Wikipedia talk:WikiProject Mathematics/Archive/2012/Jan

Galilean transformations

Could we add something about Galilean transformations as a Lie group? For example, the Euclidean transformations, Euc(n,R) can be embedded as a Lie subgroup of GL(n+1,R), if I remember correctly, by

$(X,t)\mapsto \left[{\begin{array}{c|c}1&0\\\hline t&X\end{array}}\right],$

where X is a special orthogonal transformation and t is a translation. Could (or should) we add something similar for Galilean transformations? — Fly by Night (talk) 16:11, 23 December 2011 (UTC)

There is something on this topic in the Representation theory of the Galilean group article. But in a notation similar to yours, there is an embedding to GL(n+2, ℝ) :

$(X,\mathbf {v} ,\mathbf {t} ,t_{0})\mapsto \left[{\begin{array}{c|c|c}1&0&0\\\hline t_{0}&1&0\\\hline \mathbf {t} &\mathbf {v} &X\end{array}}\right],$

where X is a special orthogonal transformation, v is a relative velocity, t and t₀ are spacial and temporal translations. Incnis Mrsi (talk) 19:25, 1 January 2012 (UTC)

Many EoM links still broken

Not long ago, there was a discussion about links to Springer's Encyclopedia of Mathematics now being broken due to a restructuring of that website. I just noticed that many of the links are still broken. Is someone making a systematic effort to repair these, or are we supposed to do it on an ad hoc basis? Sławomir Biały (talk) 14:12, 30 December 2011 (UTC)

a working patch would be to replace the line "contribution-url=http://www.encyclopediaofmath.org/index.php?title={{{id|{{{urlname|Main_Page}}}}}}" with something like "contribution-url=http://www.encyclopediaofmath.org/index.php/{{{title|{{{urlname|Main_Page}}}}}}" (to make it work, "title" should be replaced with a regexp which substitutes underscore for a space, I do not know how to do it)

another solution would be to make a bot replace the id with the title in all the pages that link to the template.

Sasha (talk) 15:18, 30 December 2011 (UTC)

Yes, I was thinking that some sort of automated mass edit would be the way to do it. I lack the skill myself. Sławomir Biały (talk) 00:08, 31 December 2011 (UTC)

Automated edits wouldn't work if you're linking to a specific version of an article, which is something you'd need to do if you're using the EoM as a reference instead of an external link. (I know there are objections to it being used as a ref. but it's being done.) It would at least help avoid having people land on EoM's main page when they click the link, but there would need to be a lot of manual checking and corrections.--RDBury (talk) 03:41, 31 December 2011 (UTC)

Whatever is done, I assume it's possible to update all of the old links so they at least link somewhere. At the moment, they all seem to give 404 errors, which doesn't work for references or external links. Sławomir Biały (talk) 11:48, 2 January 2012 (UTC)

Superior intellects and infinitesimal knowledge

An incident is being discussed here. Tkuvho (talk) 13:41, 3 January 2012 (UTC)

Resolved Brad7777 (talk) 17:11, 4 January 2012 (UTC)

Thanks, 'Here I am, superior to Newton, Leibniz and Cauchy'. That's my one a day essential of something no vitamin pill contains :) Dmcq (talk) 18:20, 4 January 2012 (UTC)

page Philip Ehrlich proposed for deletion

The page is being proposed for deletion even though there are suitable secondary sources there. Tkuvho (talk) 10:39, 4 January 2012 (UTC)

See WP:BLPPROD (the 'policy' link in the PROD template): "the BLP deletion template may be removed only after the biography contains a reliable source that supports at least one statement made about the person in the article" (my emphasis). The one source is a review of one of his works, not about him. The other link is to his department home page, so not a reliable source.--JohnBlackburne^words_deeds 10:50, 4 January 2012 (UTC)

The link is not to his personal homepage, it's to his department's index of him. This is a reliable source for his academic affiliation. I'd say that your being a bit heavy-handed with BLP prod. There may be good reasons to delete the article, but this surely isn't one of them. Sławomir Biały (talk) 11:35, 4 January 2012 (UTC)

Steven G. Krantz

How many things wrong can be found here: Steven G. Krantz? Main thing I can see is that it seems to have been written (or at least contributed to) by himself. Also see some weasel words: "Krantz is widely considered to be a charismatic and galvanizing teacher. Many students consider him to be the best mathematics teacher that they have ever had." What do we do with pages like this? --Matt Westwood 19:00, 6 January 2012 (UTC)

The article is very detailed, but it does have a lot of flowery phrases and weasel words that need to be attributed to a source. Moreover, much of it lacks sources. Whatever we do, let's try not to be gentle with the new editor User:Sgkrantz. Steven Krantz actually is a very well respected mathematician and brilliant expositor. He would definitely be an asset to the project. Sławomir Biały (talk) 10:39, 7 January 2012 (UTC)

I have done a general tidy up to try to remove peacock terms, weasel words, repetition, self-promotion and a story about a 20-year old dispute with Mandelbrot. I haven't addressed the sourcing issue, apart from tagging a couple of the most obvious unsourced facts e.g. Erdős number. User:Sgkrantz is not exactly a new editor - the account was opened in June 2010 and the editor has been sporadically active since then, but has only ever edited the Steven G. Krantz page as far as I can tell. If User:Sgkrantz is indeed Steven G. Krantz then there is obviously a COI issue here. More work needs to be done on the article, but I'll let someone else take it from here. Gandalf61 (talk) 12:35, 7 January 2012 (UTC)

Template:mvar

I have just learned of {{mvar}} through its installation on Quaternion. It applies {{math}} and additionally surrounds its argument in HTML <var> tags.

