathematics. Has there been discussion about this issue before?

--Jacobolus 06:01, 6 Mar 2005 (UTC)

I believe the Wikipedia norm is the correct one. Dysprosia 06:19, 6 Mar 2005 (UTC)

As do I. Surely, it's a case of using one letter followed by another: theta ($\theta$) then phi ($\phi$). If varphi ($\varphi$) were correct, surely we'd use vartheta ($\vartheta$) for the first angle we designate? --stochata 13:32, 6 Mar 2005 (UTC)

I think that the "var" in "\varphi" just means "variant phi symbol", and doensn't necessarily imply that "\vartheta" should be used for theta. In all of the math books I just looked at (many of which are layed out in TeX), spherical and cylindrical coordinates were laid out using varphi. In the two physics books I looked at, the phi symbol was used. So I'll stick with phi I guess, as it appears (see discussion below this one) that the physicists' notation is winning out for other coordinate systems. --Jacobolus 18:19, 6 Mar 2005 (UTC)

I use \varphi when I write mathematics in TeX (In fact, I \let\phi\varphi), but I prefer \phi here. The wiki software is able to display \phi as an actual character, whereas it generates an image for \varphi. dbenbenn | talk 17:59, 6 Mar 2005 (UTC)

One pesky problem is that in many html fonts, phi displays inline as the varphi symbol, which means that there is visual inconsistency between rendered formulae and inline variable names. --Jacobolus 18:19, 6 Mar 2005 (UTC)

Note that in my comment below on the notation used by mathematics tutors for my undergrad -- I link to their book. They use phi rather than varphi. (Indeed, Jacobolus, the inline phi appears as varphi on my browser) --stochata 11:58, 8 Mar 2005 (UTC)

use of phi and theta in spherical coordinates

Hi all. I noticed recently that the articles on Vector fields in cylindrical and spherical coordinates and on Nabla in cylindrical and spherical coordinates have theta as the polar angle, phi as the longitude angle, r as the length of the vector, and rho as the length of the vector projected into the plane. In the article about Coordinates however, these uses of phi and theta, and respectively rho and r, are switched. This seems unnecessary conflict. I realize that physicists don't agree with mathematicians on the correct order of these terms, but at least some explanation should be given for the unwitting visitor, who might otherwise be very confused to see rho's and r's swapped so casually.

And then, some consistent drawings of coordinate systems and vector operations, etc. in these coordinate systems should be made. Here's my drawing of spherical coordinates: Image:Spherical_Coordinates.png. I'd be willing to make more drawings. But first some decision should be made about which convention to follow. That used in math or that used in physics.

Tied to this issue is my previous question about varphi and phi. Is one preferred as a coordinate name?

--Jacobolus 08:16, 6 Mar 2005 (UTC)

It should be only a matter of picking one standard and sticking to it. Dysprosia 09:49, 6 Mar 2005 (UTC)

I have never noticed a difference! I was taught to use theta, phi, r in my mathematics lessons at school, and later simply continued to use it through a physics degree. Which do we suppose is used by which category of people? (And maybe country of origin also affects the system used!) --stochata 13:38, 6 Mar 2005 (UTC)

I would agree with stochata that r is the prefered notation for the length of the vector, and so then ρ is the projection. And I agree with Dysprosia that consistency is what matters above all. So since you raised this issue, could you go through the pages using spherical coordinates, (like start at spherical coordinates, see what links there, etc), and change the notation in those places to keep things consistent? That would be much appreciated.

About the picture, I like it. Just one small remark. You will need to of course use a scaled version of it. In the scaled version you will need to make sure the fonts are the right size, and that aliasing is not too bad (pictures which have thin lines and thin curves tend to look ugly unless antialiasing is employed in some way). Oleg Alexandrov 16:24, 6 Mar 2005 (UTC)

I would argue in favor of the usage in Vector fields in cylindrical and spherical coordinates. Where

• (r, θ, φ) are spherical coordinates with θ being the colatitude (angle with the positive z-axis) and φ the azimuthal angle.
• (ρ, φ, z) are cylindrical coordinates with φ the azimuthal angle

The reason is that this usage is almost universally used by physicists. I think the reason stems from the fact that this is the notation used in Jackson's Classical Electrodynamics — the de facto textbook on electodynamics, where these coordinate systems are heavily utilized. Mathematicians may differ in their usage, but at least this way we include many mathematicians and nearly all physicists. -- Fropuff 17:34, 2005 Mar 6 (UTC)

Ok. So the notation used in Jackson and Griffiths and elsewhere in physics will be the norm. I'll make a prominent note at the top of the Coordinates (elementary mathematics) page (Aside: why is this called "elementary" mathematics... maybe just Coordinates (mathematics) would be better??), and then go with the physics notation. One last question. For inline text, is using the <math> and </math> tags frownned on? I've seen conflicting reports, and the usage seems to vary greatly between articles. I would generally be inclined to use them, but I'll try to stick to whatever the accepted standard is. --Jacobolus 18:12, 6 Mar 2005 (UTC)

One could argue that coordinates (mathematics) should discuss coordinates on arbitrary manifolds (or even more general spaces, i.e. with singularities). As far as inline TeX goes: the reason we try to avoid it is that the inline PNG's are too large and look bad with the surronding text. There has been lengthy arguments about this (see /Archive4(TeX)) and not everyone agrees. -- Fropuff 19:04, 2005 Mar 6 (UTC)

I've just checked the book by my undergrad tutors [1], and they certainly use theta, phi, r for spherical polars (and phi, rho, z for cylindricals as Fropuff suggests). Note that Riley was originally from a mathematics background. --stochata 11:55, 8 Mar 2005 (UTC)

My 2 cents: I am a mathematician, and I prefer the physics/engineering convention for several reasons.

