Wikipedia talk:WikiProject Mathematics

Conventions

Following a suggestion of Emil J., I've created a new section of the math MOS: Wikipedia:Manual of Style (mathematics)#Conventions. This is mostly a link to the current page on conventions, Wikipedia:WikiProject Mathematics/Conventions. I feel like it would be a big improvement if the conventions page were merged into the MOS: The conventions page is short, is highly relevant to the MOS, and would be easier to find and maintain. Does anyone else have an opinion on this? Ozob (talk) 15:57, 11 August 2009 (UTC)

In the past sometimes people have objected to including things in MOS subpages that are not strictly speaking style issues. But I think that was often motivated by unrelated political concerns, and I hope there are no such politics involved here. I support the move. It's not entirely clear to me whether the logic conventions should be merged as well, since they are also used by philosophers, who might not otherwise be interested in MOSMATH. But that can be decided later (and in the logic project). Hans Adler 16:10, 11 August 2009 (UTC)

Probably inevitable. We do need to recognise the implications, and that the MoS generally has taken on a much more prescriptive role in recent years. Which is not always for the best. Charles Matthews (talk) 17:00, 11 August 2009 (UTC)

It is not clear to me how many of our articles follow the conventions page, and when they do it is possible they do so only because the conventions described are already somewhat common elsewhere. But I don't have any strong objection to the merge as long as some cautionary language about not applying them blindly is present. I added that to the MOS just now. — Carl (CBM · talk) 12:15, 12 August 2009 (UTC)

I'm sorry if this is the wrong place to write this (please delete if so), but there needs to be more consistency with respect to how formula are presented. For example, consider the difference between how relations are written in the definition of an asymmetric relation and an anti-symmetric relation (i.e. aRb vs. R (a, b)). Conventional consistency seems to always be preferable here. —Preceding unsigned comment added by 72.90.67.27 (talk) 18:27, 17 August 2009 (UTC)

This is a fine place to write it, but I don't agree with you. Yes, there is some advantage to keeping an eye on how things are presented in different articles, to avoid confusing readers who click on a link where "compact" implies "Hausdorff" and arrive at an article where it doesn't, especially if the difference is not mentioned. But trying to prescribe prefix versus infix notation for relations is a waste of effort in a project as sprawling as this one, and will just annoy contributors. Any reader who has a chance of understanding the material in the first place, will be able to handle notational diversity at this level. --Trovatore (talk) 18:50, 17 August 2009 (UTC)

Differential of a function

The definition of differential of a function that appears in that new article has appeared in calculus textbooks for more than 30 years now, and that's an unfortunate gap between mathematicians and authors of calculus textbooks. You'd hope that authors of calculus textbooks would be mathematicians, but it seems they're a different culture (I don't mean Spivak and Apostol, and I think there are a few others....). And they write books by zeroxing each other's books. It might not be politic to propose burning them at the stake as heretics, so I won't mention anything like that. But I've made some comments here.

Would other mathematicians here agree with me that this abomination is an abomination? Michael Hardy (talk) 02:36, 17 August 2009 (UTC)

Yes, I completely agree. In fact, what is presented in the article is rather worse than what I've found in most calculus textbooks I've looked at lately. In my experience, most 21st century calculus textbooks are written so as to never say something that is mathematically incorect, because mathematicians who teach calculus complain more vocally about actual mathematical errors than other deficiencies. Plclark (talk) 03:58, 17 August 2009 (UTC)

Thank you. Now if possible, can you add some comment to the linked-to talk page? I'm not at all sure the creator of that article is reading this present page. Michael Hardy (talk) 04:46, 17 August 2009 (UTC)

Yes, I'm reading. I'm following all the disscusion [1] [2] [3] [4]. You may read my last input in the discusion on the article's talk page. Usuwiki (talk) 02:27, 18 August 2009 (UTC)