Is this a good idea? I recall the discussion Wikipedia talk:Manual of Style/Text formatting/Archive 2#Variable markup where consensus was that manually applying <var> was undesirable. It seems to me that {{mvar}} really isn't any better. Ozob (talk) 23:07, 6 January 2012 (UTC)

Reviewing that discussion, my impression is that the consensus was more along the lines that a guideline recommending the use of a manually inserted <var> is undesirable, but that individual editors have some freedom. It was also apparent that the semantic markup value in HTML was pretty much a lost cause in the math context, but that font formatting is necessary. The implementation of {{mvar}} is not important (i.e. whether it uses <var> or '' to italicize), as this can be changed in principle in the template. The question then becomes whether use of {{mvar|x}} in place of {{math|''x''}} is to be discouraged - i.e. whether the template {{mvar}} should be deprecated. I see no urgency in doing so. Its only real value is a shorthand for italic-serif. Its use does show up the continued shortcomings of the HTML output of <math>, and the inconvenience of formatting both italic and serif in-line, resulting in the (IMO unfortunate) de facto use of sans-serif for math. — Quondum^t_c 05:32, 7 January 2012 (UTC)

{{mvar}} is better than <var>, as a wikicode level (i.e. higher than HTML) tag which may be eventually customized. The same reason for which CSS is "better" than physical formatting, <span> better than <font> etc. Concerning the HTML output of <math>, the most annoying shortcoming IMHO is a space after unary minus: $-x$, compared to −x. Sometimes this puts a formula to the edge of unlegibility, like in $[x,y]=xy-(-1)^{|x||y|}yx$ . Sadly, I do not know much about TeX math typesetting. Could we remove that space and, possibly, also add half-spaces ( ) to some positions, like [x, y] ? Incnis Mrsi (talk) 10:58, 8 January 2012 (UTC)

Template:Mactutor once again

Hello colleagues,

{{MacTutor/sandbox}} now implements a suggestion of Daniele Tampieri: O'Connor & Robertson are downgraded to editors, and there are author fields (last, first, last2, ...) It seems to work on the examples that I have checked. I suggest to replace {{MacTutor}} with this version.

Please criticise this suggestion (and the implementation) before it's too late.

Sasha (talk) 23:37, 30 December 2011 (UTC)

Many of the articles, e.g. the one on Gauss, actually were written by O'Connor & Robertson, so changing the template would cause these cites to be inaccurate. Maybe make the template default to them as authors unless another author is given.--RDBury (talk) 03:31, 31 December 2011 (UTC)

you are quite right, but my template skills are very poor (I did not succeed to do this). If yours are better, could you help (or at least explain how to do it)? Sasha (talk) 04:14, 31 December 2011 (UTC)

I'll try to look at the template code this weekend, even if I'm not so skilled in programming: as a matter of fact, RDBury is right when he says that most of the biographies are authored by O'Connor & Robertson. I also would like to praise Sasha's work, since he was able to construct an almost perfectly working (in my opinion) alternative template. Daniele.tampieri (talk) 06:50, 31 December 2011 (UTC)

Unfortunately I was not able to modify the {{MacTutor/sandbox}} yesterday: I'll try to do it this week but I'll probably succeed from next Saturday on, i.e. during next weekend. However, I tried some working solutions that resulted flawed by following shortcomings

1. I was able to introduce O'Connor & Robertson names as a default (i.e. when no other names are specified) in the first two author-related fields, but I was not able to conditionally remove them from the editor fields: is the wiki markup able to deal with flow-control statements? However, this could be considered a minor problem, since adopting one of those solutions would imply the two coordinators of the MacTutor project appearing both as authors and as editors, an situation which is commonly encountered in the proceedings of scientific conferences or collections of scientific papers.
2. This one is worst, and it is still related to the possibility of using flow-control statements in the wiki markup. I was not able to conditionally control the correctness of the author-link field. As an example, if I use the same pattern used to solve (partially) the author fields problem, then when an author-link is not specified since the author doesn't have a dedicated wikipedia entry, a link to O'Connor and/or Robertson wikipedia entries would be placed instead, and this would be damn wrong.

I hope to have a look to the wiki markup syntax rules and solve this issues. Daniele.tampieri (talk) 09:51, 2 January 2012 (UTC)

Conditional statements are available. See Help:Magic words. --Salix (talk): 10:36, 2 January 2012 (UTC)

Thank you very much Richard (aka Salix alba): I'll give a look to 'em and work on a new solution. :-D Daniele.tampieri (talk) 12:11, 2 January 2012 (UTC)

Hi everybody: today I succeeded in modifying the template in order to make it able to perform the format shown here, while leaving intact all its standard features and formats: this means that if there is not a guest author name to provide, the template will show the citation in the same way the actual one does, otherwise it will show the provided authors names, linked to their Wikipedia pages if possible/desired, and will credit O'Connor and Robertson for their work as editors. Everyone can check the template structure looking to the Template:MacTutor/sandbox page, and can see a comparison with the actual template in its testcase page (including many extra cases). Please Enjoy! :-D Daniele.tampieri (talk) 21:37, 6 January 2012 (UTC)

looks perfect on the examples which I checked. Sasha (talk) 01:10, 8 January 2012 (UTC)