Foremost is that, despite the beliefs of many ignorant American mathematicians and the usage of almost every American calculus textbook, the physics/engineering convention is simply by far the most widely-used convention of the two, throughout the world. It is the convention for virtually all (American and non-American) scientists, and for many, if not most, non-American mathematicians. American mathematicians are really the only group of users who enjoy a majority POV on this issue; it is only because of calculus textbooks that the whole world does not agree.

My second reason for favoring the physics/math convention is that it has far deeper historical origins in physics and science than the American usage does in math. The effort required for Americans to change would be far less than the effort required to re-write classical physics texts.

But, my most important reason is that the American convention is fundamentally flawed from a mathematical viewpoint. If this were simply a matter of two symbols getting interchanged, that would be one matter. But the American convention produces a left-handed coordinate system, and I don't think I need to explain why that poses a tremendous problem.

I taught a vector calculus class a couple years ago, doing something perhaps against better judgment -- teaching the non-American convention while the text used the American one. Of course, I also freely used differentials and the type of informal arguments physicists use for deriving tangent vectors, and so forth. I just made sure that I never assigned any problem using the textbook convention, and I told them not to read that part of the text. There wasn't too much confusion resulting, I mean, at least among those who weren't already confused by the time we reached general coordinate systems. Revolver 07:17, 12 Apr 2005 (UTC)

Relevant proposed naming convention: ambiguous adjectives

There is a proposal at Wikipedia talk:Naming conventions (ambiguous adjectives) that could affect several mathematics articles. -- Toby Bartels 08:40, 2005 Mar 7 (UTC)

Soliciting input on Estimation theory

Just seeking input on a new article: estimation theory. (Estimation didn't take a purely statistical explanation and I better know it as estimation theory.) Please leave article specific commentary on it's talk page instead of here. Thanks. Cburnett 06:56, 8 Mar 2005 (UTC)

straight or italic d?

What are your opinions about the use of upright d versus italic d in integration and for the exterior derivative? Currently, probably because it is less LaTeX, italic d seems predominant. Personally I prefer upright d as this more clearly contrasts with possible use of d as a function or number(distance). Examples

$\int f\,d\mu$	$\int f\,\mathrm {d} \mu$
${\frac {dy}{dx}}$	${\frac {\mathrm {d} y}{\mathrm {d} x}}$
$\int d(vx,z/x^{2})\ln(x+1)\,d(x\mapsto \cos(x)d(x,w))$	$\int d(vx,z/x^{2})\ln(x+1)\,\mathrm {d} (x\mapsto \cos(x)d(x,w))$
$\int fdt\wedge dx\wedge dy\wedge dz=\int f\,dt\,dx\,dy\,dz$	$\int f\mathrm {d} t\wedge \mathrm {d} x\wedge \mathrm {d} y\wedge \mathrm {d} z=\int f\,\mathrm {d} t\,\mathrm {d} x\,\mathrm {d} y\,\mathrm {d} z$
$d\det \left({}_{c}^{a}{}_{d}^{b}\right)=d(ad-bc)=add+dda-bdc-cdb$	$\mathrm {d} \det \left({}_{c}^{a}{}_{d}^{b}\right)=\mathrm {d} (ad-bc)=a\mathrm {d} d+d\mathrm {d} a-b\mathrm {d} c-c\mathrm {d} b$
$d\det \left({}_{c}^{a}{}_{d}^{b}\right)=d(ad-bc)=a\,dd+d\,da-b\,dc-c\,db$	$\mathrm {d} \det \left({}_{c}^{a}{}_{d}^{b}\right)=\mathrm {d} (ad-bc)=a\,\mathrm {d} d+d\,\mathrm {d} a-b\,\mathrm {d} c-c\,\mathrm {d} b$
$\int f(x_{1},\ldots ,x_{d})\,d_{d}x$	$\int f(x_{1},\ldots ,x_{d})\,\mathrm {d} _{d}x$
$df(V)=V(f)=\left.{\frac {d}{dt}}\right|_{t=0}f(\gamma _{t})$	$\mathrm {d} f(V)=V(f)=\left.{\frac {\mathrm {d} }{\mathrm {d} t}}\right|_{t=0}f(\gamma _{t})$
$\Delta :=(d+d^{*})^{2}=dd^{*}+d^{*}d$	$\Delta :=(\mathrm {d} +\mathrm {d} ^{*})^{2}=\mathrm {d} \mathrm {d} ^{*}+\mathrm {d} ^{*}\mathrm {d}$
$\Delta :=(d+d^{*})^{2}=dd^{*}+d^{*}d\,$	$\Delta :=(\mathrm {d} +\mathrm {d} ^{*})^{2}=\mathrm {d} \mathrm {d} ^{*}+\mathrm {d} ^{*}\mathrm {d} \,$

Also, when defining something, do you use := instead of = and why? MarSch 17:30, 11 Mar 2005 (UTC)

It is standard to use italics for differentials such as dx (e.g., see Wolfram: [2]). The spacing ought to give you a clue to the nature of the symbol, note that you should add a little space to distinguish the variable (see Lamport p.50). e.g., $\int d\,x\,dx$. --stochata 23:35, 11 Mar 2005 (UTC)

I like the idea of using a vertical "d", but it is not common. I think that in Wikipedia we are not supposed to be trend-setters but should follow common practice, so we have to use the italic ''d". --Zero 02:22, 12 Mar 2005 (UTC)

