Wikipedia talk:WikiProject Mathematics/Archive/2009/Jul

Self-referential function

Is anyone interested in trying to salvage something from the fairly new article self-referential function ? At present, the first sentence of the article "Cantor's diagonalisation produces a function that makes reference to itself" is simply wrong; the definition "A self-referential function is a function that applies to itself" is hopelessly vague; and the references are not actually related to the contents of the article. See Talk:Self-referential function for further discussion.

We already have fine articles on self-reference, recursion and functional equation. There may be a useful article to be written on self-referential functions, but the current article is not close to it, in my opinion. Gandalf61 (talk) 09:24, 25 June 2009 (UTC)

I removed the text about the Cantor function, which is unrelated to the references and is also wrong; there is no self-reference there.

It looks like this title should simply redirect to the article on recursively-defined functions. The second reference given (of two) uses the term in this way. The first is in theoretical physics, which is concerning. — Carl (CBM · talk) 12:18, 25 June 2009 (UTC)

It's also concerning that the link is both broken and to the statistics department of the government of Malaysia. Algebraist 12:48, 25 June 2009 (UTC)

After removal of irrelevant content the article was left as a stub with a disputed and probably incorrect definition - so I have been bold and replaced it with a redirect to self-reference. Gandalf61 (talk) 07:54, 29 June 2009 (UTC)

Calculating residues

Hi. I made an edit to the section of Residue (complex analysis) on calculating residues, and I'm posting here requesting a few more pairs of eyes look at it and make sure I didn't introduce any errors or anything. -GTBacchus^(talk) 18:24, 30 June 2009 (UTC)

Minimal subtraction scheme

I would be grateful for some expert opinions on the example I propose to add to Minimal subtraction scheme. Comments at the article talk page would be welcome. A.K.Nole (talk) 20:08, 30 June 2009 (UTC)

Pentation etc.

Family of successors to Tetration are being created....

• Pentation
  • Proposed merge into Hyperoperation, substantive material which might be merged is disputed
• Hexation
  • on AfD; I don't see any substantive material
• Heptation
  • redirected to Hexation, when I remember. There hasn't yet been substantive material.
• Octation
  • on AfC, but as a redirect (!)

Any assistance in keeping this in order would be appreciated. — Arthur Rubin (talk) 02:29, 30 June 2009 (UTC)

• There's also an AfC for heptation: Wikipedia talk:Articles for creation/Heptation. — Charles Stewart (talk) 12:34, 30 June 2009 (UTC)
• I've closed the hept* and oct* AfCs as neologisms. — Charles Stewart (talk) 11:32, 1 July 2009 (UTC)

Help

Resolved

Hi, I'm posting this on the Maths Wikiproject talk as we need editors who are knowledgeable about Mathematics to evaluate the following discussion and check out the editors and articles affected. Please follow the link below and comment if you can help.

Wikipedia:Administrators'_noticeboard/Incidents#Block_review_-_uninvolved_admin_request.

Thankyou. Exxolon (talk) 18:30, 1 July 2009 (UTC)

Aise Johan de Jong

We don't have an article about Aise Johan de Jong (notable for resolution of singularities in characteristic p; a Cole prize winner). I'm not so much into biography articles, but if somebody is, he's certainly deserving an article. Jakob.scholbach (talk) 12:59, 27 June 2009 (UTC)

de Jong didn't resolve singularities in positive characteristic; that's still open, though there's been recent progress. What he did was find a way around it using a type of morphism he called an alteration. Ozob (talk) 02:29, 2 July 2009 (UTC)

In the meantime, prior to creating an article, any biographical details can be added to:

Wikipedia:WikiProject Mathematics/missing mathematicians. Charvest (talk) 13:59, 27 June 2009 (UTC)

I didn't know that page; doesn't it duplicate the list of mathematicians at Wikipedia:Requested articles/Mathematics? (I mean, it does doesn't it?) -- Taku (talk) 18:10, 27 June 2009 (UTC)

Hmm. A merge seems to be in order. Should all the requested mathematicians be put into the missing page or should the missing page be put into the requested page. And are all the requested names notable ? Charvest (talk) 18:18, 27 June 2009 (UTC)

The Requested articles list is longer, but has attracted less information; it would be better to merge into Missing mathematicians, which has a format which encourages notes. I don't know whether they're all notable, but I'm shocked to se Vinogradov on both - how did we miss him? Septentrionalis PMAnderson 23:03, 27 June 2009 (UTC)

We do need an article for A. I. Vinogradov. N.B.: don't confuse him (as I have done) with Ivan Matveyevich Vinogradov. CRGreathouse (t | c) 21:36, 28 June 2009 (UTC)

Short of a full merge (since some names may not be notable), I plan to remove names from the requested list that are also in the missing list and put a notice at the top of the requested list asking names to be moved to the missing list whenever there are some biographical details available. Charvest (talk) 20:29, 5 July 2009 (UTC)

Bow and arrow curve

Bow and arrow curve has been proposed for deletion. Opinions? Michael Hardy (talk) 03:57, 2 July 2009 (UTC)

Could someone have a look at Diffequa contribs ? They seem to be odd. --El Caro (talk) 12:57, 2 July 2009 (UTC)

One possibility is that there is some textbook that gives these as examples. — Carl (CBM · talk) 13:10, 2 July 2009 (UTC)

At first I assumed it was just innocent exploration, but the claim that the bow and arrow was named by Euler pushes into hoax territory. If Euler had really named this thing, Google would know about it. Melchoir (talk) 18:26, 2 July 2009 (UTC)

What are the appropriate terms in Latin and German? I'd search for those in Google Books, with "Euler" as the author's name.

In German:

"Bogen" = bow

"Pfeil" = arrow

"Bogenschiessen" = archery

"Bow and arrow" has some plausibility, since the line y = x is part of the graph, and a curve crossing that line is as well. It's not implausible that Euler wrote about these curves and someone later called them by that name. Michael Hardy (talk) 19:22, 2 July 2009 (UTC)

Hmm, no dice there either. Melchoir (talk) 22:28, 2 July 2009 (UTC)

It's now an AfD rather than a proposed deletion: Wikipedia:Articles for deletion/Bow and arrow curve. As Michael Hardy often writes, please contribute with a reason for your decision rather than a simple keep or delete vote. —David Eppstein (talk) 23:02, 6 July 2009 (UTC)

Help at Kepler Conjecture

A persistent anon keeps editing Kepler conjecture to add a supposed counterexample attributed to Archimedes Plutonium. I have reverted twice today already, but anon has just inserted their nonsense for a third time. Please can someone keep an eye on the article and revert and/or semi-protect as you see fit. Gandalf61 (talk) 16:41, 3 July 2009 (UTC)

• That's the IP address range that M. Plutonium has edited from many times before. Uncle G (talk) 00:32, 7 July 2009 (UTC)

Gate-keeping on Wavelength

I have been trying for some time to add some material to Wavelength quoted below:

Spatial and temporal relationships

The mathematical form for the wave involves the argument of the cosine, say θ, given by:

$\theta ={\frac {2\pi }{\lambda }}\left(x-vt\right)\ .$

Using θ, the amplitude of the wave is:

$y=A\cos(\theta )\ ,$

which shows a particular value of y corresponds to a particular value of θ. As time advances, the term (−vt) in θ continuously reduces θ, so the position x corresponding to a chosen value of θ must increase according to:

$x=vt+\theta \ {\frac {2\pi }{\lambda }}\ ,$

in order that the value of θ stay the same. In other words, the position x where the amplitude y has the value Acos(θ) moves in time with the wave speed v. Thus, the particular mathematical form x − vt expresses the traveling nature of the wave.

In the case of the cosine, the periodicity of the cosine function in θ shows that a snapshot of the wave at a given time finds the wave undulating in space, while an observation of the wave at a fixed location finds the wave undulating in time. For example, a repetition in time occurs when θ increases by 2π; that is, when time increases by an amount T such that:

$\theta (t+T)=\theta (t)+2\pi \ ,$  or  $vT=\lambda \ .$

Likewise, a repetition in space occurs when x increases an amount Δx enough to cause an increase in θ by 2π:

$\theta (x+\Delta x)=\theta (x)+2\pi \ ,$  or  $\Delta x=\lambda \ .$

Thus, the temporal variation in y with period T at a fixed location is related via the wave speed v to the corresponding spatial variation with wavelength λ at a fixed time.

Using the same reasoning, it may be noted that any function f(x − vt) propagates as a wave of fixed shape moving through space with velocity v. However, to obtain a wavelength and a period, the function f must be a periodic function of its argument. As noted, the cosine is a periodic function and that is why a wave based upon the cosine has a wavelength and a period.