Ok, if there's anyone interested in the discussion in the template page, please contribute: otherwise tomorrow we'll place the {{edit protected}} template and start other standard procedures, just to use the supplementary flexibility of the new template version (obviously keeping all standard features). Daniele.tampieri (talk) 20:45, 8 January 2012 (UTC)

Templated {{MacTutor}} has been updated and its documentation have been changed accordingly: please check the template and report/correct any new issue. Daniele.tampieri (talk) 09:08, 10 January 2012 (UTC)

Two new articles up

Hi: I recently moved Double centralizer theorem and a related article on balanced modules into the mainspace. Feel free to take a look if you have spare time. Thanks! Rschwieb (talk) 21:41, 8 January 2012 (UTC)

please check that my copyediting did not introduce mistakes. Also, are the indices in the section "Polynomial identity rings" correct? Sasha (talk) 22:44, 8 January 2012 (UTC)

I tried to spot differences with "diff" but I wasn't sure I spotted them, it looked like entire paragraphs were shifted. After reading it all again though everything looks OK. (If it was an expression that needed changed, do you remember which you changed?) There was a subscript typo in the PI ring section yep, I corrected it. Thanks for taking a look! Rschwieb (talk) 03:27, 9 January 2012 (UTC)

I probably would have made a single article instead of two stubby ones, especially since 'Balanced module' has somewhat questionable notability. It may be just me though.--RDBury (talk) 13:50, 9 January 2012 (UTC)

If you search mathsci.net with "double centralizer property" instead of "balanced module" you get four times as many hits, but it makes for a poor article title. The two topics are of course related, but are not really intertwined, so they don't really make a good single article, especially if one intends to offer examples. Both stubby? I think double centralizer theorem is about an ideal length... Rschwieb (talk) 00:43, 10 January 2012 (UTC)

This also brings me to another question, since I made one of the articles to satisfy a requested mathematics article entry. Does the requested articles page ever get cleared of bluelinks? I had thought a bot was doing it, but it seems to me the bluelinks stay pretty much the same over time. Rschwieb (talk) 00:51, 10 January 2012 (UTC)

Real algebraic geometry and Selman Akbulut

There is a dispute on Talk:Real algebraic geometry#Edits by user:Estater need to be reverted which needs the intervention of other people. The subject of the dispute is edits unambiguously aimed to promote Selman Akbulut's work. Tentative to revert these edits has led to an edit war, which, for the moment, is won by the supporters of Akbulut (most probably Akbulut himself, with several login names). For non specialist people, I precise that Real algebraic geometry is a stub, almost reduced to an historical "guideline", which, before the edits, provided a good idea of the history of the area. D.Lazard (talk) 12:47, 9 January 2012 (UTC)

Too bad a goodwill effort on one math page gets rewarded by an accusation of causing fight or conspiracy on another gossip page. Shouldn't the wiki editors be discussing the mathematical merits of entries and intelligently evaluate their worth with experts, and then insert further edits (e.g. take them out or expand if necessary), as opposed yakety-yak about peoples reputation? generate conspiracy theories as to whose supporters doing which edits. If you behave like this how can you expect to extend the pool of wiki editors? Remarksen (talk) 22.20, 11 January 2012 (UTC)

Too bad this is an encyclopedia and not a goodwill diary. Brad7777 (talk) 23:17, 12 January 2012 (UTC)

Additive synthesis

More of a signal processing than a mathematical article you may think; and you should be right. But this is a needy article with a hefty chunk of mathematical notation, in need of: restructuring, rewriting, and admin attention, I hope in that order (but don't count on it - it has been briefly protected after heavy edit-warring). I'd regard it as a personal favour if people could weigh in and make it all make some sense. The page protection expires in the next few seconds ... Charles Matthews (talk) 19:03, 12 January 2012 (UTC)

Egorov's Theorem

I'd like to add another article about the other Egorov's Theorem which I mention on the talk page of Egorov's Theorem and a disambiguation page (because the two theorems are really not related). Any guidance or input on how to do this? Holmansf (talk) 23:33, 13 January 2012 (UTC)

Sokhotskii-Plemelj formula

Hello colleagues,

following a suggestion of Pym1507, I have added placed a "propose move" template at Talk:Sokhatsky–Weierstrass_theorem#Requested_move. Please comment.