It's my estimate that this is largely a US/UK thing (with Americans using italics and the Brits using an upright shape). Personally, I prefer to use both a thin space and an upright shape -- why be coy? (I've added a row to the determinant example, so that we can all see what all four possibilities amount to there.) As usual, I oppose any sort of policy decision for all articles; we should follow the usual rule of tolerance for variation that applies to US/UK spelling differences. -- Toby Bartels 23:56, 2005 Mar 12 (UTC)

Toby, I am British (and currently in Britain) and I prefer the italic version (although I have seen the upright 'd', it doesn't strike me as that common -- although my area doesn't tend to use derivatives that much). I look forward to articles with phrases such as "dx, or dx in American mathematics" :-) --stochata 12:18, 13 Mar 2005 (UTC)

The Brits have spoken. :) I would say we need to restrict transatlantic differences to spelling (and politics) only. Italic dx has been the style on Wikipedia, and I think it should stay this way. Oleg Alexandrov 19:45, 14 Mar 2005 (UTC)

Reformat of Participants list

I'm thinking about changing the format of Wikipedia:WikiProject Mathematics/Participants, making it into a table like so:

User (T1 C2)	Areas of interest	Comments
Andrewa (T C)
AxelBoldt (T C)
Charles Matthews (T C)		I've added about 300 mathematics pages, many biographies, and lists of mathematical topics. I now also work on other areas of WP, but a well-organised and credible collection of mathematical articles is very much what is needed. We now pretty much have the house style and topic classification in place; there are some missing areas, and a great need to explain current research areas, as well as good history. I'm a sysop - one of not too many on this list.
Chas_zzz_brown (T C)	abstract algebra, group theory	My knowledge of topics outside of group theory is a monotonically decreasing function of their relationship to abstract algebra.
Mark Dominus (T C)
FunnyMan3595 (T C)	abstract algebra	I'm a freshman majoring in mathematics, but I already have quite a few courses under my belt. My specialty is abstract algebra.
irrªtiºnal (T C)		Let ε < 0 (hehe...) I am a highly unsuccessful mathematician. I am a man. I am single. I am free. I am an existentialist, therefore I am not.
Jeff (T C)	dynamical systems, complex systems, real analysis	I love to edit.
Kevin Baas (T C)		I started the fractional calculus section. Though it is still embryonic, it is very much 'my style', which is still under development. -Also started Information geometry section. I am just learning about this, though.
Ling Kah Jai (T C)		I have contributed an interesting article called last stone game.
LittleDan (T C)	geometry, group theory, vector spaces	I know up through geometry, and a fair amount of group theory and vector spaces. I can usually pick things up from wikipedia articles, if not from mathworld, then I can edit wiki articles for clarity.
Markus Krötzsch (T C)		I think many math articles still lack: general intros/motivation, links to relevant literature, objective account of alternative definitions (even if one definition is prefered in Wikipedia).
MarSch (T C)	geometry, category theory, physics
Miguel (T C)		How come Toby didn't tell me about this?
Pierre Abbat (T C)
Ram-Man (T C)
Revolver (T C)		Hi, I'm back.
Taku (T C)
Toby Bartels (T C)
Tomo (T C)

Notes: ¹ User's talk page; ² User's contributions

Any comments? Paul August ☎ 22:40, Mar 11, 2005 (UTC)

Much better, go for it -- so long as people aren't scared off to add their own entry. --stochata 14:36, 13 Mar 2005 (UTC)

Yes I had wondered about that. Figuring out the table syntax might discourage some. Although, perhaps we could consider a kind of IQ test, sort of like figure out the next term in this sequence … ;-) I'd be willing to write some instruction and/or provide a template. What do others think? It is a bit of work, so I don't want to undertake it if it is not deemed useful, or if we think it will put people off unnecessarily. Paul August ☎ 14:49, Mar 13, 2005 (UTC)

Well, trying to overcome the apathy...

I am against the table. I never learned the syntax of the Wiki table (all those absolute value signs everywhere :) and never plan to. And I don't see the gain of the table, besides the obvious rosy background. :)

Other thoughts? Oleg Alexandrov 16:21, 13 Mar 2005 (UTC)

PS And the background ain't even rosy! :) Oleg Alexandrov 16:21, 13 Mar 2005 (UTC)

Well I guess the main advantage of the table, in my mind, is that it encourages participants to enter fields of interest, plus it is eaisier to read, and I think the links to the user's talk page and contributions is helpful, for me at least. I'd be glad to help anyone with the syntax — or add a "rosy background" if that would help ;-) (Oleg: tables are fun! :) Paul August ☎ 16:56, Mar 13, 2005 (UTC)

I like it. Tomo 23:21, 13 Mar 2005 (UTC)

OK, although the response has been somewhat limited, I've decided to go ahead with the new format. Three users have expressed support, stochata, Tomo and MarSch (on my tak page). Oleg's was the only dissenting voice, but he has since warmed up enough to the idea to create a script to generate the table from the existing list ;-) So he is hoist on his own Perl petard, so to speak ;-) I would have preferred to have heard from some of the more senior participants (Charles Matthews, are you listening? ). Hopefully people are at worst indifferent. If anyone doesn't like it we can always revert it ;-) Paul August ☎ 21:41, Mar 18, 2005 (UTC)

"monotonicity" merged with "monotonic function"

After some discussion on talk:montonicity involving me, Toby Bartels, Michael Hardy, and Markus Krötzsch, it was agreed that monotonicity should be merged with monotonic function, which I have now done (monotonicity now redirects to monotonic function).

However there was a bit on a generalized notion of convergence for function between posets, which Toby thinks is worth keeping, but which I don't think necessarily belongs in the monotonic function article. Toby has suggested that perhaps it should be moved to its own article titled "order convergence". I made a stab at converting the orphaned text into a first draft for such an article (see: talk:montonicity) but I'm unfamiliar with this concept and am reluctant to actually create the new article myself. So If anyone knows anything about this, and would like to salvage this now orphaned content please do so.