I think there is a bit of a culture clash here. As far as I can make out, and I could very easily be wrong, this has come from an analysis/numerical viewpoint and may have started in Russia investigating linear differential operators including both Δx and dx and suchlike, and they'd want them in the same terms and comparable. I'd guess more people here see differentials as being more part of studying manifolds and start with a topological outlook and aren't so interested in finite differences. You got them both using linear maps and the same symbols so it grates. Dmcq (talk) 06:22, 17 August 2009 (UTC)

Sorry I see I should have gone to that page, okay will copy my comment there. Dmcq (talk) 06:26, 17 August 2009 (UTC)

I for one have tried to redirect the new article to a section of the existing article, plus I have made some other comments in the new article's page. As for calculus textbook, I can't say much: I am Italian, and textbooks when I was a student had, if anything, the opposite problem, being a bit too formal for, say, first-year students. But I see that presently there is a tendency towards "American" calculus, using new books translated from English and even renaming courses from "Analisi matematica" to "Calcolo". [[::User:Goochelaar|Goochelaar]] ([[::User talk:Goochelaar|talk]]) 07:34, 17 August 2009 (UTC)

A triviality: are tuple and word (mathematics) the same concept?

Clearly the notion of an n-tuple is distinct from that of a word, but I but a quick search in google books failed to find a set theory definition for tuple; only n-tuple is defined. This is related to a debate on List (computing), but the article on tuple could use some clarification as well. Pcap ping 12:49, 17 August 2009 (UTC)

Word (mathematics) is not being explained in String (computer science) and shouldn't redirect there.  Cs32en  13:01, 17 August 2009 (UTC)

Whether it should redirect there or not, it is explained there. Pcap ping 13:02, 17 August 2009 (UTC)

I've just changed the redirect to point to that section. Pcap ping 13:05, 17 August 2009 (UTC)

Normally one does not use the term "word" unqualified, it is always a word over some given finite alphabet. But otherwise there is no real difference, both word and tuple mean a finite sequence. — Emil J. 13:07, 17 August 2009 (UTC)

I agree. It is mostly a matter of consuetude: probably one would not say that a vector space such as ${\mathbb {R} }^{n}$ consists of words. Similarly, the operations on tuples one would spontaneously think of are mostly termwise ones, while two words tend to be concatenated, or shuffled, and the like. So, in a sense, if you use one of the two terms rather than the other, you predispose the audience to a certain set of properties and operations. [[::User:Goochelaar|Goochelaar]] ([[::User talk:Goochelaar|talk]]) 13:13, 17 August 2009 (UTC)

No, because "words" in ${\mathbb {R} }^{n}$ are all n-tuples, i.e. the words have all the same length. Pcap ping 13:42, 17 August 2009 (UTC)

Indeed. One would not usually describe ${\mathbb {R} }^{n}$ as consisting of all words on $\mathbb {R}$ of length n either. [[::User:Goochelaar|Goochelaar]] ([[::User talk:Goochelaar|talk]]) 14:41, 17 August 2009 (UTC)

Actually, I think that the definition of tuple from that article is a Wikipedia original, and that it was caused by renaming the article some four years ago from n-tuple; according to MathWorld "tuple" means just n-tuple for some fixed n obvious from context; it does not mean word. See further discussion at Talk:Tuple#Problem_with_def_of_tuple. Pcap ping 13:42, 17 August 2009 (UTC)

Apparently the word "tuple" (without n) is mostly used by computer scientist, especially in Python programming language, where it is the actual name of a data structure. [[::User:Goochelaar|Goochelaar]] ([[::User talk:Goochelaar|talk]]) 14:44, 17 August 2009 (UTC)

Indeed. In Python a tuple is an immutable list. Gandalf61 (talk) 14:54, 17 August 2009 (UTC)

The term is also in wide currency among relational database theorists, who use it to refer to a row of a table. (Each table is a relation, in the mathematical sense, and rows in the table are elements of the relation, and so are tuples.) —Dominus (talk) 16:10, 17 August 2009 (UTC)