Sasha (talk) 23:34, 13 January 2012 (UTC)

Glossary of areas of mathematics

So i have created the page Glossary of areas of mathematics which at the moment is more of a list with few annotations. i think it has potential and would compliment Areas of mathematics in the same way Outline of mathematics compliments mathematics. It would be useful to see thoughts on this page, and for any help completing it. Ultimately, should it be kept? (btw few entries may not be relevant but i figured it is easy to delete them) Brad7777 (talk) 13:27, 26 December 2011 (UTC)

It seems like a content fork where there already are several competing versions. 'Areas of mathematics' already has a merge tag and the 'Outline of mathematics' article has caused some controversy here as well (see e.g. Wikipedia talk:WikiProject Mathematics/Archive 45#Topic outlines).--RDBury (talk) 14:10, 26 December 2011 (UTC)

I have added computer algebra in both Glossary of areas of mathematics and Areas of mathematics. This area has several other names (mainly "symbolic computation" and "algebraic computation") which have not the same initial letter. Should this area appear 3 times in the glossary? D.Lazard (talk) 14:56, 26 December 2011 (UTC)

I think so; an annotation saying "see computer algebra" next to symbolic computation and algebraic computation would probably be ideal, with an annotation next to computer algebra including the fact that it has several other names such as symbolic computation and algebraic computation. Brad7777 (talk) 15:15, 26 December 2011 (UTC)

I'm not convinced that it's worth developing this article. I'd rather see the time spent on improving Outline of mathematics. Jowa fan (talk) 07:45, 31 December 2011 (UTC)

Isn't the page mathematics an outline of mathematics? i.e, an improved version of outline of mathematics? I think its important to note that Glossary of areas of mathematics can be completed objectively as opposed to outline of mathematics and does exactly what outline of mathematics was trying to do: provide the possiblity of gaining information on mathematics on the macro scale. In essence, the page is like a category, linking all pages relevent and most importantly it is easy to navigate. The beauty of course of outline of mathematics is that it isnt just focused on areas of mathematics, but the lists it contains are unavoidably biased (although the sections are split very efficiently). outline of mathematics would not be needed if the category system of mathematics was made to be more efficient to navigate through (think more along the lines of the sections of the page outline of mathematics) .

Look at

Mathematics

Mathematics by country

Fields of mathematics

Mathematics-related lists

Mathematicians

Women in mathematics

Works about mathematics

Mathematics and art

Mathematical classification systems

Mathematical concepts

Mathematical constants

Mathematics and culture

Eponyms in mathematics

Mathematical examples

FL-Class Polyhedra articles

History of mathematics

Mathematical notation

Mathematical science occupations

Outlines of mathematics and logic

Philosophy of mathematics

Mathematical projects

Mathematical proofs

Pseudomathematics

Set index articles on mathematics

Mathematical terminology

Mathematical theorems

Mathematical tools

Mathematics stubs

Who would click on for example Category:mathematical comparisons?? or Category:mathematical examples? or Category:mathematical tables? Category:mathematics-related lists? these are apart of the outline of mathematics? Brad7777 (talk) 14:52, 14 January 2012 (UTC)

Category:Indexes of mathematics topics

Of the 12 pages already in this category,

• 5 are called "Index of ..."
• 7 are called "List of ..."

Just to clarify, an index is just a list that is in alphabetical order? If so, should all the articles in this category called "list of ..." that are in alphabetical order be renamed to "index of ..."? And what are thoughts about the renaming of Category:Indexes of mathematics topics to Category:Mathematics-related indexes to include all the relevant indexes, as im assuming there will be more from the 230 pages currently in Category:Mathematics-related lists. Brad7777 (talk) 20:18, 14 January 2012 (UTC)

GA nomination for Catenary

Last month I put Catenary up for GA and have put a lot of work into it since in response to the reviewer's comments. If interested, see Talk:Catenary/GA1 for the discussion, especially if you'd like to help resolve the outstanding issues. For some reason this isn't showing up on the current activity page.--RDBury (talk) 14:57, 16 January 2012 (UTC)

More specifically, if someone would like to take a look at the lead section and do what needs to be done I'd appreciate it. This is my first time with the GA process so I'm not really sure what's expected with it.--RDBury (talk) 15:17, 19 January 2012 (UTC)

Because of the hatnote, I would suggest to move from the history section to the lead the mention of the other names of catenary. May be also mention that "chainette" is the French name of the catenary, which means "small chain". D.Lazard (talk) 15:50, 19 January 2012 (UTC)

I moved the alternate names to the lead, good idea btw. Not sure that chainette being the French name is needed since it's already listed as an alternate English name.--RDBury (talk) 01:28, 20 January 2012 (UTC)

I have suggested to insert the French origin of "chainette" only because this name could be strange for a non French speaker. D.Lazard (talk) 10:33, 20 January 2012 (UTC)

The Method

The page The Method used to be a disambiguation page, one of the meanings being The Method of Mechanical Theorems of Archimedes. An editor redirected it to Method acting, claiming that the other meanings are rarely used. Tkuvho (talk) 13:08, 19 January 2012 (UTC)

It now redirects to The Method (disambiguation) which is probably a more appropriate title.--RDBury (talk) 14:27, 19 January 2012 (UTC)

Why The Method (disambiguation) is different of Method, which is also a disambiguation page? I suggest to merge them with the name of Method. — D.Lazard (talk) 15:30, 19 January 2012 (UTC)

I guess they could be merged and a redirect done. I'd keep the contents in separate sections though as The Method normally refers to something different from just Method. Dmcq (talk) 15:45, 19 January 2012 (UTC)

Tricomplex number at AfD

The article Tricomplex number has been nominated for deletion.  --Lambiam 00:57, 22 January 2012 (UTC)

Serious problems with entailment

It appears that the lead example involving John, being a bachelor, and being a man, is actually an example not of logical inconsequence as written, but of tautological inconsequence. That is, if Γ = {“John is a bachelor”}, S1 = “John is a bachelor” and S2 = “John is a man,” then S2 is not a tautological consequence of Γ. S2 is still, however, a logical consequence of Γ. And this is only the beginning of the article. It appears there is severe confusion between the concepts of logical consequence (which currently redirects to entailment) and tautological consequence. This article needs to be thoroughly reviewed. Hanlon1755 (talk) 01:05, 22 January 2012 (UTC)