Here is the text under discussion:

(Beginning of quoted text)

The notion of monotonicity allows one to express the principal instances of convergence (to a limit):

Given that a commensurate difference relation is defined between the members of S; that is, such that for any four (not necessarily distinct) members g, h, j, and k of S, either g − h ≤ j − k, or g − h ≥ j − k, and given that M from T to S is a map of equal monotonicity, then the values M(s) are called converging (to an upper limit), as the argument s increases, if either:

• the set T has a last and largest member (which M maps explicitly to the corresponding limit value l in set S); or
• for each member m of T, there exists a member <n > m such that for any two further members x > y with y > n, M(n) − M(m) ≥ M(x) − M(y).

As far as the set of all values M(s) does therefore have an upper bound (either within set S, or besides), and as far as every set which is bounded (from above) does have a least upper bound l, the values M(s) are called converging to the upper limit l as the argument s increases.

Similarly one may consider convergence of the values M(s) to a lower limit, as the argument s decreases; as well as convergence involving maps of opposite monotonicity.

(End of quoted text)

Paul August ☎ 21:13, Mar 14, 2005 (UTC)

Algebraic solution

Could someone here confirm that this new one sentence article is correct? An algebraic solution is a solution that is either a number or can be computed. That strikes me as so general as to be essentially meaningless, but google's been no help & I'm not competent in this area. Thanks. Michael Ward 03:06, 18 Mar 2005 (UTC)

It seems the definion does not make sense unless the term computation is explained. Maybe one should add a reference to or redirect to algebraic number or algebraic equation. Tomo 06:54, 18 Mar 2005 (UTC)

I've redirected this to closed-form solution. Charles Matthews 08:34, 18 Mar 2005 (UTC)

periods at the end of formulas -- request for comment

This is an edited version of my conversation with Omegatron, about periods at the end of sentence. I just wonder, what are your opinions about this? Thanks!

Is there a consensus that [period] is needed? looks bad to me. - Omegatron 00:19, Mar 19, 2005 (UTC)

I wonder if the reason it looks bad has to do with a peculiarity of using TeX on Wikipedia, as opposed to using TeX in the usual way. That is that if you put the period or comma outside the math tags, it gets mis-aligned. If you put it inside, however, it looks good. Michael Hardy 23:45, 19 Mar 2005 (UTC)

Period at the end of formula is the universal style in math. I am aware that in engineering for example, people do not do that. Did it happen that I modified something outside math (I try to stick to math, but sometimes the links from the list of mathematics topics lead into related subjects). If you would like, we can have a wider discussion about this. Oleg Alexandrov 00:24, 19 Mar 2005 (UTC)

Yeah it was an electronics article common drain, and they weren't sentences, either. I think even in mathematics articles it doesn't look good. I don't remember seeing it in my math books. It looks like a symbol, which could certainly confuse me; I don't know about other people. $Q\cdot Q.$ ${\dot {Q}}.$ $...,1,2,3,....$ Perhaps it's something from typesetting that doesn't carry over perfectly to the web? - Omegatron 00:30, Mar 19, 2005 (UTC)

I just pulled two math books off my shelf (math math, not engineering math) :-) and they are different. One has no punctuation next to formulas unless they are inline with the sentence. The other has periods the way you are using. - Omegatron 00:35, Mar 19, 2005 (UTC)

I just randomly pulled 5 applied math and probably books off my shelf. They all use period at the end. Would you like us to discuss this at Wikipedia talk:WikiProject Mathematics. Or would you take my promise that I will not mess up with any articles which are not either linked from list of mathematics topics, or in some math category, or listed as a math stub? Either way is very fine with me. Oleg Alexandrov 00:41, 19 Mar 2005 (UTC)

The encyclopedia of physics uses periods, too.  :-) You are winning my bookshelf 2 to 1 so far. The engineering books don't, as you said. - Omegatron 00:42, Mar 19, 2005 (UTC)

If it's standard mathematics practice I guess go for it, and leave the engineering articles without. Of course, there are some articles that exist on the intersection between these two worlds. Has there been any discussion about it before you started adding them? - Omegatron 00:44, Mar 19, 2005 (UTC)

No, I did not consult anybody [about this]. But, I am already at letter "C", and at at least 5 Wikipedians I know had one or more of those on their watchlist (well, I assume so, as they contributed to those). I can certainly stop until we talk this over at Wikipedia talk:WikiProject Mathematics. All up to you. Oleg Alexandrov 00:47, 19 Mar 2005 (UTC)

Let's just move this conversation there and see what other people have to add, and you can keep going with the math articles. - Omegatron 00:49, Mar 19, 2005 (UTC)

I don't care for them when the formula is on its one line (I see a lot of "cleanup" on my equations). Inline with sentences is fine like this $\sum _{x=0}^{N-1}f(x)^{2}$. But the period *not* inside the math tags. Cramér-Rao inequality is mixed with and without periods: Cramér-Rao inequality#Single-parameter proof doesn't but Cramér-Rao inequality#Multivariate normal distribution does.