There is a distinction: perhaps it should be clarified by means of the concepts of internal operation and external operation. The "point" of words is that concatenation is an internal binary operation - we are living in the free monoid. Obviously you can concatenate tuples of any finite length, but this then appears as an external operation on two Cartesian powers ending up in a third. In other words (in other tuples?) as soon as you write * for concatenation with its type data you become conscious of an overloading of the notation. Charles Matthews (talk) 14:54, 17 August 2009 (UTC)

Matrix calculus: Definition of the matrix derivative

Content from the archive. The issue is still unresolved.  Cs32en  13:04, 17 August 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)

This really should be resolved by verifying that the formulae stand as stated in the references (and noting the conventions in operation, per reference). I edited the section on the nature of the so-called "matrix derivative" - and there doesn't seem to be controversy about that. So that leaves only the formulae collected from the literature. Charles Matthews (talk) 14:47, 17 August 2009 (UTC)

Leibniz function

With respect to article Leibniz function, can someone please verify its meaning in regards to its derivative ( f ( x ) f ' ( x ) = 1 ). Not familiar with the term in this context and the word "Leibniz" is not found anywhere inside the books listed as references.

My addition/contribution to the article is with respect to Lie groups/algebra, with cleanup under the good-faith assumption that such an identity exists and is named after Leibniz. Henry Delforn (talk) 16:56, 17 August 2009 (UTC)

I haven't seen that usage before, and I find it at least a little bit implausible that any such convention is widespread. Michael Hardy (talk) 22:41, 17 August 2009 (UTC)

Category:Type theory and Category:data types

Cat Data types lists Cat Type theory as sub-category, which causes a lot of data types articles, e.g. some, but not all in Category:Composite data types, to be added (manually) to type theory as well. This appears wrong to me as a way of organizing this stuff. Pcap ping 03:20, 18 August 2009 (UTC)

At a quick glance, I agree. Type theory is not about data types, at least not as data types are understood in computer science (although there are certainly analogies). Neither should be a subcat of the other. Possibly a few pages belong in both, but not very many, I think. --Trovatore (talk) 03:25, 18 August 2009 (UTC)

I think you're confusing data types with data structures. Pcap ping 05:33, 18 August 2009 (UTC)

I don't think so. Type theory and data types are quite different things. --Trovatore (talk) 06:38, 18 August 2009 (UTC)

Most articles on this wiki in this area are crappy and fail to explain the link, but see initial algebra, and [5] for more details. How categories and types are related, I probably don't have to explain to you, but given that we don't have an article on the syntactic topos (as Steve Awodey calls Lambek's topos generated by a type theory), and that neither topos or type theory mentions the notion (or the other article), you may want to read about it in Lambek's book Introduction to Higher Order Categorical Logic, or if you want an executive summary, see Steve Awody's paper. Pcap ping 07:05, 18 August 2009 (UTC)

P.S. Bart Jacobs in Categorical Logic and Type Theory (1999), appears to call the syntactic topos, effective topos, but that might be a more general notion; I haven't read close enough his book, and I don't have the time currently to do so. But Jacobs book also explains in more detail how these notions relate to date types in ML etc., including a chapter on parametric polymorphism etc. Pcap ping 08:49, 18 August 2009 (UTC)

On that point, "effective topos" is something based on realisability; "syntactic topos" as you define it sounds like a general construction from a language. Charles Matthews (talk) 14:19, 18 August 2009 (UTC)