Of course "John is a man" is not, under the usual translation into first-order logic, any sort of consequence of "John is a bachelor". In this case the article is correct about that point. — Carl (CBM · talk) 01:27, 22 January 2012 (UTC)

Please centralize discussion at Talk:Entailment#Lead example mistakenly refers to logical consequence when it should refer to tautological consequence? — Arthur Rubin (talk) 01:43, 22 January 2012 (UTC)

Cosine 404

Hi all,

I'm worried that an article about Sine exists, but not one for Cosine. There is an ongoing discussion at Talk:Trigonometric functions, and a draft for this article is available within my userspace.

Here are some excerpts from the discussion:

This user was for the move:

Sine can be treated independently [of the other trigonometric functions] and it's clearly useful to do so... it seems foolhardy to suggest you delete an article that's accessed 1000+ times a day, has hundreds of internal inbound links, and exists on 34 other language Wikipedias, just because you think people need to simultaneously learn cosine, tangent, cotangent, secant, and cosecant. If someone wants to know about sine, let them learn about sine.

Try reading this article with the goal of finding a definition of "sine". First, you have to get to the second sentence of the second paragraph. And then you have to decipher a 443 word sentence. It's absolutely shockingly bad at defining sine, yet you want the hundreds of references to sine to redirect here?

All the same arguments apply equally for cosine. Cosine, although conceptually very similar to sine, has its own properties, some of which are trivial, and others are trivial for sine but more complex for cosine (e.g. fixed point). I really hope I don't have to argue this point further, and I hope no one else has to deal with deletionist trolls when it comes to basic mathematics articles.
— User:Pengo

This user was against the move:

In fact I'd get rid of the sine article and redirect to this article. It already has accumulated ridiculous cruft compared to this article. There is no sine topic, the topic is the trigonometrical functions. Sine is just one of those functions. A name is not the same as a topic.
— User:Dmcq

You may discuss here as well, but please check the simultaneous discussion at Talk:Trigonometric functions and in my userspace before you say something someone else has already said.

Thanks,

The Doctahedron, 21:22, 7 January 2012 (UTC)

At first glance i was for the creation of cosine, but having a look at [[sine] and trigonometric functions first off it would be important to note that the definitions are not hard to find at all (for anybody who can use a contents!) Try looking at "1.Right-angled triangle definitions" followed by "1.1 Sine, cosine and tangent". The user is not forced to look at the reciprocal trigonometric functions at all, they are under "1.2 Reciprocal functions". However, comparison of the contents reveals that sine contains an "inverse" section, which trigonometric functions ideally needs. It also contains a section on "quadrants", "continued fractions" and an "etymology" section which are also needed. Sine also goes into more detail regarding complex analysis, which i also think trigonometric functions needs. I would vote that sine is merged into trigonometric functions with trigonometric functions being expanded. Perhaps also include a section that explains the relation between sine and cosine (in terms of the translation), because this is only done formally on trigonometric functions Brad7777 (talk) 22:23, 7 January 2012 (UTC)

A clear problem with the proposed "Cosine" article is that it defines the cosine as the ratio of the hypotenuse to the adjacent side of an angle in a right triangle, and then immediately purports to "prove" that the cosine is the derivative of the sine by differentiating a power series. That bit needs to go, I think. (There are more elementary proofs of this. First show that $\sin x/x\to 1$ as $x\to 0$ using geometrical arguments, then apply the angle sum formula. See any standard textbook on calculus. Whether such an argument should be added, I have no opinion.) Sławomir Biały (talk) 23:09, 7 January 2012 (UTC)

Exactly. It "proves" that the derivative of sine is cosine by differentiating the Taylor series of sine. But to find the Taylor series of sine you need to differentiate sine indefinitely. To do that you need to know that the derivative of sine is cosine and that the derivative of cosine is minus sine. So to "prove" that derivative of sine is cosine he assumes that the derivative of sine is cosine. Moreover, after differentiating the Taylor series for sine, he finds that it is the Taylor series for cosine. But how does he know that that is the Taylor series for cosine? To find the Taylor series for cosine he needs to be able to differentiate cosine indefinitely. — Fly by Night (talk) 01:13, 8 January 2012 (UTC)

In analysis, the sine and cosine are sometimes defined by the power series. This makes the proof legitimate, but trivial. However, if we mix the two approaches, then we get this absurdity. As you say, using the geometrical definition of the sine and cosine, the Taylor series becomes a consequence of the differentiation rules rather than vice versa. Sławomir Biały (talk) 11:08, 8 January 2012 (UTC)

I guess this is a question of how people view what Wikipedia is in aid of. I view articles as being about topics rather than terms, that Wikipedia is an encyclopaedia rather than a dictionary or index. So sin an cosine might have separate entries in a dictionary but they don't have separate chapters in maths books. Perhaps we need a separate class of articles in Wikipedia which correspond more with terms that are looked up and we'd know to just put the bare basics in them?, then we'd combine the functions of an encyclopaedia and a technical dictionary. For instance MathWorld which started off as a dictionary has a separate article about each function in Mathematica so it has articles not just about sine and cosine but things like the Bessel functions of the first kind. Encyclopaedia Britannica has a small page which points to various topics which cover sine in some detail. Dmcq (talk) 01:23, 8 January 2012 (UTC)

Wikipedia is not a dictionary. — Fly by Night (talk) 01:28, 8 January 2012 (UTC)

I'm open to improvements

Please remember that Wikipedia is not paper. I am open to suggestions as to how to improve the Cosine article. You may also edit my article as necessary, as long as you refrain from vandalism, trolling etc.