The sinusoidal wave solution describes a wave of a particular wavelength. This might seem to make it a specific solution, not applicable to more complicated propagating waves. In particular, the sinusoid is defined for all times and distances, whereas in physical situations we deal with waves that exist for a limited span in space and duration in time. Fortunately, an arbitrary wave shape f(x − vt) can be decomposed into a set of sinusoidal waves using Fourier analysis. As a result, solutions describing the simple case of a single sinusoidal wave can be applied to more general cases.

This well-sourced material has been reverted by Srleffler on grounds found at Talk:Wavelength#Spatial_and_temporal_relationships, along with my response.

I would not take too much notice of this event were it not simply one more instance of reversion of my efforts based upon rather weak premises.

Can someone take a look at this example, and possibly look over the talk page itself to see what might be done here? Brews ohare (talk) 12:12, 6 July 2009 (UTC)

I tend to agree with those who do not think it belongs in the article on wavelength. Perhaps a general article on waves? — Arthur Rubin (talk) 12:59, 6 July 2009 (UTC)

Rannow's Theorem

Some quick observations on the new article titled Rannow's Theorem:

• Wikipedia:Manual of Style (mathematics) is conspicuously ignored. So are some frequently needed provisions of Wikipedia:Manual of Style.
• The use of an asterisk for ordinary multiplication in TeX is uncouth.
• No google hits. (And no references.)
• I've never heard of it. That's rather odd, for a "key theorem of calculus". And it's not just that I don't know it by this particular name (that happens).

As to actual content:

• The statement looks as if it would need to rely on some continuity assumptions, but none are stated.

So I am somewhat suspicious.

I'll say more after I've read it more closely. Michael Hardy (talk) 22:16, 6 July 2009 (UTC)

... OK, now I've looked at it closely enough to see what it says. I've nominated it for deletion. See the discussion at this link: Wikipedia:Articles for deletion/Rannow's Theorem. Don't just say Keep or Delete; give your arguments. Michael Hardy (talk) 22:49, 6 July 2009 (UTC)

Citation formatting, discussion in Talk:Matroid

There's a discussion in Talk:Matroid re citation formatting that probably applies more broadly to mathematics articles on Wikipedia in general. —David Eppstein (talk) 06:22, 4 July 2009 (UTC)

It does; but I disagree very strongly with what David has been saying there. Insofar as the {{citation}} templates are formatting tools, they are nearly useless; even if the format they enforce were optimal (which I dispute), they take me longer and more trouble than formatting by hand. The Harvard style links are useful, but unimportant for most mathematical articles. Septentrionalis PMAnderson 22:53, 7 July 2009 (UTC)

I suggest using a creation of our own Jakob.Scholbach to help you format {{citation}} templates: [1]. I don't format them by hand anymore, ever. Ozob (talk) 18:06, 8 July 2009 (UTC)

Thanks. Still easier to cut and paste an already formatted one. Easier to read and maintain, too. Septentrionalis PMAnderson 22:58, 8 July 2009 (UTC)

Algebra articles on WP

Recently, I have attempted to improve some algebra-related articles to a reasonable standard. I feel that there are far too many stubs in this field, as well as many articles which deserve more content. Mainly, I think that we need to improve the somewhat less well-known articles on algebra so that people who read algebra articles, other than laymen, may benefit. I understand, however, that User:Jakob.scholbach has done significant work on the well-known concepts and hence my motivation.

In particular, if you happen to come across an algebra article which I have edited, and notice something incorrect by Wikipedia standards, please comment/criticize if possible for I am not particularly experienced in WP when it comes to expanding articles. Thus far, I have improved Jacobson radical and created Quasiregular element. I am mainly focusing on related concepts at the moment, such as Nakayama's lemma, Nilradical and Simple module. Any comments would be most appreciated.

With respect to citations, I am mainly citing the book by Isaacs. Although I am aware that there are other excellent books in algebra, I think that other books can easily be cited if necessary. I have chosen Isaacs because in my view, this is one of the better books in the field. You might notice, however, that Jacobson radical and Quasiregular element have more citations than necessary. --PST 06:36, 7 July 2009 (UTC)

I may be showing my age, but it would be nice to see citations of Jacobson's own Algebra. For numbers of citations, see WP:SCG. Septentrionalis PMAnderson 21:54, 7 July 2009 (UTC)

Nah. I always preferred van der Waerden's book. What does that make me? Sławomir Biały (talk) 22:18, 8 July 2009 (UTC)

I should point out that there are books out there other than the one by Isaacs. I don't have this book, but it seems to make rather a wreck of Nakayama's lemma. It is better to stick with more standard sources, like Matsumura, Atiyah-MacDonald, Zariski-Samuel, or Eisenbud. Sławomir Biały (talk) 04:46, 9 July 2009 (UTC)

I certainly do not challenge the assertion that there are better books than Isaacs. Furthermore, I have not used his book in any way, in the recent improvements of Nakayama's lemma. Rather, I have cited facts in the article using his book. Your edit summary, "what is going on with Nakayama's lemma, drop the Isaacs book for a minute please" is rather rude in my view. Although I do not claim the new version to be better than the old, note that (essentially) no-one has added significant material to the article for sometime (for one year, precisely), and at least my additions constitute some advance in writing the article. Could you please state what you dislike about the current version? I am more than happy to discuss this, but I do not appreciate rude remarks. --PST 05:24, 9 July 2009 (UTC)

Certainly. The article now has an entirely one-sided view on Nakayama's lemma that is not at all helpful in understanding the typical applications of the lemma and is more or less at odds with the general usage in the mathematical community. It is first and foremost a result in commutative algebra, not chiefly a result of ring theory more generally (as your current version suggests). Most references to Nakayama's lemma in the literature are to the commutative version. Secondly, the lemma itself is rather difficult to appreciate as such. The current structure of the article emphasizes maximal generality over understandability, whereas I think the article should focus exclusively on the commutative case (which is fairly typical in dealing with the result), and give a variety of examples how it can be used for "geometrical" problems. This can then be followed by a short section on how it generalizes to non-commutative rings. As for whether "there are better books than Isaacs", as I've already said I cannot really evaluate the Isaacs book. But it does seem a rather poor source on commutative algebra, given the article it produced. Sławomir Biały (talk) 05:44, 9 July 2009 (UTC)

Blahtex and mathml support in Mediawiki (and Wikipedia)

Is anyone still working on Blahtex and mediawiki's support for blahtex? The blahtex's site doesn't work (well, actually works only main page), so doesn't blatex wiki. There is project called blatexml (the only source I know where it is now possible to download blahtex). In preferences there is option to show MathML if possible (experimental), but doesn't work anywhere. So does anyone know what with progress of the project? Or is it dead? Anyone could post any informations about it? Maybe someone informed could create article blatex on Wikipedia?

Also, if blahtex isn't "mature" enough to handle Wikipedia's math formulas, maybe should Wikipedia consider other tools like itex2mml (used, for example, with instiki)? ;) Silmethule (talk) 20:08, 8 July 2009 (UTC)

Third set of eyes requested

Could someone please have a look at Talk:Dirac delta function#too many directions? Sławomir Biały (talk) 20:42, 4 July 2009 (UTC)

The article might need a more careful consideration of the "concentric" style of presentation, which returns to topics in a more sophisticated way later, rather than introducing entirely new ideas. Charles Matthews (talk) 21:28, 6 July 2009 (UTC)

Uh, what is "concentric style"? (I know concentric circles in mathematics.) -- Taku (talk) 11:24, 7 July 2009 (UTC)

The "concentric style" is just defined, a line above, isn't it? Boris Tsirelson (talk) 12:18, 7 July 2009 (UTC)

I think the article already is fairly concentric in your sense. Each of the initial sections is either written in a non-sophisticated way, or begins with a paragraph explaining things in an intuitive sense for non-mathematicians. Is this what you mean? Sławomir Biały (talk) 13:58, 7 July 2009 (UTC)

No, I was thinking more about getting to section 7.2 and "suddenly" we are talking about probability theory. This is an organisational problem, mainly. I don't have so much sympathy with the criticism in general, but here I think "too many directions" might be a valid point. There is some point here about what I think of as the Lighthill-style approach to distributions (it doesn't matter so much whether you make a Gaussian narrower and taller, or some other shape); but if probability theory is really central, one should be warned earlier. (So I think it isn't central to telling people what the idea is). Charles Matthews (talk) 21:38, 8 July 2009 (UTC)

Yes. That's a valid point about bringing in probability distributions. It was my own clearly less than ideal attempt to consolidate some facts that had been carelessly dumped into an earlier incarnation of the article. But there is still no suitable home for this errant paragraph. Sławomir Biały (talk) 03:53, 10 July 2009 (UTC)