In the end, I don't see you can really justify either no more than if why it should be Jones' or Jones's. Entirely style. Cburnett 02:13, 19 Mar 2005 (UTC)

I did not get to Cramér-Rao inequality yet. I think one needs to be consistent at least on a per-page basis. Oleg Alexandrov 02:33, 19 Mar 2005 (UTC)

That's primarily from one section having already been there. Might as well wait and see what results from this discussion. :) Cburnett 04:33, 19 Mar 2005 (UTC)

Yes, this is standard style in mathematics textbooks. But on screen I think it looks clumsy, is potentially confusing, and is unnecessary - I think the effect on continued fraction, for example, has not improved the article. My vote would be not to do this - and certainly to stop until you have a consensus. Gandalf61 13:46, Mar 19, 2005 (UTC)

I am reluctant to comment on this rather trivial matter, but I think the convention to treat formulas as part of the text for the sake of punctuation rules is useful and logical, and widespread in maths style guides. So I support Oleg's efforts. I don't see Gandalf's point that there is a distinction between maths in books and maths on the screen in this matter. -- Jitse Niesen 15:36, 19 Mar 2005 (UTC)

Agree. Charles Matthews 17:20, 19 Mar 2005 (UTC)

Also agree. Now may I get a pardon from Oleg for being one the worst offenders against this commandment? CSTAR 18:56, 19 Mar 2005 (UTC)

Penance required - start the Weil representation article ... Charles Matthews

OK, OK I suppose that's better than saying 500 padre nuestros.--CSTAR 18:00, 11 Apr 2005 (UTC)

From User talk:CesarB

I am now doing myself a bad service, but there is discussion going on at Wikipedia talk:WikiProject Mathematics about period at the end of formula if formula is at the end of sentence. So, you can go there and put your vote (which will be against me). I would like to ask you to specify there your background. It seems that mathematicians are mostly for period at the end of formula, while engineers (and now I see, computer scientists) are against.

In the future, I will avoid modifying non-math articles, like bra-ket notation, which is physics. I try to stick to math, but sometimes non-math articles (again, like bra-ket notation) are put in a math category, and then this kind of disagreements arise. Cheers, Oleg Alexandrov 19:42, 19 Mar 2005 (UTC)

I don't care either way, as long as it's obviously separate from the formula (like a big fat period). You not only added a period which looked like part of the formula, but you added it inside the <math> tags, which made it even more like part of the formula. cesarb 19:45, 19 Mar 2005 (UTC)

Often all it takes is to precede the period by a little bit of space and it no longer intrudes on the formula. --Zero 12:07, 20 Mar 2005 (UTC)

Agreed. Of course, how much space is needed depends on the formula (a formula full of whitespace would need more space than a formula with no whitespace at all). cesarb 13:42, 20 Mar 2005 (UTC)

I am for proper punctuation of formulae. BTW the bra-ket article is a really bad example IMHO, since it has lots and lots of miniscule formulae, which would probably benefit from inlining.MarSch 15:27, 20 Mar 2005 (UTC)

Period before or after </math> -- please comment on this as there are opinions on both sides.

It seems that the opinion leans (I would say overwhelmingly) towards putting period at the end of formula. There are situations in which there needs to be some space between formula and period, and in some situations one could be better off without a period if that would confuse things, but these are rather special cases, when careful and individual judgement needs to be made.

There is another quite dividing issue which needs to be settled. Shoud the period before or after </math>?

I would agree with Michael Hardy that the period should be before </math> so that it becomes part of the PNG image. Otherwise, if the period is separate, if the formula is at the edge of browser window, the period moves to the next line. Also, this introduces a big space between formula and period (and comma) which can look quite unnatural (I don't mean one quarter space, like \, in LaTeX, rather a full space).

On the other hand, Cburnett believes that (taken from his talk page):

I'm vehemently opposed to having to make an article work around bugs or unexpected behavior (see discussion above to see what I mean [there Cburnett argues that one should put one category and language link per line, even if that causes some extra space at the bottom]). I did get my browser to wrap periods to the next line with equations (images really). However, I don't readily see this as a WP issue but rather a browser issue. Either way, whatever is decided on the wikiproject page I'll go with. Just can't promise I'll always remember. :) Cburnett 04:04, 19 Mar 2005 (UTC)

I wonder what everybody else thinks. Comments would really be much appreciated. Thank you. Oleg Alexandrov 17:21, 20 Mar 2005 (UTC)

Another point to go for after </math> is like with the new grammar bot. Rending the period in the tags means a bot might see the period if HTML rendered or might not if PNG rendered. It makes for an inconsistency even if the period is placed consistently. If placed external to the tags then it will always be there. And, no intention of insulting here, you have to be ****extremely**** pedantic to worry about a browser wrapping a period. :) Cburnett 18:32, 20 Mar 2005 (UTC)

About the bot thing. The bot does the queries based on the wiki source, not the final html, so will have no problems sticking its nose in math formulas. Oleg Alexandrov 02:48, 21 Mar 2005 (UTC)

The grammar bot (I forget the exact user name, perhaps User:GrammarBot) ignores math tags because of the commas. If you're going to require a bot to parse math tags then you've just added more complexity to it......to keep a period from wrapping. Cburnett 03:26, 21 Mar 2005 (UTC)

I think so far GrammarBot was very sucessfully messing inside of formulas. Maybe it will be a new feature that it will not do that anymore. Now, about your concern. Let me tell you that the bot I wrote to put periods at the end of formulas semiautomatically had to deal with issues similar but worse than that (there is lots of variabitity to how people type formulas). Besides, the GrammarBot has nothing to do in or around a math formula anyway, since after the period (or comma) in an aligned formula one goes to a new line. Either way, I think our concern for bots should probably be the last thing to worry about. Oleg Alexandrov 03:59, 21 Mar 2005 (UTC)

If the bot is to detect sentences without a period then it'll have to parse inside and around formulas. Really, though, if you want to worry about wrapping periods then I'll worry about bots. Both are equally pedantic and both are concerned about a mundane detail instead of actually writing or editting articles. Cburnett 04:05, 21 Mar 2005 (UTC)

If you are not pedantic yourself, and if you don't care if there is a period at the end of formula to start with, why are you so pedantic about where the period is? :) I think you are right. We are wasting time here. You can do what you love most, editing articles, and I will continue with the issue which has been concerning me me for at least one month, that is, proper punctuation of math articles. How's that? :) Oleg Alexandrov 04:18, 21 Mar 2005 (UTC)

Try rereading what I wrote. Notably, the second sentence. Cburnett 04:27, 21 Mar 2005 (UTC)

You are right again. I focused on your very provocative third sentence. So let us not imply that what the other is doing is irrelevant, because then you should not take part in this discussion to start with.