Thanks for your feedback!

The Doctahedron, 22:55, 19 January 2012 (UTC)

Hi. In case you didn't know, I'm really interested in continuing this discussion. Please contribute to the discussion so that we can reach a consensus as to whether this article should be mainspaced. Cheers, The Doctahedron, 02:36, 25 January 2012 (UTC)

Negative idea

i have came up with a theorem and this may sound crazy but stick with me. i would like to ask you all what you think the definition is of the word "negitive". to me, negitive is more than the absence but the inverted space. by this i believe that a simple problem, for example, -1*-1=1, may not be true because 1 can be described as a "ditto" number. anything times 1 is itself so for example, if x*1, it = x. but if we have a problem like x*-1 then then it gets rid of that number and ends up with zero. i would like to hear back about this idea. p.s. this is a 14 year old. — Preceding unsigned comment added by 50.39.254.225 (talk) 04:35, 11 January 2012 (UTC)

Facts like −1×−1 = 1 are unavoidable consequences of the desired properties of addition and multiplication.

0 + x = x

0×y + x×y = (0 + x)×y = x×y

0×y + x×y − x×y = x×y − x×y

0×y + 0 = 0

0×y = 0

(1 + −1)×y = 0

1×y + −1×y = 0

y + −1×y = 0

−1×y + y = 0

−1×y + y + −y = 0 + −y = −y

−1×y = −y

Taking y to be −1, we get

(1 + −1)×−1 = 0

1×−1 + −1×−1 = 0

−1 + −−1 = 0 = −1 + 1

−−1 + −1 + −−1 = −−1 + −1 + 1

0 + −−1 = 0 + 1

−−1 = 1

−1×−1 = −−1 = 1

So I hope you see that this is unavoidable, unless we discard one of: the additive identity, multiplicative identity, additive inverse, commutative law, associative law, distributive law or the properties of equality. JRSpriggs (talk) 06:40, 11 January 2012 (UTC)

Words like "negative" can be kind of confusing. In normal English it often has a very different meaning from the way it is used in maths. In English it often means "the absence of", but in other contexts like maths it might mean something like "the opposite of", which is a very different concept. There are thousands of words like this, especially ones used in maths, that have such incompatible meanings. — Quondum^☏✎ 07:05, 11 January 2012 (UTC)

I think JRSpriggs and Quondum have explained the situation very clearly. Remember that in math, the rules in place have been developed for a long time and they've done a very good job of making sense internally as well as explaining the real world, via science. Perhaps this will help you: what do you think x times 0 should be, if x times -1 is already 0?

You might also take a look at this page, or a forum like math.stackexchange, where people have asked questions similar to yours. They are very helpful over there. Leonxlin (talk) 02:01, 24 January 2012 (UTC)

Baker's theorem on linear forms in logarithms

Coincidentally, I happened to run across Baker's theorem and Linear forms in logarithms within a few days of each other. They look very closely related to me — do they really warrant being two separate articles, or should they be merged? —David Eppstein (talk) 02:35, 16 January 2012 (UTC)

I support merging: The only thing which is in Linear forms in logarithms and not in Baker's theorem is Baker-Wùstholz bound, which is much better than Baker (1977) bound, given in the other page (exponent reduced from 200n to n+2). Thus merging could consist in creating a new section "Explicit bounds" in Baker's theorem and moving the two bounds, with harmonized notation, in this new section. I have no opinion if it is worthwhile to keep Baker's 1977 bound and do not know if there are better, more recent bounds to add. This could be decided after merging. — D.Lazard (talk) 11:56, 16 January 2012 (UTC)

'Linear forms in logarithms' was actually created first and is the more general subject; it appears that the only reason it's still a stub is it hasn't been worked on much. So I would think the merge should really be from 'Baker's theorem' to 'Linear forms in logarithms'. Perhaps 'Linear forms in logarithms' is not the most descriptive name for the subject, but that's what Baker is calling it in the references cited.--RDBury (talk) 14:10, 16 January 2012 (UTC)

I agree that they should be merged, but under Linear forms in logarithms, with a redirect from Baker's theorem. The reason is that there are now many other results that are called linear forms in logarithms, but they were not proven by Baker. For example, there is a large literature devoted to the theory of linear forms in elliptic logarithms, so this topic certainly merits a section on the main linear forms in logarithms page. It would also merit cross-links with the page on elliptic curves. JosephSilverman (talk) 20:55, 26 January 2012 (UTC)

Authors of books on hyperreals

Category:Authors of books on hyperreals is being discussed here Tkuvho (talk) 15:29, 25 January 2012 (UTC)

Proposed Category:Mathematical comparisons for deletion

Brad7777 (talk) 18:58, 14 January 2012 (UTC)

Is a comparison of mathematical software, a mathematical comparison? Brad7777 (talk) 12:55, 16 January 2012 (UTC)