Links to exampleproblems.com

The site exampleproblems.com is linked to from several articles[2]. As the site is a wiki and not as such a reliable reference per our usual standards I was going to delete these per WP:EL. However, on closer inspection I noticed that these links have been added by established user Tbsmith (talk · contribs) who doesn't seem to be active here on a regular basis. I asked on the reliable sources noticeboard and was (wisely) told to ask for input from this project before removing them[3]. I'd like to know if these links are normally considered acceptable by this project or not. If not, I'll remove them from mainspace. I know this may sound like I'm being overly cautious but I'm trying to avoid a conflict by not ignoring some consensus I may not be aware of. Thanks, Vyvyan Basterd (talk) 15:30, 7 July 2009 (UTC)

Look at User:Tbsmith: "Todd Smith, a mathematician and creator of ExampleProblems.com". --El Caro (talk) 19:18, 7 July 2009 (UTC)

Exactly, I noticed that too. I was going to assume good faith though and ask if the project want these links kept or not. I don't think he added them in bad faith, I question if they meet the usual standard required here. Vyvyan Basterd (talk) 19:37, 7 July 2009 (UTC)

I do see some merit to relevant links to the site: deep links to a particular article hosted by ExampleProblems.com. However, many of these are links to the main ExampleProblems.com page. To me this crosses the line from providing a useful resource to outright promotion of the site. I would suggest replacing these main page links with more targeted links if possible. Perhaps deletion should be entertained as a last resort. Sławomir Biały (talk) 15:28, 8 July 2009 (UTC)

I think that links to the main page should be deleted if not replaced. I don't mind good-faith external links, even to a wiki, if appropriate -- but the general page won't really be helpful anywhere. CRGreathouse (t | c) 02:18, 10 July 2009 (UTC)

Pageview stats

After a recent request, I added WikiProject Mathematics to the list of projects to compile monthly pageview stats for. The data is the same used by http://stats.grok.se/en/ but the program is different, and includes the aggregate views from all redirects to each page. The stats are at Wikipedia:WikiProject Mathematics/Popular pages.

The page will be updated monthly with new data. The edits aren't marked as bot edits, so they will show up in watchlists. If you have any comments or suggestions, please let me know. Thanks! Mr.Z-man 20:31, 9 July 2009 (UTC)

Changes to popular pages lists

There are a few important changes to the popular pages system. A quick summary:

• The "importance" ranking (for projects that use it) will be included in the lists along with assessment.
• The default list size has been lowered to 500 entries (from 1000)
• I've set up a project on the Toolserver for the popular pages - tools:~alexz/pop/.
  • This includes a page to view the results for projects, including the in-progress results from the current month. Currently this can only show the results from a single project in one month. Features to see multiple projects or multiple months may be added later.
  • This includes a new interface for making requests to add a new project to the list.
  • There is also a form to request a change to the configuration for a project. Currently the configurable options are the size of the on-wiki list and the project subpage used for the list.
• The on-wiki list should be generated and posted in a more timely and consistent manner than before.
• The data is now retained indefinitely.
• The script used to generate the pages has changed. The output should be the same. Please report any apparent inconsistencies (see below).
• Bugs and feature requests should be reported using the Toolserver's bug tracker for "alexz's tools" - [4]

-- Mr.Z-man 00:10, 12 July 2009 (UTC)

Function

In spring 2007, after long discussions and painstaking consensus forming, the article Function (mathematics) reached a decent state. After a long period of relative calm, a new editor restarted a discussion about the rigorous mathematical definition of the function. This opened some of the old splits between "formalists" (those who pay most attention to the definition and syntax) and "encyclopaedists" (those who try to convey the meaning and illustrate uses). As a result, Rick Norwood wrote a new lead to the article. Several people objected to his changes, and I tried to reach a compromise by restoring part of the old lead and improving upon it. Sadly, this was followed up by a wholesale revert and chest-pumping at the talk page. I request that members of the project try to help form a consensus. This is one of the most important and frequently viewed mathematics articles here, and we cannot be too careful in making it as broadly appealing as possible. Thanks, Arcfrk (talk) 14:19, 12 July 2009 (UTC)

Category:Relations

I emptied it, rather than leaving it set for a merge back to Category:Mathematical relations, because the creator of the category mangled other categories some of the articles were in, such as Category:Closure operators. I had hoped that the cfm I created would have been sufficient, but then I noticed removal of other appropriate categories. If this was improper, please let me know. — Arthur Rubin (talk) 10:17, 27 June 2009 (UTC)

Not to endorse that; but I notice that Category:Set theory requires a fair amount of work placing articles into appropriate subcategories. Charles Matthews (talk) 13:51, 29 June 2009 (UTC)

I can see that. Can someone provide a current category tree for categories which should be subcategories of Category:Set theory? I don't want to kick articles down one level, requiring further sorting.... — Arthur Rubin (talk) 02:16, 30 June 2009 (UTC)

As a followup question: Should Category:Relational algebra be in Category:Mathematical relations? Seems to me to be a different concept entirely. In fact, Category:Relational algebra does seem to be exactly part of mathematics at all.... — Arthur Rubin (talk) 06:32, 6 July 2009 (UTC)

I don't follow your reasoning. This is database theory, but the theory used is mathematical - what else would it be? Charles Matthews (talk) 21:42, 12 July 2009 (UTC)

I'd say yes Category:Relational algebra should be in Category:Mathematical relations given the first sentence of the article Relational algebra: "Relational algebra, ..., deals with a set of finitary relations". Also although Relational algebra is probably mostly studied by computer scientists, I'd say theoretical computer science is part of mathematics, and the book Universal algebra, algebraic logic, and databases is definitely mathematical. I mean it even has a chapter on Galois theory of databases. How cool is that? Charvest (talk) 08:31, 13 July 2009 (UTC)

Matrix calculus: Definition of the matrix derivative

We could use some help to resolve a controversy about the correct formulae for the matrix differential and the matrix derivative at the article Matrix calculus. See the talk page, especially the section Disputed information: Matrix derivative.  Cs32en  22:52, 11 July 2009 (UTC)

I concur we need assistance, primarily as to the notation(s) actually used in serious mathematical works. — Arthur Rubin (talk) 15:49, 13 July 2009 (UTC)

See Talk:Matrix calculus#Scope of questions for my view as to the matters in dispute, and my take on them. My desired outcome is not necessarily represented in all cases. — Arthur Rubin (talk) 21:19, 13 July 2009 (UTC)

Certain hyphens

How many size-3 subsets does a size-8 set have?

The set of dimension-2 subspaces of a dimension-4 space is an example of a Grasmannian.

He was wearing size-10 shoes.

${\begin{aligned}{\text{size-3 subsets of a size-8 set}}\\8-3=5\end{aligned}}$

In the second case above, I'd prefer "2-dimensional subspaces". But it would never have occurred to me that those could be mistaken for minus signs. But user:r.e.b. wrote on my talk page:

Putting hyphens - that look rather like minus signs in front of numbers seems a bad idea, whatever the MOS says. r.e.b. (talk) 19:39, 12 July 2009 (UTC)

This discussion is complicated by the fact that the traditional use of hyphens is a slightly endangered species, still used by book publishers, magazines, and newspapers, often no longer used in package labeling and advertising. It is a splendidly efficient disambiguating or clarifying tool in some cases. "The correlation between maternal alcohol use and small for birth weight" is a phrase I had to look at several times to parse it. Why was someone concerned with correlations between "small", on the one hand, and on the other hand, maternal alcohol use, and why just for birth weight? "The correlation between maternal alcohol use and small-for-birth-weight" would not have caused any mental hesitation. "The German occupied town of Caen" and "the German-occupied town of Caen" is an example of very efficient disambiguation. "A man-eating shark" scares people away from beaches, whereas "a man eating shark" is a customer in a seafood restaurant.

Opinions? Michael Hardy (talk) 20:33, 12 July 2009 (UTC)

A referee recently chided me for writing "depth first search" when I should have used depth-first search, so I think hyphenation as a part of English grammar is alive and well. But I agree that "size-10" could easily be misread as "size −10", so rephrasing to avoid digits after hyphens seems like a good idea. —David Eppstein (talk) 20:46, 12 July 2009 (UTC)

I agree with you! I would in fact find the absence of hyphens—"size 3 subsets", or "size 10 shoes"—confusing or at least somewhat odd, and to my eyes the hyphen in "size-10 shoes" is at no risk of being confused for a minus sign. I do agree that it is possible that they are confused, so rewriting might be a good idea, but I think simply dropping the hyphen isn't. Shreevatsa (talk) 21:42, 12 July 2009 (UTC)

Just to complicate the issue, American and British English differences#Punctuation suggests that omitting the hyphen is more acceptable in British than American English. —Blotwell 13:23, 14 July 2009 (UTC)

This also (implicitly?) has something on the use of hyphens in mathematics:

A key ingredient of the proof is a Borsuk-type theorem on the existence of a pair of antipodal 2-faces of a 5-polytope whose boundaries are linked in a given embedding of the 1-skeleton in 3-space.