On your second sentence, I do not buy the bot argument. We will probably not agree on this. Let us see what others have to say. Oleg Alexandrov 04:32, 21 Mar 2005 (UTC)

When did I call it irrelevant? Cburnett 05:06, 21 Mar 2005 (UTC)

My fault. I overreacted. I read it (the third sentence) to mean that some people spend their time in an useful way writing good articles, and some other people have nothing better to do than argue about pedantic issues ultimately of little importance. But I had time to think about it, and agree that what you said can be interpreted as saying that there are two kind of issues, one of writing articles and the other one of taking care of the fine details. So, sorry!

Either way, I think better arguments can be found than the bot thing, and it seems that ultimately nobody really cares about this issue except us two and cesarb. Let us see if more developments happen. Oleg Alexandrov 05:12, 21 Mar 2005 (UTC)

I would put it after </math>, because it's not part of the formula. Only things that are part of the formula should be inside the tags. As a bonus, it gives some extra spacing before the period.

I found an easy way to prevent breaking: the <nobr> element. Since it's not supported by mediawiki (and in fact not part of the HTML standard), I created a template nobr using the standard way of doing a <nobr> (and in fact, the way used by Mozilla's default HTML stylesheet).

Here's how to use it:

$1+1=2\;$.

I disagree with Cburnett about it being pedantic; with some large formulas (I've seen formulas that take more than half of my screen, and I use a huge resolution), it's quite easy when using lower resolutions to end up with a period by itself in the next line.

A more extreme example (you can comment it out after the discussion is over, it will cause scrollbars to appear):

$a+b+c+d+e+f+g+h+i+j+k+l+m+n+o+p+q+r+s+t+u+v+w+x+y+z+a+b+c+d+e+f+g+h+i+j+k+l+m+n+o+p+q+r+s+t+u+v+w+x+y+z+\;$.

cesarb 19:40, 20 Mar 2005 (UTC)

Oh, and by the way, if this is too verbose, it would be easy to create a template to simplify it, containing something like:

{{nobr|<math>{{{1}}}</math>.}}

cesarb 19:57, 20 Mar 2005 (UTC)

Vote for after. We should not compromise logic. There should be better workarounds. Isn't there a Unicode character specifically to glue parts together? – Sebastian 05:33, 2005 Mar 21 (UTC)

If you are thinking of the non-breaking space, it won't work (it would only work if it was replacing a space character; there is no space character). The nobr template I made works. --cesarb 10:01, 21 Mar 2005 (UTC)

The template cesarb suggests would work. However, I don't see it getting widely adopted (it is hard enough to convince people to care about putting that period to start with).

I agree with Sebastian about the logic thing. When I type LaTeX papers I don't like the period to be inside of the formula. However, on Wikipedia we have just three options (a) put the period after /math and not worry about misalignment, as this is a browser bug — this is what Cburnett says (b) put the period after, but do some kind of quick fix like a template, which cesarb suggests and (c) put the period inside, which is kind of a hack too.

Dealing with numbered formulas, like

$\int _{a}^{b}f(x)\,dx=F(b)-F(a)\quad \quad \quad \quad (1)$

does not make things easier. Here, probably the period should go before (1) rather than after (with some spacing between the formula and the period in some situations — if necessary — but probably not in this case).

So, no perfect solutions, but I would still think the third option is better than the first two. Oleg Alexandrov 12:50, 21 Mar 2005 (UTC)

I don't see the problem with the numbered formulas. The number is not part of the formula. In fact, it usually is written in the same font as the text. Sometimes you even find a name for the equation before the number - so it should really be outside of the ${\displaystyle }$. Moreover, it is not uncommon to put the punctuation after the the number, which I also regard as more logical. Example: Eddington, The Constants of Nature in The World of Mathematics, Vol. 2. — Sebastian 09:45, 2005 Mar 22 (UTC)

Well, it is not standard to put the period after the equation number. (Actually, LaTeX does not even give you a choice.)

It seems that people are pretty split about this (2 for period inside, 3 for period outside), and there were not as many people involved in this as could have been.

So, I guess a solution would need to wait until the browser and display technology will advance — do you hear that Cburnett? — like switching to MathML where hopefully this will not be an issue.

However, there was broad agreement that sentences with formulas at the end must have a period. Unless I hear any objections, in several days I will resume putting the periods. I will put them inside the math tags, as again, it seems to me that this is the least problematic way. But, I will not attempt to convert the formulas where the period is there, but outside the math tag, as I had originally planned.

If, again, I hear no objections, I am aware that there could be disagreements about individual instances, where one might feel there needs to be some spacing between the period and the formula, or that a period does more harm than good in that instance. Since my work will be semi-automatic anyway, just feel free to revert or change those cases. In most situations however, I do not expect these to be an issue.

Anyway, let us see how it goes. Oleg Alexandrov 21:18, 23 Mar 2005 (UTC)

Objection. The (admittedly narrow) majority voted for outside, and it's technically feasible with the stub mentioned above; so there's no reason to put them inside. I also disagree with using LaTeX's inability as an argument. Our criterium should be what we deem most straightforward logically. — Sebastian 22:09, 2005 Mar 23 (UTC)

Vanity references?