Still open to votes

The current votes:

Nominator's rationale: It contains 1 category and only 2 pages. It is useless Brad7777 (talk) 18:52, 14 January 2012 (UTC)

• keep falls under the "part of a large overall accepted sub-categorization scheme" exception of WP:SMALLCAT as one of the subject-specific subcategories of Category:Comparisons.--JohnBlackburne^words_deeds 19:16, 14 January 2012 (UTC)

  I don't think that's the case here, actually. The "accepted sub-categorization scheme" exception applies to cases where every or almost every element of a set (ideally, a finite set) is expected to have a category – e.g., Category:Flags by country. In the case of Category:Comparisons, there is no fixed or defined population of topics that would form the basis of a scheme of {Topic} comparisons categories. That being said, mathematics is a subject with a significant and broad scope, so I don't think it's correct to dismiss the category entirely. Also, if there is no consensus to keep it, it would need to be upmerged rather than deleted. -- Black Falcon ^(talk) 19:51, 14 January 2012 (UTC)

• Weak keep. I found one more article to add, bringing the total to three in the category itself and seven more in its subcategory. That seems enough to head off arguments based purely on numerics (as the nominator's is). —David Eppstein (talk) 02:47, 16 January 2012 (UTC)
  • Comment I would not say "comparisons of mathematical software" is a "mathematical comparison", but more of a "technological comparison", so i don't think it strictly belongs there... This would leave only 3 articles (should ideally have 10+). However i think this would not matter if the category under discussion was renamed to Category:Mathematics-related comparisons? Brad7777 (talk) 12:44, 16 January 2012 (UTC)
• Delete. But keep the sub category Comparison of mathematical software‎ as a subcategory of Mathematics and Comparisons. I agree that there is nothing mathematical in these comparisons. Among the three other pages:
  • One (Comparison of topologies) is the study of a specific partial ordering and would better be named Partial ordering of the topologies of a set. It has nothing to do here.
  • One,(Comparison of general and generalized linear models) is a stub for which it is difficult to know what is really compared. If, as one could expect, the models are associated to software implementing them, the page may be put in the category Comparisons of mathematical software‎
  • The last one (Comparison of vector algebra and geometric algebra) is a comparison of two mathematical theories, and is the only page which really corresponds to the name of the category.

I may add that "mathematical comparison of algorithms" could contain interesting pages comparing the complexity and the practical efficiency of various mathematical algorithms. But for most algorithms, such a comparison would be original research and thus has not (yet) its place in Wikipedia. — D.Lazard (talk) 14:41, 16 January 2012 (UTC)

• Delete as rather vaguely ambiguous. At the very least rename. Any equation is a mathematical comparison, just for one example. See Comparison, and Comparison (mathematics) in particular. - jc37 19:46, 27 January 2012 (UTC)

Park test

Park test is a new article by a new user that is a mess. It definitely needs a look over from an expert from Mathematics or Statistics. I will also leave a note on the Statistics project page. Thanks. Safiel (talk) 16:32, 27 January 2012 (UTC)

New contributor needs help

Hello. User:Ab konst would like to contribute a new section at L'Hôpital's rule, but is having a little trouble getting the concepts across in English. Specifically, some undefined notions of "conversion" and "comparability" are involved, and a connection to Hardy fields. I'm unable to help (I don't know what the user is referring to) but I'm hoping someone else can. The subject matter is probably very straightforward to an analyst. See Talk:L'Hôpital's rule#Conversion. Thanks, Rschwieb (talk) 16:37, 27 January 2012 (UTC)

Apparently "conversion" means "finding the converse of" and "comparability" is similar to "~" as used in asymptotics; Hardy fields are a bit more arcane. In any case, it might be easier to just point to a reference rather than try to communicate the concepts in a second language. Another idea would be to add the material to the Russian article and request a translation.--RDBury (talk) 18:34, 27 January 2012 (UTC)

Homogeneous redirects

Currently 'Homogeneous', 'Homogenous', 'Inhomogeneous', 'Homogeneous (mathematics)', 'Heterogenous', 'Homogenisation', 'Homogeneous equation', etc. redirect to Homogeneity and heterogeneity which, for the most part, concerns itself with the chemical definition of the terms, though there is an odd mathematical dab section within the article. Most of the mathematical meanings of Homogeneous have nothing to do with chemistry and there are several other cases where the meaning intended in the article has nothing to do with the chemical meaning. So I'm thinking that many of these redirects, and in particular the mathematical ones, should link to Homogeneity (disambiguation) instead and the the articles that link to them should be matched to the article with the intended meaning. I'm going to go ahead and start with the most obvious misplaced redirects, and if there are no objections or better suggestions merge the dab section of 'Homogeneity and heterogeneity' into the actual dab page.--RDBury (talk) 23:02, 26 January 2012 (UTC)

Comments on Homogeneity (disambiguation):

• I suggest to remove the qualification in algebra for homogeneous polynomial, which is useless and non homogeneous :-) with the other items.
• Homogenization is an operation which exists for polynomials, related to the relation between affine and projective space. Thus an item Homogenization of a polynomial should be added
• For this reason, Homogenization (mathematics) should be renamed Asymptotic homogenization

D.Lazard (talk) 09:01, 27 January 2012 (UTC)