(But maybe not bearing directly on the present question.) Michael Hardy (talk) 23:11, 12 July 2009 (UTC)

"Valentina Harizanov" nominated for deletion

See Wikipedia:Articles for deletion/Valentina Harizanov. Don't just vote Keep or Delete; give your arguments. Michael Hardy (talk) 05:30, 15 July 2009 (UTC)

Equation solving

I have just added the Wikiproject Mathematics template to the talk page of Equation solving. The article seems to have been pretty much ignored until now and it needs a lot of work. I have filled in the bits on ratings etc.. If someone wants to do a more official assessment then please do. Yaris678 (talk) 18:03, 15 July 2009 (UTC)

Pseudo-edge

Pseudo-edge needs attention. In particular, there is no definition. Michael Hardy (talk) 05:43, 16 July 2009 (UTC)

A quick googling suggests that the word "pseudo-edge" has been used in different context in a fairly ad-hoc manner, just like someone might define and use terminology such as "blue edges" to refer to something that does not have a generally accepted name. Delete? — Miym (talk) 06:52, 16 July 2009 (UTC)

Judging from the creator's comment on the talk page and some other anonymous edits from the same IP range, this is just some guys from Hampshire College fooling around. After a removed speedy and a removed prod, AfD seems to be the only option. The English Wikipedia is quite good at wasting hours of productive editors' time with each minor incident of vandalism of this type. Hans Adler 07:46, 16 July 2009 (UTC)

Actually, the problem with it is that this is an (implicit) definition: a pseudo-edge is a requirement, in a graph coloring problem, that two non-adjacent vertices differ in color, and nothing else. Wiktionary exists for statements like that. Septentrionalis PMAnderson 15:26, 17 July 2009 (UTC)

Well-behaved functions

Well-behaved is currently all about mathematics. However, in my opinion, it is very poorly written. I am not a mathematician, and a lot of mathematical content pages link to it - but the page does not tell me what all those pages actually mean when they write that a function needs to be 'well-behaved', and instead claims the meaning of the word is up to "fashion", and gives a bunch of examples of which functions are "better behaved" than others, according to "someone" (there are no citations, and the talk page seems to indicate people disagree on these matters). I've left a comment on the article's talk page to this effect, then checked the history and noticed it seems not to really ever have gotten a lot of attention. I was wondering if there were people here who would be able to fix this. I would do it myself, but don't know enough about the subject to write anything that would actually be usable (that's why I wanted to read up on it!). Thank you! :-) Gijs Kruitbosch (talk) 20:01, 17 July 2009 (UTC)

Well-behaved (or, more often, "sufficiently well-behaved") is a piece of hand-waving = "under some narrow set of conditions which (probably) will be specified later." I see this in the article, but it may not be visible to the lay reader. Septentrionalis PMAnderson 20:38, 17 July 2009 (UTC)

The term is not very well-defined ;-) That doesn't prevent us from writing an article about it, however, as long as the term is notable. Whether a function is well-behaved or not depends on the context - this at least is the way I have seen the term being used. The article doesn't make that sufficiently clear. I'm a bit too lazy to look for reliable sources on this at the moment, so I hope someone else will fix this problem (and, potentially, other problems) of the article.  Cs32en  21:38, 17 July 2009 (UTC)

GA Review of Obstacle problem

I am conducting a Good Article review of this article. Have just scraped a pass at Maths A Level over forty years ago, I am unable to comment on matters pertaining to the accuracy of the article. I have concerns over whether the article is accessible to the general reader, whether it uses too much un-explained jargon, some unreferenced statements and I cannot determine whther the article is broad in scope, focussed and contains no original research. Please comment at Talk:Obstacle problem/GA1. Thanks. Jezhotwells (talk) 09:34, 12 July 2009 (UTC)

I really could do with some input into the discussion at [[Talk:Obstacle problem/GA1], otherwise I will have to fail the nomination. Thanks. Jezhotwells (talk) 00:22, 20 July 2009 (UTC)

• Second Could somebody with some analysis or PDEs background please have a look at this article? Thanks, Ray^Talk 00:25, 20 July 2009 (UTC)

List of mathematical examples

The ancient article titled List of mathematical examples is still in a somewhat neglected and stagnant condition. (I just added another item to it.) Does it deserve our attention? Michael Hardy (talk) 00:04, 18 July 2009 (UTC)

Awesome article, but does anyone read it? Anyways, should we link to the section that contains the example, instead of the article? - Peregrine Fisher (talk) (contribs) 07:59, 20 July 2009 (UTC)

Adding Near set to the "See Also" section on the page Set (mathematics)

Hello all,

I would like to add the page on Near Sets to the "See Also" section on the page Set (mathematics) and I was told this is the place to start a discussion on the matter.

To borrow from the Wikipedia set page:

By a "set" we mean any collection M into a whole of definite, distinct objects m (which are called the "elements" of M) of our perception [Anschauung] or of our thought.

In near set theory, the elements of a near set are distinct objects that are elements of our perception. A set $X$ is considered a near set relative to a set $Y$ in the case where the feature values of one or more of the objects in the set $X$ are almost the same (within some epsilon) as the feature values of one or more of objects in a set $Y$. In effect, any traditional Cantor set $X$ is called a near set whenever the nearness requirement is satisfied. I would be more than happy to send a copy (or post a link) of an article giving the underlying theory on near sets.

Thanks,

Christopher Henry NearSetAccount (talk) 19:07, 20 July 2009 (UTC)

I think perhaps an addition to Set might be appropriate, rather than to Set (mathematics). It appears not to be a mathematical object.

That is, provided that any of the sources in the article show the concept is used at all. — Arthur Rubin (talk) 19:33, 20 July 2009 (UTC)

Agree with that. I'd have put it into the see also links of some pages about automatically classifying and grouping data rather than mathematical sets. Also near set doesn't have any see also section - surely that would be a good guide to related articles? Dmcq (talk) 20:06, 20 July 2009 (UTC)

(edit conflict) First of all, the context of this doesn't seem to be mathematics at all, but the kind of computer science that deals with topics that are so trivial that one has to complicate everything by inventing application-dependent non-standard terminology for all basic terms.

According to your definition, whenever two sets X and Y have non-empty intersection, X is considered a near set relative to Y. Is that what you want? Unfortunately your definition is undistinguishable from pseudo-mathematics because

• in the first sentence "near set" refers to a type of mathematical object more general than a normal set,
• in the second sentence "near set" is a relation between two ordinary sets (and it doesn't look like a particularly useful one, I would say), while
• in the third sentence, being a near set is a property that an ordinary set may or may not have.

I would not have used this strong language if upon looking it up in the article near set I hadn't encountered the following:

• A lead that doesn't define anything but only gives a very vague idea that even leaves it open whether "near sets" are objects or being "near sets" is a relation.
• A section "Definition" that fills several screens with what looks like The Emperor's New Clothes mathematics. It's also extremely badly written. For example Definition 2:

A perceptual system $\langle O,\mathbb {F} \rangle$ is a real valued total deterministic information system where $O$ is a non-empty set of perceptual objects and $\mathbb {F}$ is a countable set of probe functions.

The most straightforward reading is that a perceptual system is a real valued total deterministic information system with additional properties. But what is a real valued total deterministic information system? You don't tell us. (You don't even tell us in which branch of science or the humanities we should look for a definition.) Is it an information system with additional properties? Is it an information system? Probably not. You are linking to rough set, an article that defines information system as attribute-value system, which turns out to be an obfuscated way to refer to a matrix with named rows and columns. I will just call it a "matrix" for simplicity. At this point I came to the conclusion that the words "total" and "deterministic" are probably completely redundant and simply express that the matrix doesn't have holes, i.e. undefined entries (which according to the definition it can't have anyway), and that it's really just a single matrix, not a set of similar matrices with us not being sure which one it is (also implicit in the definition). So we are one step further (I am also using the fact that by "probe function" you mean a real-valued function defined on some set of "physical objects", although that's not actually what your Definition 1 says):

A perceptual system $\langle O,\mathbb {F} \rangle$ is a real-valued matrix where $O$ is a non-empty set of perceptual objects and $\mathbb {F}$ is a countable set of real-valued functions.

This doesn't make any sense, but assuming "perceptual objects" = "physical objects" we can now guess what you mean:

A perceptual system $\langle O,\mathbb {F} \rangle$ consists of a non-empty set $O$ (called perceptual objects) together with a set $\mathbb {F}$ of real-valued functions $f:O\to \mathbb {R}$.