You're right, there is a difference. I don't pretend to understand it well enough to write about it on Wikipedia though. Sketches of an Elephant, chapter D1, has more general construction of a syntactic category (wrong article on the wiki) for a first order language, of which first order logic is a particular case. Johnstone then introduces sketches as being "in some sense intermediate between a theory [of a first order language] and its syntactic category [...]; it has some of the advantages of each, but also some of the disadvantages of each.", p. 861, and goes on to explain those advantages and disadvantages. He then generalized these notions in chapter D4 over higher-order signatures, of which simply typed lambda calculus (with product types) is particular case (a lambda signature has no relation symbols). Then he gets to Lambek's well-known result of the correspondence between simply typed lambda calculus and CCCs. This correspondence is rather technical, there's no "classical completeness theorem" for lambda-theories; I won't try to describe it here. He then goes on to define tau signatures (tau stands for topos/type), which are more general than lambda-signatures in that they allow primitive relation symbols. As you guessed, the syntactic category of tau-theory is a topos, and rather surprisingly, there is a completeness theorem for tau calculus. He then introduces mu-lambda-calculus (Martin-Löf type theory), which corresponds to LCCCs. Quite an interesting expose. Pcap ping 18:57, 18 August 2009 (UTC)

Look, you can find all the connections you like. It isn't even remotely the point. Neither of those categories should be a subcat of the other, period. They are from different fields of endeavor. --Trovatore (talk) 10:03, 18 August 2009 (UTC)

How so? Is type polymorphism for instance not applicable to programming (thus data), or not covered by type theory as an endeavor? Category:data types is a bit of a misnomer by using the adjective "data", but is anyone willing to have something called just Category:types? Pcap ping 18:57, 18 August 2009 (UTC)

Types in general are not amenable to treatment by computer. For example they tend to be uncountable. Even when they're not, they're not things you find in a programming language — they're at least one level more abstract than that, the Platonic ideal objects underlying what you find in a programming language. On the other hand, data types as I understand them are something you would find in a programming language, something with language-specific syntax. --Trovatore (talk) 20:03, 18 August 2009 (UTC)

Simply not true. Pcap ping 20:09, 18 August 2009 (UTC)

Which part? --Trovatore (talk) 20:11, 18 August 2009 (UTC)

Data types and types are the same thing as explained at Type system#Fundamentals, not Platonically removed as you see it. Pcap ping 20:12, 18 August 2009 (UTC)

They aren't. Types are essentially the structure V_ω+ω, except that you can't mix ranks. --Trovatore (talk) 20:15, 18 August 2009 (UTC)

Yes they are. A type system is a countable collection of ideals of V. See Cardelli and Wegner, section 3, starting on page 14. Pcap ping 20:27, 18 August 2009 (UTC)

Who mentioned type systems? The category is called type theory. The obvious thing people are going to think of is Russell's type theory. The natural interpretation of that is the one I said. --Trovatore (talk) 20:29, 18 August 2009 (UTC)

← Which "people" are we talking about? See the pretty picture in theoretical computer science. Pcap ping 21:08, 18 August 2009 (UTC)

Even if you want to focus on the things there, they still aren't data types. Come on, I think you're just being argumentative here. Data types are things like int and bool and double, structs and classes, things that you find in a specific language or an IEEE spec. They're not part of theoretical computer science at all, which takes at least one extra step towards Platonic abstraction. This is how almost everyone is going to interpret them. If the data types category intends something else, then it's misnamed. --Trovatore (talk) 21:29, 18 August 2009 (UTC)

I did my best to explain it, but you just don't get it, or don't want to get it. Bye. Pcap ping 21:31, 18 August 2009 (UTC)

Don't let the door hit you on the way out. --Trovatore (talk) 21:34, 18 August 2009 (UTC)

Henry Gordon Rice was...

At Henry Gordon Rice, we are informed that:

Henry Gordon Rice was a logician and mathematician best known as[.....]

No dates of birth and death. Only the word "was" implies he is deceased. But on the talk page it says the article must comply with Wikipedia's policy on biographies of living persons.

Which is it? Michael Hardy (talk) 04:20, 18 August 2009 (UTC)

That's probably undecidable based on what's available on google. :p Pcap ping 04:48, 18 August 2009 (UTC)

SSDI gives a Henry G. Rice (20 July 1920 - 14 April 2003) which was probably him.John Z (talk) 22:49, 19 August 2009 (UTC)

Element (mathematics)

Someone just created symbol (formal) with a redirect from symbol (logic). In my opinion such mini-articles with no potential are a maintainability nightmare and should be merged. In a note to the editor I was about to write that symbol (formal) is redundant with formal language in the same way that element (mathematics) doesn't exist because it's redundant with set (mathematics). Fortunately I checked this first: It turns out that we do have this article.