I have implemented my suggestions. D.Lazard (talk) 15:49, 27 January 2012 (UTC)

Also homogeneous equation was a redirect to homogeneity and heterogeneity which has nothing to do with equations. I have redirected it instead to homogeneous linear equation, and put a see also there to homogeneous differential equation. There seem to be some more math articles listed at [[1]], if anyone wants to fix these. Sławomir Biały (talk) 13:47, 29 January 2012 (UTC)

Graph isomorphism problem

We seem to have a little edit war going on (again) in Graph isomorphism problem. Can I find an uninvolved admin here to semiprotect it, or would RFPP be a better choice? —David Eppstein (talk) 23:19, 27 January 2012 (UTC)

Solved. Hopefully... —Ruud 14:18, 29 January 2012 (UTC)

The edit war is solved, the G.I.P. is still open (and probably will be for a while to come).--RDBury (talk) 19:39, 29 January 2012 (UTC)

Training = belief ?

I just linked to the Percentage page from the Sourdough page. The How to banner at the top of Percentage struck me, particularly the phrasing, "The purpose of Wikipedia is to present facts, not to train", with the emphasis, "present facts, not ... train". The implication that training is not presenting facts seems odd. If one doesn't have facts, then one has non-facts. Non-facts might include beliefs. It just struck me as unusual any training would consist of Belief. The connection to Mathematics project was the banner on Percentage, and I don't have available time to debate, although if anyone has any clarity on the above implication, which I distill to training = belief ?, your thoughts would be appreciated. Gzuufy (talk) 21:33, 27 January 2012 (UTC)

I think it's simply referring to Wikipedia:Wikipedia is not a textbook. The mathematical idiom, as it appears in journals and textbooks, is much more explanatory/pedagogical/psychological than an encyclopedia is supposed to be. The Percentage article has a bit of this flavor --- hence the notice at the top. Mgnbar (talk) 22:04, 27 January 2012 (UTC)

This is largely a matter of wording: the percentage article is largely written in the mode of an instruction manual ("this is what you should do") which is very different in style (if not necessarily in content) from a typical encyclopedic presentation. Similarly, the collection of Example Problems, which undoubtedly make this article more helpful for some readers, are not something that really belong in an encyclopedia. --Joel B. Lewis (talk) 01:11, 28 January 2012 (UTC)

(ec)The Howto template is often used to cover any issue relating to the whole "Wikipedia is not a manual, guidebook, textbook, or scientific journal" section but it's phrased to cover only part of it, hence the confusion. In this case the tag is probably referring to the "Example problems" section in the article since it should be trimmed by at least half, otherwise the article looks ok. Maybe Template:Textbook would have been more appropriate but now it would be better to just fix the article and move on.--RDBury (talk) 01:32, 28 January 2012 (UTC)

Thank you for all your replies. A related issue is that deleting the Example problems section essentially loses information in the Hall of obscure records, while moving the article to, was it Wikiversity or Wikibooks, as the banner also says, does not necessarily entail such a loss. Gzuufy (talk) 20:02, 28 January 2012 (UTC)

The article doesn't need to be moved, it just needs to be trimmed and copy edited. I'll take a whack at it since no one else seems to be working on it.--RDBury (talk) 23:50, 28 January 2012 (UTC)

"The mathematical idiom, as it appears in journals and textbooks, is much more explanatory/pedagogical/psychological than an encyclopedia is supposed to be." It's that word "supposed" that gets me. Ever since the first encyclopedia was published, it has been cast in stone that "all encyclopedias must be in this format". We have a brand new medium here, so why are we constrained to sticking to the same format that may or may not be appropriate for printed paper? --Matt Westwood 00:10, 29 January 2012 (UTC)

I think one should try and do the one thing well rather than many things badly. There's other people who do things like this well, there's no need to set up competition. Anyway you're welcome to try and improve the Wikiversity where you can see how that sort of thing has gone with the wiki model. Or perhaps Wikibooks might be what you're looking for. Dmcq (talk) 01:35, 29 January 2012 (UTC)

All very well, but this site seems to be doing one thing badly. Yes, there are plenty of wiki maths sites out there which are far superior to this one. The trouble with wikipedia is it's shackled to some tediously bureaucratic rules and a thrice-damned bunch of deletionist lawyers. --Matt Westwood 19:50, 29 January 2012 (UTC)

I really don't know which sites you're talking about. We're immensely superior to MathWorld and somewhat superior to PlanetMath. Springer might compete in the sense that their worst articles are a lot better than our worst articles, but I still think we're more useful overall. --Trovatore (talk) 00:50, 31 January 2012 (UTC)

Filtrator on AfD

Hi folks, Wikipedia:Articles for deletion/Filtrator could use some input. Sławomir Biały (talk) 19:30, 30 January 2012 (UTC)

Theorems in abstract algebra

I have created Category:Theorems in abstract algebra, please help fill it. Many articles can be found in Category:Theorems in algebra and Category:Abstract algebra. Thanks Brad7777 (talk) 14:58, 31 January 2012 (UTC)

How do you tell what is to remain in Category:Theorems in algebra ? Rschwieb (talk) 15:09, 31 January 2012 (UTC)

If the theorem is from another branch of algebra in which it is not worth making its own category, or you are not sure where it would go, I would leave it in there. Brad7777 (talk) 18:46, 31 January 2012 (UTC)