Then, under the heading "Perceptual relations", you pretend to define without further assumptions what the "description" of an object $x\in O$ is. Of course that's not what you do. What you really do is, you fix a finite sequence $\phi =(\phi _{1},\phi _{2},\ldots ,\phi _{i},\ldots ,\phi _{l}),$ of real-valued functions defined on $O$ and then call $\phi (x)$ the description [vector] of $x$. Since $\mathbb {F}$ seems to have been lost in the process, we are supposed to guess that when you called $\mathbb {F}$ a set you actually meant a finite sequence, and $\phi =\mathbb {F}$. (In particular, I would guess that the same function is allowed to occur twice, so if you want to think of it as a set, it's a "linearly ordered multiset".)

Now you get into a long-winded tangent about the Euclidean norm, announcing your intent to apply it to the difference of two descriptions.

We are still far from the section "Perceptual tolerance relation" (which in turn is very far from the end of this tour de force of senseless obfuscation of what is presumably a totally simple definition), but my tolerance is already completely exhausted. Hans Adler 21:08, 20 July 2009 (UTC)

I question whether Near set should be in the Category:Systems of set theory where it has been placed. JRSpriggs (talk) 10:34, 21 July 2009 (UTC)

It certainly should not. Algebraist 15:14, 21 July 2009 (UTC)

I'd like to thank Hans Adler for his explanation of the article, without which I would have been lost. It's clearer now that it does not belong in set theory (the article or category). CRGreathouse (t | c) 17:05, 21 July 2009 (UTC)

I think I should be offended by Hans equating computer science with bad mathematics, but otherwise it's a very helpful summary. —David Eppstein (talk) 17:36, 21 July 2009 (UTC)

Sorry for almost offending you. That's not what I meant. I know that there is some brilliant mathematics going on in computer science, although even some of that suffers from very poor terminology. I said "the kind of computer science that...". I don't think the bad mathematics in computer science can be defined in terms of subfields . I first encountered this bad kind of computer science when a friend of mine who was doing a PhD in artificial intelligence gave a talk about geometric reasoning in the plane. He spent at least 20 minutes motivating, defining and explaining an apparently novel concept (not of his invention) named by an acronym assembled from terms such as "disjoint" and "covering". It turned out to be a synonym for "partition". Hans Adler 17:53, 21 July 2009 (UTC)

There's plenty of reinvention of the wheel within computer science, but isn't that just an instance of Sturgeon's law? I don't think it's a defining property of the field. —David Eppstein (talk) 17:57, 21 July 2009 (UTC)

That and Not Invented Here syndrome. Exactly because it's not a defining property I don't accept the excuse: "It's only computer science." Hans Adler 18:12, 21 July 2009 (UTC)

Wow! This has generated a lot of comments. Great, I always enjoy a healthy discussion. I think some of the confusion about what is written in the current version of the Near set Wikipedia page is good indicator of the need to clarify and simplify the page content.

$>$ That is, provided that any of the sources in the article show the concept is used at all.

Yes, it has been shown that near sets provide, for example, an effective way to solve the image correspondence problem, i.e., retrieving images from a database that are similar to a given query image. See, e.g.,

Peters, J.F. Tolerance near sets and image correspondence. Int. J. of Bio-Inspired Computation 4 (1) 2009, 239-245.

Hassanien, A., Abraham, A., Peters, J.F., Schaefer, G., Henry, C. Rough sets and near sets in medical imaging: A review, IEEE Trans. Info. Tech. in Biomedicine, vol. 13, 2009, In press.

$>$ Also near set doesn't have any see also section - surely that would be a good guide to related articles?

An oversight on my part. I will a See also section in the revised page.

$>$ First of all, the context of this doesn't seem to be mathematics at all, but the kind of computer science that deals with topics that are so trivial that one has to complicate everything by inventing application-dependent non-standard terminology for all basic terms.

Interesting comment. Sure, initially, the concepts are simple. However, formal concepts from mathematics are needed to establish a framework for near sets. Admittedly, it is a straightforward task to write a computer program that implements the near set approach to measure the correspondence between perceptual objects such as digital images. We are interested in a formal method of describing the process being used to solve the problem so that we can write theorems, proofs, propositions, etc. The goal is to establish a formal system that makes it possible to prove that our algorithms are correct rather than relying on empirical evidence from the output of our simulations. Furthermore, the theory presented in the Wikipedia page on Near Sets is well-published and grew out of Rough Set theory which is a well-established (over 25 years) and also a well-published research area.

$>$ According to your definition, whenever two sets $X$ and $Y$ have non-empty intersection, $X$ is considered a near set relative to $Y$. Is that what you want?

No, that is not what is intended. Sets $X$ and $Y$ are disjoint. For example, sets $X$ and $Y$ could represent different digital images obtained from an image archive. It is then possible to extract a description of each subimage and compare the descriptions of $x,y$. Furthermore, descriptions are formulated using probe functions (a term introduced by M. Pavel in 1993 as part of a study of image classification [M. Pavel, Fundamentals of Pattern Recognition, 2nd Ed. NY, Marcel Dekker, Inc., 1993.], and it is possible to measure the degree of similarity of $X$ and $Y$ based on a comparison of the image descriptions. If the degree of similarity of $X$ and $Y$ is non-zero, $X$ and $Y$ are considered near sets.

$>$ In the first sentence "near set" refers to a type of mathematical object more general than a normal set.

Incorrect. The first sentence states: "In mathematics, sets containing objects with similar descriptions are called near sets." This does not imply that a near set is a generalization of a traditional set, but rather a near set is a special case of a Cantor set. In fact, near sets are defined with respect to two or more Cantor sets, i.e., sets of perceptual objects with descriptions that are, in some degree, similar. The idea is to look for similarities among sets of perceptual objects which can be described by probe functions.

$>$ in the second sentence "near set" is a relation between two ordinary sets (and it doesn't look like a particularly useful one, I would say),

Yes, it is a relation between two "ordinary sets" as long as the objects in the sets can be described by some probe functions.

$>$ in the third sentence, being a near set is a property that an ordinary set may or may not have.

Generally, one considers two or more sets when using near set theory. Yes, a set can be "near" itself, but this is a trivial case. Sets can be near each other in some degree depending on the objects in the sets and the method used to describe them.

$>$ A lead that doesn't define anything but only gives a very vague idea that even leaves it open whether "near sets" are objects or being "near sets" is a relation.

Thank you for pointing that out. I will change the lead sentence. We are dealing with a relation between two sets.

$>$ A section "Definition" that fills several screens with what looks like The Emperor's New Clothes mathematics. It's also extremely badly written. For example Definition 2: A perceptual system $\langle O,\mathbb {F} \rangle$ is a real valued total deterministic information system where $O$ is a non-empty set of perceptual objects and $\mathbb {F}$ is a countable set of probe functions.

Again, thank you for pointing that out. Some terms in a given research area are so well known that one does not need to define them. However, for the sake of clarity, I will insert a link (or directly explain) for each of the technical terms in the definition of a perceptual system. The information system considered here is the same as in Rough Set theory, i.e., a perceptual system can also be called an attribute-value system in the case where it defined relative to information tables.

$>$ You are linking to rough set, an article that defines information system as attribute-value system, which turns out to be an obfuscated way to refer to a matrix with named rows and columns. I will just call it a "matrix" for simplicity. At this point I came to the conclusion that the words "total" and "deterministic" are probably completely redundant and simply express that the matrix doesn't have holes, i.e. undefined entries (which according to the definition it can't have anyway), and that it's really just a single matrix, not a set of similar matrices with us not being sure which one it is (also implicit in the definition).

I can see where you are coming from. The only problem is that I did not create this definition. As you correctly guessed, it is used in both Near set theory and Rough set theory. I chose to leave the definition as it stands in two well-established research areas. I also know that there is a group of researchers currently working a revision of the Rough set Wikipedia page.

$>$ This doesn't make any sense, but assuming "perceptual objects" = "physical objects" we can now guess what you mean:

Thanks again. I can clarify this point. Yes, a "perceptual object" is an object that has it origins in the physical world. The idea is that Near Set theory is only concerned with physical objects that can be described in some manner. I see now that it would help to define this concept beforehand.

$>$ Then, under the heading "Perceptual relations", you pretend to define without further assumptions what the "description" of an object $x\in O$ is. Of course that's not what you do. What you really do is, you fix a finite sequence $\phi =(\phi _{1},\phi _{2},\ldots ,\phi _{i},\ldots ,\phi _{l})$ of real-valued functions defined on $O$ and then call $\phi (x)$ the description [vector] of $x$. Since $\mathbb {F}$ seems to have been lost in the process, we are supposed to guess that when you called $\mathbb {F}$ a set you actually meant a finite sequence, and $\phi =\mathbb {F}$.

Thanks again. $\mathbb {F}$ is the set of all probe functions that can describe the objects in $O$. For instance, when comparing two sets, $\mathbb {F}$ will contain all possible ways of describing the objects, yet the comparison is only made on a small subset of $\mathbb {F}$.