I wanted to alert everyone to some edits I've just noticed. Take a look at IP 84.94.98.49's contribution list: [3]. Notice that all of the edits were adding links to abstracts or papers by someone named " J.Foukzon". They were not, as far as I could tell, particularly relevant to the articles (I could be wrong). I'm wondering if someone might be engaging in something which could be called "vanity references". This could be a particularly insidious form of vandalism. One that could be difficult to deal with, since it can be hard to verify that a reference is really relevant. Paul August ☎ 20:37, Mar 20, 2005 (UTC)

Certainly references like both the ones on Path integral formulation (now only visible in the history) are unnecessary and, while broadly 'relevant' to the subject at hand, at best add nothing to the article and at worst distract from more suitable references. The Foukzon references in that article are in fact conference papers that have not yet been presented (appearing July 2005); sheesh! Well spotted, Paul. Ben Cairns 22:06, 20 Mar 2005 (UTC).

I would say, delete without further fuss. Oleg Alexandrov 22:16, 20 Mar 2005 (UTC)

Structure of math articles

I have seen some mathematics articles that suffer from too narrow a perspective, like laplace operator, which completely ignored generalization to forms and still ignores a discription in terms of covariant derivatives so it would apply to all tensors. The laplace article is still very far from decent since it does not say anything usefull about the (general) Laplace operator, but that's another issue.

Also I have seen some mathematics articles which are now physicist territory, like Noether's theorem and Lagrangian. I think that a good article should start at it's highest level and then explain how lower levels are special cases of it. These lower levels may then also have their own page if necessary. And if something has application to physics or anything else, these should then be treated. Sometimes people say that this is an encyclopedia as a reason for excluding certain information that is considered too specialised/difficult. I don't see their point. Any comments? MarSch 16:07, 26 Mar 2005 (UTC)

I agree that we should discuss generalizations. However, I strongly disagree with your statement that "a good article should start at its highest level". Instead, we should "start simple, then move toward more abstract and general statements as the article proceeds" (quote from Wikipedia:WikiProject Mathematics). This has the advantage that we don't scare away people that are not interested in the generalizations; people that do want to read about the most general case will understand (and skip) the lower levels. For instance, I think the article on the Laplace operator should start with the definition

$\Delta f=\sum _{i=1}^{n}{\frac {\partial ^{2}f}{\partial x_{i}^{2}}}.$

But by all means, proceed to treat the definition $\Delta =dd^{*}+d^{*}d$.

The split mathematics/physics should be handled on a case-by-case basis. I definitely agree with you for Noether's theorem and I would be very happy if somebody will tackle this article. For another view, read Wikipedia:Village pump (miscellaneous)#where are the chemists?, from which I quote: "Turning to physics, I often find articles which appear to have been hijacked by mathematicians, causing them to loose insight into _physics_ principles." -- Jitse Niesen 22:31, 26 Mar 2005 (UTC)

Ugh. I completely disagree with the form of the recent edits to Laplace operator by User:MarSch. As a geometer, I like the fact that the full abstract definition has been added, but it should appear later in the article, after a simpler high-school/college-level definition.

Please keep in mind why people come to Wikipedia in the first place: to learn something new, to refresh thier memory, to look up a forgotten formula. There is nothing worse that one can do to a reader than to overwhelm them with abstractions they don't understand. For example, any chemist, who may have had a few semesters of quantum, would be lost in this article as it currently stands. Ditto for any structural engineer, or electronics engineer. These are people who would use wikipedia, and frankly, they outnumber the geometers by a hundred to one. The article should cater to that level of understanding first, and then, only later, turn to the more abstract definitions. As an example of where this works, see the definition of the discrete laplace operator, which appears at the end of the article, not at the beginining. linas 02:02, 27 Mar 2005 (UTC)

Agree with Jitse and Linas. Most people will not appreciate seeing things in their higher perspective upfront. Besides, bottom-up, from particular to general, is the natural way of learning things. Oleg Alexandrov 02:44, 27 Mar 2005 (UTC)

Thanks for your comments. My above viewpoints reflect my feeling of a lack of modern math content. I agree that by making the article more difficult I have, hopefully temporarily, made Laplace operator worse, because there wasn't and still isn't any informal stuff. I have been reading the project pages on structure of mathematics articles and searching for a good example article, and I have not been able to find what a good article should look like. I have given it some thought and I think what is most lacking from, as far as have seen, all articles is a good motivation at the beginning of the article (everything before the TOC) of why that article is interesting to read. After that should come a good informal treatment with few or no formulas and still after that should come the formal treatment. After this section should come some applications. What i was trying to say earlier was about the formal section, it should be as general as the article title warrants and then reduce to some special cases. At the moment Laplace operator has only a formal section, which is why it is very difficult to understand right now. Writing good motivational and informal stuff is probably one of the most difficult things one can do, because they require a very clear understanding of a subject. MarSch 11:34, 28 Mar 2005 (UTC)

I think we will all agree that math articles here need more motivation, more applications, more connections with other articles and relevant real world examples. This is mentioned at Wikipedia:How to write a Wikipedia article on Mathematics (maybe not in such uncertain terms as MarSch would like). However, I think no amount of motivation or explanation is going to make Laplace operator a good article, if instead of starting with the Laplacian as a sum of partial derivatives one goes right to the Laplacian on manifolds, a huge number of formulas, and a very general abstract treatment. I think that some kind of consensus was reached that going from most general to the particular is not the way to go. Oleg Alexandrov 18:29, 28 Mar 2005 (UTC)