Do we really need this? Hans Adler 10:26, 18 August 2009 (UTC)

Element (mathematics) is in Category: Basic concepts in set theory; set (mathematics) is in Category:Set theory. This indicates to me a difference in pedagogic level. So which "we" are we talking about? Charles Matthews (talk) 14:22, 18 August 2009 (UTC)

I think it is a useful article. Paul August ☎ 14:30, 18 August 2009 (UTC)

Bhatia–Davis inequality

I've just written a short article titled Bhatia–Davis inequality. I could use work both on itself and on links to it from other articles. Michael Hardy (talk) 18:11, 18 August 2009 (UTC)

I didn't find the result hard to believe, once I'd understood the extremal case; but I was a little surprised it wasn't more classical. I found this PDF which has plenty of context, at one level: http://www.collectionscanada.gc.ca/obj/s4/f2/dsk1/tape10/PQDD_0027/MQ50799.pdf. (Not either of the things you were asking for, I know). Charles Matthews (talk) 14:35, 20 August 2009 (UTC)

Algorithm up for GA reassessment

Algorithm has been nominated for a good article reassessment. Please leave your comments and help us to return the article to good article quality. If concerns are not addressed during the review period, the good article status will be removed from the article. Reviewers' concerns are here. Wizardman 22:15, 18 August 2009 (UTC)

I found that article pretty terrible for me as lecture, like other work of Wvbailey's I've looked at; Random access machine comes to mind. It focuses on minutiae, most of which is barely relevant, to the point that one cannot see the forest because of the trees. The writing style making very frequent direct references to the sources with page numbers and in-text are very distracting to me. The first thing that came to my mind after I finished reading it is how true is what User:Donhalcon said in his goodbye to Wikipedia: "this is a multi-subject fan site." I'm not going to spend my time pissing on Wvbailey's parade. Just not worth the return on investment like Don said.Pcap ping 18:37, 22 August 2009 (UTC)

Stanford Encyclopedia of Philosophy

Shouldn't we cite this as a reference instead of external link in math logic articles? The two math articles I've looked at Type Theory, and Second-order and Higher-order Logic are written by published academics, and in the type theory case, by a well-known researcher in that area (despite the fact that he doesn't get a Wikipedia article), so the article is much better than what we have here, which describes type theory up to 1941 or so. Pcap ping 16:38, 19 August 2009 (UTC)

I agree. I think in the past I have changed several references in this way. We could consider a specific template for such references to encourage this and make the citations uniform. Like Template:PlanetMath or Template:ScienceWorld. Hans Adler 17:10, 19 August 2009 (UTC)

A template would be good. But the difference between a "reference" and an "external link" should be determined structurally (notionally, references are used in putting the article together), with the "External links" section having the same status as "Further reading". Charles Matthews (talk) 19:41, 19 August 2009 (UTC)

The other point is that encyclopedias in general are not usually thought of as high-quality references. Tertiary sources like Wikipedia are supposed to reference mainly secondary sources and possibly a few primary, but not other tertiary sources. It could be that the SEP is something more than an "encyclopedia" in that sense, and in that case it might be OK. But it's understandable that editors would be reluctant to use as a reference a work with Encyclopedia in its name. --Trovatore (talk) 19:46, 19 August 2009 (UTC)

Count me among the people who do not want to see us citing SEP. The problem is not the word "encyclopedia", although that is related. There are two sorts of refernces that we should cite predominately in our "content articles" (for lack of a better term).