$>$ Now you get into a long-winded tangent about the Euclidean norm, announcing your intent to apply it to the difference of two descriptions.

Thanks again. I agree with you. Instead of what is written about the Euclidean norm, I will replace what is written with a link to Norm (mathematics).

In sum, I have addressed the specific comments in response to my post. I now plan to revise the Near set Wikipedia page, taking into account the comments that have been made. The goal will be to simplify and reduce what has been written and, hopefully, reach a point where there is agreement. Thank you to all who have posted. Christopher Henry(NearSetAccount (talk) 18:44, 21 July 2009 (UTC))

Thanks for taking my comments in this way. I am afraid the way I said it didn't make it easy! I will comment as I am reading your response. I saw one misunderstanding: By the "first sentence" I wasn't referring to the article yet. I meant "In near set theory, the elements of a near set are distinct objects that are elements of our perception." Which repeats a vague definition of "set" except that it drops "definite". So it's more general. Hans Adler 18:54, 21 July 2009 (UTC)

OK, just one more thing: I guess that instead of perceptual/physical objects this theory can start with whatever you want. You just have to fix some set of probe functions. If that is the case, based on normal mathematical conventions it is misleading to "define" them before you define the perceptual systems. The normal mathematical approach would be the following:

A perceptual system $\langle O,\mathbb {F} \rangle$ consists of a non-empty set $O$ together with a set $\mathbb {F}$ of real-valued functions $f:O\to \mathbb {R}$. The elements of $O$ are called perceptual objects or physical objects. The elements of $\mathbb {F}$ are called probe functions.

Just like we don't say "A vector is a physical quantity. A vector space is a set of vectors together with...". Instead we define the vector space first, and then the vectors are simply its elements. If this is no longer the normal way to express this kind of thing in theoretical computer science, then the schism is already worse than I thought. Hans Adler 19:16, 21 July 2009 (UTC)

Thank you Hans. I see exactly what you mean. Do not worry, the schism is not as bad as you think. Us non-mathematicians need guidance every once in a while.(NearSetAccount (talk) 18:20, 22 July 2009 (UTC))

To go back to the original question, it seems clear that this belongs to the same niche as fuzzy sets, rough sets, and dynamically varying sets, all of which seems closer in spirit to concept analysis than what logicians mean by set theory. Is there any way that we could have an article on this, that we could link to in place of such specific articles in see also sections? I can't think how best one would give such an article coherence, but ther is some sort of common thread. — Charles Stewart (talk) 22:44, 21 July 2009 (UTC)

Perhaps we could have a section at the bottom of the Set (mathematics) article, called "Generalizations". Charvest (talk) 23:15, 21 July 2009 (UTC)

It doesn't sound like a generalization to me. It is just a different subject with very little connection except the word 'set' as far as I can see. Dmcq (talk) 23:57, 21 July 2009 (UTC)

Dmcq, Could you clarify your comment? To borrow from the Wikipedia page "Sets can be used as a foundation from which nearly all of mathematics can be derived." Such is the case with Near Sets. The whole theory is based on observing/measuring the degree of similarity between sets of objects based on the description of the objects contained in the sets.(NearSetAccount (talk) 18:20, 22 July 2009 (UTC))

Sets are a foundational subject. Near sets are not a foundational subject. They are not a basis for deriving much in mathematics from, they are a leaf subject and look like a heuristic for classification like lots of other ways of grouping objects. They are possibly of great practical application but I see very little likelihood of them being used in number theory or topology for instance. As far as I can see you might as well try saying they are part of category theory because they put things in categories. Dmcq (talk) 22:23, 22 July 2009 (UTC)

They're all trying to be formal theories of collections, which we might classify as three kinds:

1. Set theory, type theory, domain theory — complete accounts of notion of collections, trying to encompass all mathematical objects, perhaps relative to a restricted notion of mathematics;
2. Combinatorial species, study of collections in abstract datatypes — algebraic theories of representation of theories, typically interested in studying the properties of various collection composition operators;
3. These things — interested in studying relations that hold between the elements of a homogenous collection of objects.

How about calling these last group as "Qualitative set theories", if we can't find an established term? It's a neologism, but I think we should have some name for the ensemble of these things. — Charles Stewart (talk) 05:57, 23 July 2009 (UTC)

I like the name but it would be WP:OR to use it I think. There is an article alternative set theory which contains a mish-mash including fuzzy sets and alternative axioms unfortunately. Whatever fuzzy sets falls into would I guess be suitable. I think of fuzzy sets as being quite distinct from sets. The closest I can think of where real numbers and norms comes into the subject and yet is close to foundational in treatment and possible development that I can think of is Quantum logic, and even there I'd probably try abstracting out as much as possible that doesn't depend on cranking numbers for the logic side. My idea of an alternative set theory is one where one has something like the Axiom of determinacy instead, but you can't mix that up in the same paragraph as fuzzy sets in a meaningful way. Personally I'm sorry the title Alternative set theory has been hijacked the way it has and I wish the article just died but I guess it's not wikipedia's place to go saying how the world should be. Dmcq (talk) 06:55, 23 July 2009 (UTC)

I can see the problem looking at the see also section of Set (mathematics). It contains a whole bunch of stuff that are only very loosely related and I'd have put into the Set page for disambiguation instead. I don't think even a dense set belongs there. Probably the top of the article shoudl sy it is principally to do with maths foundations and direct to Set for everything else. Dmcq (talk) 00:16, 22 July 2009 (UTC)

James Stirling (mathematician)

Hello,
Is James Stirling's date of birth right on James Stirling (mathematician) ? Many sources give "may" instead of 22 april. Is it a Old Style and New Style dates problem ? --El Caro (talk) 06:56, 22 July 2009 (UTC)

 Done by Lilyu. --El Caro (talk) 12:09, 22 July 2009 (UTC)

Branches of combinatorics?

The section of outline of combinatorics titled Branches of combinatorics lists only the following two items:

• Combinatorial chemistry
• Graph theory

Does combinatorial chemistry really constitute a "branch" of combinatorics? And the section omits virtually everything. Would someone with competence in that area clean this up? Michael Hardy (talk) 01:43, 14 July 2009 (UTC)

Combinatorial chemistry isn't a branch, it's application. --EsfirK (talk) 19:02, 23 July 2009 (UTC)

Diophantus II.VIII

Hi

Would like to invite comment on the above article ie Diophantus_II.VIII. Readership stats do not appear to justify a stand-alone item and I am wondering if it should not rather be moved to be a subsection of another article - eg Arithmetica or Diophantus. An alternative might be to put links in from these pages and any others to which it is relevant.

Neil Parker (talk) 05:48, 24 July 2009 (UTC)

As far as I can see this looks to be about constructing Pythagorean triples. Perhaps that would make a more specific merge target. —David Eppstein (talk) 05:51, 24 July 2009 (UTC)

Erdős–Bacon number

Erdős–Bacon number was shrunk a fair bit: Before After (diff). As I'm not too attached to the article, I don't have an opinion, but perhaps someone else, with different ideas of what's OR and what's obvious, may be interested. :-) Shreevatsa (talk) 18:15, 25 July 2009 (UTC)

I am not convinced this belongs into Wikipedia at all. It seems to have happened mostly in blogs, with some very restricted coverage in the news (Daily Telegraph and BBC) by a single journalist. Of course it's OK to mention the Erdős number in six degrees of Kevin Bacon, and to discuss the Bacon number in Erdős number. And in this context it makes sense to mention the Erdős–Bacon number in a sentence or two. But more than that doesn't seem to be reasonable, especially not a separate article. Hans Adler 18:57, 25 July 2009 (UTC)

Extensive discussion at WP:OR/N#Erdős–Bacon number. Hans Adler 13:28, 26 July 2009 (UTC)

I admire your forceful, complete, pertinent, and entirely correct summation of the matter. —Dominus (talk) 03:17, 27 July 2009 (UTC)

Squaring the circle

This diff and this one identify a circle-squarer posting "original research" among us. Michael Hardy (talk) 19:00, 25 July 2009 (UTC)

I put the page on my watchlist. Magidin left an explanatory note on the user's talkpage already. — Carl (CBM · talk) 19:15, 25 July 2009 (UTC)

Their web site looks like an attempt to score high on John Baez's "crackpot index" by conforming to stereotypes of a certain flavor of crackpot. Michael Hardy (talk) 19:22, 25 July 2009 (UTC)

Jensen's formula

Can someone address the issues I raised at talk:Jensen's formula? Michael Hardy (talk) 16:08, 26 July 2009 (UTC)

Routh's theorem

MathWorld's page about this states two separate results. The first of them might be called a generalization of Ceva's theorem, and the second is an equivalent generalization of Menelaus' theorem. But all the other web sources I've looked at, and the WP page, only give the first equation. Does the second equation have a name? Is it due to Routh? Should we have it, either on the Routh's theorem page or elsewhere? —Blotwell 19:45, 24 July 2009 (UTC)

The current diagram is inconsistent with the current text. JRSpriggs (talk) 14:05, 25 July 2009 (UTC)

Good catch, I've fixed the text. (Hopefully the problem I fixed was the same as the one you noticed.) —Blotwell 16:20, 27 July 2009 (UTC)

That is it. Thank you. JRSpriggs (talk) 02:01, 28 July 2009 (UTC)

Sieve of Atkin

The addendum that was added last year (!) seems questionable to me. Can anyone verify this?