The ideal on Wikipedia is to give a 'concentric' treatment: brief lead paragraph, then more details, then further details for the reader who needs them ... and even link to other pages when the extra details become very long. This is actually the opposite of the Bourbaki idea that you start with the supposedly 'correct' general definition. Now, we as mathematicians have some problems doing it that way; but in the end it is better to give an accessible treatment. Charles Matthews 15:00, 1 Apr 2005 (UTC)

This discussion and the one on Laplace operator have changed my mind. All parts of the article should start simple and end very very hard ;) -MarSch 14:34, 4 Apr 2005 (UTC)

encouraging references for formulas

formulas and constants are especially vulnerable to malicious vandalism. adding a square root, changing a single digit, etc. how do we fight it? two possible treatments:

• encourage references for every formula
• encourage people who know the formulas and numbers well to watch the pages

see Fourier_transform#Continuous_Fourier_transform for an example where I included an image from another site as a reference in comments after an anon removed an erroneous sqrt sign.

- Omegatron 16:01, Mar 28, 2005 (UTC)

the square root probably went over the 2pi? This is just a problem of definition. Do you want the Fourier transform and it's inverse to "look the same". It is a convention. You should probably mention that two versions exist.

In general I guess we gotta watch our formulas. If we use them to derive a few simple properties or prove something then mistakes will be spotted sooner.-MarSch 17:26, 28 Mar 2005 (UTC)

You're right. It was just over the 2pi. But I've seen other small changes here and there that were incorrect. - Omegatron 17:35, Mar 28, 2005 (UTC)

It's tricky to reference formulae as we often want to fit in with the style of related articles within Wikipedia, meaning we might use a "paraphrased" formula rather than one directly from a paper or book. (As a trivial example, we might write "sum nx" rather than "n sum x".) Just as for any other topic, that means those that know the subject need to watch the pages and check for subtle changes. --stochata 21:27, 28 Mar 2005 (UTC)

I agree in principle with Omegatron. I've added a section to Wikipedia:WikiProject_Mathematics/Proofs specifically deal with this type of issue. linas 03:58, 3 Apr 2005 (UTC)

Educational trampoline

I'd like to propose the creation of a new WP math policy (and category) concerning articles that are of particular educational value. I have in mind articles, such as Pi and Torus, which, if properly written and edited, could be accessible to pre-teens and still be interesting and fun for experts. Articles in this category would provide a portal for bright kids or teens (or even college freshmen) to launch into sophisticated math topics. For example: torus: when I was 9 years old, my teacher wrote formulas for a sphere, cylinder and torus on the blackboard: this is clearly a topic accessible to youth. Yet the article continues on to mention Lie groups and cohomology (and links to modular forms), which are advanced undergrad or grad-student topics. If this article is properly structured, it could provide a fine entrance to many fantastic topics in math.

The suggestion here is then only to create and apply some special editorial guidelines to articles in this class, and to create a special category so that educators could easily find them and thus suggest them for brighter students. If there is general agreement, I'd like to make this an official WikiProject Mathematics policy. linas 03:49, 3 Apr 2005 (UTC)

It would be very nice to have such articles. I suggest you choose one article to convert/improve as an experiment. Hopefully this could lead to improved structure of all our articles. -MarSch 14:25, 4 Apr 2005 (UTC)

It's Wikibooks that is the designated place for textbook development. The suggestion seems to be along the lines rather of the material in the kind of popularising, accessible book that really does have a chance of interesting readers without much background. Still, it does sound more like a Wikibook, to me. Charles Matthews 14:52, 4 Apr 2005 (UTC)

I don't believe in wikibooks. Yet. I like linas vision of the future of WP. -MarSch 13:51, 7 Apr 2005 (UTC)

Providing an introduction for math articles (or wikipedia articles in general) is a good thing. It makes the articles accessible to a wide range of people. But writing an article which can be used for studying a certain topic is an entirely different matter. Wikipedia is an encyclopedia as such is primarily used for looking up information. The structure of the articles should reflect this and present the information in an accessible and neutral way. A textbook on the other hand should be structured according to pedagogical principles. These principles vary from author to author as does the selection of material. MathMartin 15:25, 7 Apr 2005 (UTC)

I agree with MathMartin. We need to keep the encyclopedic style. So, several styles (described below) which were mentioned in places in the discussions on these pages are not quite encyclopedic. They are:

(a) Writing very concise articles containing just formulas and listing theorems (a la Abramowitz and Stegun)

(b) Writing things in a top-down approach.

(c) Making articles with pedagogical bent.

(d) For that matter, putting proofs in the articles, unless they are useful to the statement of the theorem or are otherwise instructive. Oleg Alexandrov 17:05, 7 Apr 2005 (UTC)

If you want encyclopedic then that is the Bourbaki way and thinigs should be top-down. Nobody wants this. Instead everybody wants our articles to be easily understandable. I believe linas proposed to make some articles _extremely understandable_ and thus accessible to children. In addition he proposed to make these articles more interesting by providing connections with other subjects. Don't we want interesting understandable articles? Also proofs are always usefull, and if someone is not interested than they can be skipped, but they provide a way of checking that a result is properly stated and should always be included. MarSch 12:49, 12 Apr 2005 (UTC)

These generalisations are always only indicative. It is pretty clear that some proofs should be included, others not, and so on. Some articles, particularly on recent work (from the past 40 years, maybe) are likely just to be surveys. Something no one has said yet, I think: accessible often will mean visual, so one direction in which to concentrate efforts is to add many more diagrams, not more words (waffle). Charles Matthews 12:52, 12 Apr 2005 (UTC)