1. Journal articles, for for establishing the dates of discoveries and attributing them to the correct mathematicians. Occasionally, esoteric facts are only going to be found in journals.
2. Monographs and other book-length treatments, including textbooks, Lecture Notes in Mathematics, and compilations such as the Handbook of Mathematical Logic. These can devote enough pages to cover a topic in much greater depth than we can, and will usually provide a rigorous and formal treatment. They provide enough context that the reader can really dig into the topic and come away with a depth of knowledge. These are the sorts of things I would be likely to cite in a journal paper if I needed a basic fact from graduate school.

We generally avoid the following for general content:

1. Newspaper and magazine articles: these are useful for popular culture and opinion but lack enough depth to be a useful reference for the mathematics itself
2. Short handouts people have used in classes (book-length lecture notes are a separate issue)
3. Expository articles that do not differ significantly from what our ideal article on the subject would say. These do not go any deeper than our article does, and so do not provide additional depth of understanding. Actually, WP:EL discourages even linking to these, but we have a general practice of linking to PlanetMath, Mathworld, Citizendium, the Stanford Encyclopedia, etc.

In essentially every case, the sorts of facts that we could source to these will also be covered in book-length treatments that provide much more value to the reader than these sorts of references provide. — Carl (CBM · talk) 21:02, 19 August 2009 (UTC)

"do not differ significantly from what our ideal article" - Many wikipedia articles are not ideal and may never be, so why not link to expository articles ? Also links to free online sources are useful in that it is easier to check something online than go to the library, especially if your library doesn't have the item you want. Charvest (talk) 21:30, 19 August 2009 (UTC)

I am saying we should include these as "external links", not as references, because there are better things to use as references. There is also the issue of lack of context and lack of depth in short expository articles, which do not provide enough information to allow readers to actually learn much about the topic. For example, if our article presents various theorems without proof, we want to provide "references" that include the proofs that we omit, not "references' that just list the same theorems without proof. — Carl (CBM · talk) 21:38, 19 August 2009 (UTC)

I have created an external link template for the Encyclopedia at {{SEP}}.  Skomorokh  22:42, 19 August 2009 (UTC)

Sweeping revisions to differential of a function

I have just radically revised the whole article.

I deleted the "Disputed" tag I added earlier.

You'll notice the definition of total differential and partial differential. One of the various great virtues of the Leibniz notation is that it makes ideas like this so simple. Is there any easier heuristic argument for the chain rule for partial derivatives than that?

(And at this time, chain rule for partial derivatives is a red link! Should we remedy that?)

Also, I've proposed a merger with differential (calculus).

We should consider adding to the article the more advanced and otherwise different viewpoints, including 1-forms. Michael Hardy (talk) 16:52, 20 August 2009 (UTC)

....and now I see that someone else has drastically revised it after my edits. Michael Hardy (talk) 16:58, 20 August 2009 (UTC)

The chain rule in more than one variable is already covered in the chain rule article; see here. Although it does need a lot of work to be done to it. ~~ Dr Dec (Talk) ~~ 17:02, 20 August 2009 (UTC)

With regard to your observation that someone else had drastically revised the article after your own, I think it is fairer to say that your (welcome) revision occurred sometime in the midst of my own incremental revisions. As a matter of fact, I was about to do something similar in spirit to your first paragraph, but I was unable to save my revision due to an edit conflict. I do hope that our collaborative effort has, at least, brought the article a significant step along the road to being a worthy encyclopedia article. Sławomir Biały (talk) 17:59, 20 August 2009 (UTC)

Maths Pedagogy

Every so often it seems schools come up with some yet sillier way to make maths inaccessible. Lots of different words to learn about distinctions between different triangles, funny rigmaroles when adding or subtracting, points will be taken off for misspellings and suchlike. I noticed in article Negative and non-negative numbers someone put in raised minus as in ⁻5 for instance. Seemingly they are now learning to put in ⁺5 and ⁻5 to show the numbers are positive or negative and should say subtract, negative or opposite of in the appropriate situations. I was wondering if an article on such ideas might be an idea or what it should be called? I probably would have too strong a POV for it :) I suppose it would be something referenced from Mathematics education as I can see it growing quite large so it wouldn't fit within that. Dmcq (talk) 18:25, 20 August 2009 (UTC)