Also, the article could use some work, if anyone's wiling to lend a hand.

CRGreathouse (t | c) 02:27, 27 July 2009 (UTC)

(A normal link for those who do not log in using the secure server: [5].) It seems quite dubious to me as well. It's certainly not more efficient to work with rationals instead of integers, and the algorithm to trace the quadratics suggested in the paper and implemented by D. J. Bernstein works with integers. A description of that would be nice to have in the article, actually. — Emil J. 13:40, 27 July 2009 (UTC)

Contiguity space

Contiguity space is opaquely written. There's enough there that I think I can probably figure out just what it's about, but I shouldn't have to decipher the first paragraph the way I need to. Michael Hardy (talk) 13:22, 27 July 2009 (UTC)

Married to a pseudonym

Here's one of the weirder sentences I've found in Wikipedia (as you can see, I've fixed it). (It's not a pseudonym, unless "Tom Xmith" is a pseudonym for "Thomas Xmith".)

It seems the article on Chandler Davis was initially written by people who know him as a science-fiction writer; they didn't even mention in the first sentence that he's a mathematician. I've re-written it so that it mentions that first.

One of his theorems is mentioned in eigengap. That's an orphaned article—can someone help with that?

Davis–Kahan theorem is now a redirect to eigengap. Maybe someone here can make it into an article. (If that is done, then Davis-Kahan theorem (with a hyphen instead of an endash) should then get redirected to Davis–Kahan theorem. Michael Hardy (talk) 23:12, 27 July 2009 (UTC)

Matrix calculus: Definition of the matrix derivative

Content from the archive. The issue is still unresolved.  Cs32en  18:18, 28 July 2009 (UTC)

We could use some help to resolve a controversy about the correct formulae for the matrix differential and the matrix derivative at the article Matrix calculus. See the talk page, especially the section Disputed information: Matrix derivative.  Cs32en  22:52, 11 July 2009 (UTC)

I concur we need assistance, primarily as to the notation(s) actually used in serious mathematical works. — Arthur Rubin (talk) 15:49, 13 July 2009 (UTC)

See Talk:Matrix calculus#Scope of questions for my view as to the matters in dispute, and my take on them. My desired outcome is not necessarily represented in all cases. — Arthur Rubin (talk) 21:19, 13 July 2009 (UTC)

Three year old WW Rouse Ball Copy Vio

Turns out the vast majority of the content of W. W. Rouse Ball has been a copyright violation since Aug. 10, 2006 (see this diff). It was ripped straight out of the Mac-Tutor bio. I reverted back to the pre-Aug 10, 2006 version. If anyone has time, it would be good to rewrite the article, and readd anything newer than three years ago. RobHar (talk) 03:21, 29 July 2009 (UTC)

Hoax article Base 69

Jamie.D.Mac (talk · contribs) has created an article Base 69 which purports to be a description of base-69 arithmetic but in fact is a corrupted version of the article Octal, with all the 8s replaced with 69s, and some extra garbling. Mercurywoodrose (talk · contribs) PRODed it, but this was declined without comment by the author. I have proposed it for speedy deletion under CSD G3. --Uncia (talk) 03:50, 29 July 2009 (UTC)

I have deleted it. PrimeHunter (talk) 04:44, 29 July 2009 (UTC)

Strangest edit war I've ever seen

In the article Proofs involving the totient function, the single-purpose account Prmishra1 (talk · contribs) and several IP addresses (59.180.44.246 (talk · contribs · WHOIS), 59.180.127.247 (talk · contribs · WHOIS), 59.180.127.247 (talk · contribs · WHOIS), 59.180.7.238 (talk · contribs · WHOIS)) have been engaged in the past few days in an attempt to replace one proof of $\sum _{k=1}^{n}{\frac {\varphi (k)}{k}}=\sum _{k=1}^{n}{\frac {\mu (k)}{k}}\left\lfloor {\frac {n}{k}}\right\rfloor$ for another one. I was asked for a 3rd opinion via WP:3O and sided with what had been in the article, but Prmishra1 is persisting, without any dialog. Two things:

• Is it common to have heated disputes over unsourced proofs in math articles, with one side not discussing the matter on the talk page? I don't hang out in math articles so I don't know the usual routine.
• If anybody has expertise in that area, can they please check the proofs in question, as sort of a 4th opinion? I am not a mathematician and am certainly no expert in proof style and elegance. Here is a sample diff.

Thanks. Eubulides (talk) 17:27, 28 July 2009 (UTC)

I say, scrap both. The "alternate proof" at the bottom of the section is much more clear then either version of the inductive proof. — Emil J. 17:49, 28 July 2009 (UTC)

It does not have to be phrased as a counting proof, if someone sees that as a problem. It is basically just changing the order of summation:

${\sum _{k=1}^{n}\sum _{d|k}{\frac {\mu (d)}{d}}=\sum _{1\leq k,d\leq n \atop d\mid k}{\frac {\mu (d)}{d}}=\sum _{d=1}^{n}\sum _{1\leq k\leq n \atop d\mid k}{\frac {\mu (d)}{d}}=\sum _{d=1}^{n}{\frac {\mu (d)}{d}}\sum _{1\leq k\leq n \atop d\mid k}1=\sum _{d=1}^{n}{\frac {\mu (d)}{d}}\left\lfloor {\frac {n}{d}}\right\rfloor .}$

— Emil J. 18:14, 28 July 2009 (UTC)

Dear Emil J., I think the trick where you use the fact that

$\left\lfloor {\frac {n+1}{k}}\right\rfloor -\left\lfloor {\frac {n}{k}}\right\rfloor \;=\;{\begin{cases}1,&{\mbox{if }}k|(n+1)\\0,&{\mbox{otherwise, }}\end{cases}}$

is worth preserving, especially since it generalizes, as is evident in the next section, where

$\left\lfloor {\frac {n+1}{k}}\right\rfloor ^{2}-\left\lfloor {\frac {n}{k}}\right\rfloor ^{2}\;=\;{\begin{cases}2{\frac {n+1}{k}}-1,&{\mbox{if }}k|(n+1)\\0,&{\mbox{otherwise.}}\end{cases}}$

is used. Anyhow in the meantime our unusual friend has reverted the page again to their version. -Zahlentheorie (talk) 18:38, 28 July 2009 (UTC)

These proofs are not particularly remarkable, it has to be said. If there is anything distinctive here, it could be merged into totient function. There is nothing really encyclopedic in manipulation of Sigma-notation. Charles Matthews (talk) 20:42, 28 July 2009 (UTC)

They may not be difficult but I believe the subject of proofs using the totient function is notable and deserve its place in wikipedia. Dmcq (talk) 20:53, 28 July 2009 (UTC)

That is the point at issue. "Proofs using the totient function" is not a conventional mathematical topic, to my knowledge of number theory. It seems to me less notable than proofs using the Moebius function, for example. If there is some aspect of sieve theory (for instance) where there are discernible techniques or methods worth discussing, then it might serve to establish greater notability. Simple manipulations in the style of (say) Hardy & Wright don't count, I would say. Charles Matthews (talk) 10:09, 29 July 2009 (UTC)

Actually the leader for the article says it is for proofs involving either the totient or Möbius function which is fair enough I think, I suppose sticking both in the title would make it rather too long. Perhaps there is a more all encompassing name? Dmcq (talk) 11:01, 29 July 2009 (UTC)

Hi all, I see three possibilities to resolve this: first, revert it to the version that made the slashdot listing, second, give up on it and leave it as is, third, scrap the inductive proof. And after that, LOCK the page to keep it from constantly being reverted. It seems to me that Charles Matthews would be a good mediator. What do you think? Best regards, -Zahlentheorie (talk) 16:21, 29 July 2009 (UTC)

Well, I think this page should be merged immediately into average order of an arithmetic function. These examples show techniques where the average order is accessible by elementary methods. Arguing about exactly which is not so interesting: aliter. Charles Matthews (talk) 16:30, 29 July 2009 (UTC)