Well, we can't go creating an article just to rant about things we think are silly in trends in math ed. We can't even synthesize criticisms made by others. However, if you find some self-conscious organization or movement, about which there are reliable sources, that makes these criticisms, then you can write about it. --Trovatore (talk) 22:11, 20 August 2009 (UTC)

Already done: Tom Lehrer got there first. Kan8eDie (talk) 23:38, 20 August 2009 (UTC) (Edit: I was thinking of New Math)

If you ever wrote a parser, you'd know it's not totally trivial to distinguish unary minus from binary minus. I guess they want to make it easier for the kids by simplifying their parsing function :P Pcap ping 00:35, 21 August 2009 (UTC)

Fast algorithms

I read this article a while ago, and thought that it is someone's attempt at creating a page on efficient algorithms. Perhaps I am mistaken, but what in the world is a "fast algorithm"? Is this a field of research in computational mathematics? How is this different from the usual algorithm design that computer scientists do? --Robin (talk) 21:34, 20 August 2009 (UTC)

Well, here is some web page with a definition of a "fast algorithm": [6]. It would take some research in the computational complexity literature to see if this is actually a well-established term. — Carl (CBM · talk) 21:47, 20 August 2009 (UTC)

Do we have any experts in numerical algorithms here? I avoided that topic in grad school. In complexity theory "at large", "fast algorithm" is just too vague to have a definition. Pcap ping 22:57, 20 August 2009 (UTC)

What they seem to do is to consider bit complexity instead of assuming a RAM where you can add intergers increment an integer (of any length!) in O(1). It's obviously written by fokes outside US which use their own terminology... Pcap ping 21:54, 20 August 2009 (UTC)

The algorithms and concepts listed on that page seem very well-studied in the field of algorithms: Karatsuba algorithm, Divide and conquer algorithm, Coppersmith–Winograd algorithm, fast Fourier transform. Perhaps the word "fast" is just a translation artifact from Russian to English, with the word "efficient" being used in English instead of "fast"? I haven't ever read the term "fast algorithms" in the complexity literature, but maybe I'm not reading the right stuff. --Robin (talk) 21:58, 20 August 2009 (UTC)

Me neither. The complexity difference between a RAM and a plain Turing machine, which is what the use, is a logN factor. Pcap ping 22:05, 20 August 2009 (UTC)

Is it fast, as in fast transforms: fast fourier transforms, fast wavelet transforms, fast hadamard transforms etc... Charvest (talk) 22:16, 20 August 2009 (UTC)

... fast multiscale transforms, fast gauss transforms, fast Johnson-Lindenstrauss transforms, ... Charvest (talk) 22:19, 20 August 2009 (UTC)

fast hough transform, fast hartley transform, Fast Walsh Transform, fast m-transform, fast Karhunen-Loeve transform, fast jacket transform ... Charvest (talk) 22:27, 20 August 2009 (UTC)

The article tinkles a little alarm bell for me, not very loud, but enough that I'd at least like to ask: Is it standard practice to combine these things under the rubric of fast algorithms? If not, then the article might be a neologism, or original synthesis.

Also the technical definition of fast is unreferenced. Again I would like to know whether this is standard, or something abstracted by the editor who wrote it. --Trovatore (talk) 22:30, 20 August 2009 (UTC)

Here's a page talking about automating the process of creating fast algorithms: Automatic Generation of Transform Algorithms "it is possible to automatically generate fast algorithms for discrete signal transforms". Charvest (talk) 22:38, 20 August 2009 (UTC)

That does not appear to be what our article is about though. How is matrix multiplication related to that? Pcap ping 22:42, 20 August 2009 (UTC)