Interesting suggestion. What do you propose to do with the section on inequalities? I wonder if you are aware of the fact that the average order computations listed on average order of an arithmetic function can all be done by Mellin inversion. I can do one of these for you if you like. BTW, our mysterious friend has again reverted the page to their version. -Zahlentheorie (talk) 20:14, 29 July 2009 (UTC)

I have opened up a sockpuppet investigation request at Wikipedia:Sockpuppet investigations/Prmishra1. For now I reverted the change again. Eubulides (talk) 20:29, 29 July 2009 (UTC)

Hi there, I blundered, I don't think all can be done by Mellin inversion, but some certainly can. Let me think about this some more first. -Zahlentheorie (talk) 20:44, 29 July 2009 (UTC)

What I'm referring to here is the Mellin-Perron formula:

$\sum _{k=1}^{n}\lambda _{k}={\frac {1}{2}}\lambda _{n}+\int _{c-i\infty }^{c+i\infty }\left(\sum _{k\geq 1}{\frac {\lambda _{k}}{k^{s}}}\right)n^{s}{\frac {ds}{s}}$

where the integral is evaluated by a shift to the left, picking up residues for for an asymptotic expansion at infinity. E.g. since

$\sum _{k\geq 1}{\frac {\varphi (k)}{k^{s}}}={\frac {\zeta (s-1)}{\zeta (s)}}$

the first pole that contributes is the one at $s=2$ with residue ${\frac {1}{2}}n^{2}{\frac {6}{\pi ^{2}}}$. Similarly, since

$\sum _{k\geq 1}{\frac {d(k)}{k^{s}}}=\zeta (s)^{2}$

the first pole that contributes is the one at $s=1$ with residue $n\log n+n(2\gamma -1)$. Same for $\sigma (k)$. -Zahlentheorie (talk) 22:07, 29 July 2009 (UTC)

My preference, in general, for mathematical proofs on Wikipedia, is:

1. An article about a proof should be about a notable proof, it should not be itself a proof. Likely Erdős' elementary proof of the prime number theorem and Wiles' proof of Fermat's Last Theorem deserve their own article, because in both cases what's notable is not just the fact that was proved but the proof itself. However, I think most other proofs would not qualify in this respect. And in those two cases, at least, it would be a very bad idea to try to reproduce the whole proof within the article.
2. By the same token, if content consisting of a proof of a mathematical fact belongs in Wikipedia at all, it generally belongs in the article about that fact rather than in a separate proof article. If the proof isn't notable in its own right, it shouldn't be the subject of an article.
3. Only include the details of a proof in an article when they are important for helping the reader understand the subject. If the only thing the reader gets out of a proof is "this fact is true and can be proved by induction", don't give the proof, just say that it can be proved by induction and provide a proper citation.
4. Per WP:NPOV, don't include proofs when they would severely unbalance the article.

So in this particular case, I agree with Charles Matthews that the content belongs in average order of an arithmetic function, if anywhere. I am not yet convinced that the proof details would be helpful or important to include there, though. —David Eppstein (talk) 21:27, 29 July 2009 (UTC)

Having had another look at the article I must admit it has no statement about notability nor much by way of citation. In fact it has very little straightforward text at all which is just wrong. Dmcq (talk) 23:24, 29 July 2009 (UTC)

Livermore loops article

Could someone please take a look at the Livermore loops article. There's a lot of red links there that either need articles to be created for them, or need redirecting to appropriate articles, if they exist. There may also be more terms that could use linking. Raul654 (talk) 16:15, 30 July 2009 (UTC)

One of the blue links was to Monte Carlo, a place in southern Europe on the coast of the Mediterranean Sea. Obviously that's not what was intended. People should use common sense in linking. Michael Hardy (talk) 21:04, 30 July 2009 (UTC)

Method_of_analytic_tableaux

Resolved

Do the SVG images at Method_of_analytic_tableaux look OK to anyone? To me the fonts are placed too low and too right, overlapping the lines. — Carl (CBM · talk) 22:44, 29 July 2009 (UTC)

Does not look OK to me, I also see some overlap. Ulner (talk) 22:56, 29 July 2009 (UTC)

I think I've seen this problem before. You should be able to solve it by going into inkscape and and for each text component choosing "Convert text to path". I'd do it, but my inkscape appears to be unhappy right now. I can try again later. RobHar (talk) 23:23, 29 July 2009 (UTC)

I've fixed one of the files (File:Prop-tableau-2.svg) as described above. I also had to change the font from Times new roman to arial for some presumably unrelated problem. Hopefully no one will object. I'll go about changing the other files now. RobHar (talk) 00:34, 30 July 2009 (UTC)

That's wonderful, and it fixes the display problem completely on my browser. Thanks, — Carl (CBM · talk) 01:04, 30 July 2009 (UTC)

My web browser and operating system are set up to display web pages as white text on a black background, and all the images at Method_of_analytic_tableaux appear blank, just like many of the images on Wikipedia. I'm guessing these images use a transparent layer thereby mixing the content of the image with the colour settings of the browser. HTML web pages are not in control of how they are displayed on a user's browser and Wikipedia should not assume that they are. Images should be just that - images. Not overlays. Having said that I'm now going off to tilt at some windmills. Charvest (talk) 05:47, 30 July 2009 (UTC)

I can fix that tomorrow. The background white were misaligned in the originals so I just deleted them. It didn't occur to me that a transparent background would be a problem for anyone. Sorry. RobHar (talk) 06:39, 30 July 2009 (UTC)

Oh, thanks. I really wasn't expecting anything. I just felt like raising the issue again. I mean there are many many articles in wikipedia using transparent images. I posted a comment at the village pump a while ago and the replies were along the lines of: it probably isn't practical to change them all, and there would be opposition from those who favour transparent backgrounds. Charvest (talk) 06:59, 30 July 2009 (UTC)

No problem. I too favour transparent backgrounds, but not if it's a problem for other people. However, I think the better permanent solution would just be to have wikipedia display in-article images with a white background. In the meantime, you might be able to tweak your css file to do so. RobHar (talk) 07:11, 30 July 2009 (UTC)

Ah, but that's just the point. The browser is set-up to use black and white regardless of any web site's colour and style settings and Windows desktop theme is High-Contrast Black and white. What's really needed is to rewrite Firefox (and IE) so that transparent images are rendered not as transparent but with a background that matches whatever the background would have been if the browser was following the page's suggested colours. Charvest (talk) 08:16, 30 July 2009 (UTC)

Hmm, that's weird. Anyway, I've put backgrounds on the images. Have you tried GreaseMonkey (for firefox at least)? RobHar (talk) 23:11, 30 July 2009 (UTC)

Thanks for the suggestion. I'll investigate it. Charvest (talk) 06:03, 1 August 2009 (UTC)

The text-curve alignment in the images looks ok to me, but I'm seeing a different problem: the mathematical formulas in some of the image captions are wider than the images themselves are displayed, and are cut off by the box around the caption rather than being fully visible. —David Eppstein (talk) 05:53, 30 July 2009 (UTC)

I also saw that bug. I will see if it is in bugzilla, and file a bug if it isn't. — Carl (CBM · talk) 13:18, 30 July 2009 (UTC)

After investigating, I found the issue isn't unique to math, it happens with plain text as well. I asked about it at Wikipedia:Village_pump_(technical)#Image_captions_can_be_too_wide. — Carl (CBM · talk) 13:38, 30 July 2009 (UTC)

Cusp article

I've done a bit of work on the Cusp (singularity) article. Could someone take a look at it and make any suggestions as to improvement. The classification of cusps comes down to Arnold's A_k-series (which wan't mentioned in the original article). I've tried to give examples and explanations. Is there anything that I haven't explained properly? ~~ Dr Dec (Talk) ~~ 11:49, 30 July 2009 (UTC)

Suggest an ordering of the material that is a bit less top-down. For example, mention the ramphoid cusp much earlier. Use this to explain that the issue of why it is not 'the same' as the simple cubic cusp leads to the diffeo issue. Use that to bring in the general machinery. Charles Matthews (talk) 16:58, 31 July 2009 (UTC)

A-class discussion

As these discussions have tended to suffer from a lack of participation, I respectfully request advice and constructive criticism on Wikipedia:WikiProject Mathematics/A-class rating/Maximum spacing estimation. Thank you. -- Avi (talk) 15:40, 31 July 2009 (UTC)

Reclaiming your Project's name

Hi there, here's an FYI. If you delete all content from {{WikiProject Mathematics}}, and place the following code in it's stead...

#REDIRECT [[Template:Maths rating]]

...you will successfully redirect any use of {{WikiProject Mathematics}} to your correct template. See for example {{WPLISTS}}. The old pageforces use of the correct template. One could use either {{WPLISTS}} or {{WikiProject Lists}} on talk pages and get the correct template. If you knew all this, nevermind. But if not, give it a try if you feel it is helpful at all. Prapsnot (talk) 06:56, 1 August 2009 (UTC)