From http://www.ccas.ru/personal/karatsuba/algen.htm, which what is article is based on, it appears he's concerned with Kolmogorov complexity of evaluating a function with a given precision(?!) I don't have the patience to read all the stuff on his web page. The bottom line as I see it is that the article is based solely on that guy's web page, including the overreaching terminology. It's a paper that appeared in some "internal" Steklov proceedings. I think we need a better source to have a shot at understanding what's he saying there... In the mean time, the article should be moved to the creator's user space. Pcap ping 22:55, 20 August 2009 (UTC)

I think that guy is a chick. My uninformed random guess is that this is just another east/west split, and that if the Russian sources were in English then we would see this as just another esoteric topic that we would not mind as an article topic. — Carl (CBM · talk) 23:05, 20 August 2009 (UTC)

I was confused because Karatsuba that developed the original algorithm wasn't a chick. The chick is probably related to him. Pcap ping 23:18, 20 August 2009 (UTC)

(ec) Let's recap:

• My first impression was correct: the issue is bit complexity in operations on large integers (or possibly arbitrary precision reals as well); see Karatsuba algorithm or Toom–Cook multiplication.
• This article is not about random algorithms that have "fast" in their name. Nor is it about automatically generating algorithms for some transformations. It also does not involve Kolmogorov complexity; it just happens that Kolmogorov was also interested in this.
• The generic terminology "fast algorithm" is non-standard. It appears to be an attempt to define a class of algorithms that are like Karatsuba etc. It's surely non-standard because it doesn't appear in any of our other articles linked from it. Pcap ping 23:08, 20 August 2009 (UTC)

Browsing the literature starting with the elder Karatsuba's web page, and Google scholar, suggests that the term "fast" must have some meaning to people in the area, or they wouldn't use it as often. It's a fallacy to assume that our coverage here is half complete. — Carl (CBM · talk) 23:31, 20 August 2009 (UTC)

Fast in this context is actually well-defined later in the article (I've commented on the article's talk page). But what is still unclear to me is the importance of this notion. Pcap ping 23:48, 20 August 2009 (UTC)

If I understand correctly from the article, an algorithm is said to be fast if it is only log factors slower than the best known lower bound. An interesting concept, but I've never seen it before. --Robin (talk) 23:56, 20 August 2009 (UTC)

You mean slower than multiplication by a polylogarithmic factor. But why is this definition important? The article fails convey that... Pcap ping

Oh, I see. It's slower than multiplication by log factors (log factors = polylog factor). Which means an algorithm is called fast, if it runs in time Õ(n). I have no idea why this definition is important though. --Robin (talk) 00:35, 21 August 2009 (UTC)

Õ(M(n)) time indeed. Pcap ping 01:05, 21 August 2009 (UTC)

Which is the same as Õ(n) since M(n) = Õ(n) --Robin (talk) 01:21, 21 August 2009 (UTC)

Kostant partition function

This article has been proposed for deletion. Would merging it to Weight (representation theory) be a good alternative to deletion? If so, or if there's a better merge target, could someone do the merge? My maths doesn't extend to understanding this. Fences&Windows 01:35, 21 August 2009 (UTC)

It should be kept. Someone removed the deletion tag. That is as it should be. Michael Hardy (talk) 03:48, 22 August 2009 (UTC)

Now the article has been expanded (it was very short previosly) and as Hardy writes, the deletion tag has been removed. I also think the article should be kept. Ulner (talk) 18:51, 22 August 2009 (UTC)

Excellent. It is still Greek to me, but if it's independently notable in maths then all is well! Fences&Windows 22:41, 23 August 2009 (UTC)

Anonymous recursion

Although this has marked as a computer science topic (by changing its category), it doesn't contain any programming or the like, and it tries, but fails to define a mathematical concept. The article has good number of issues. See it's talk page. Pcap ping 02:01, 21 August 2009 (UTC)

I think that this sort of thing can be discussed on the article's talk page. If every bad article were reported on this page, everyone would be overwhelmed. — Carl (CBM · talk) 02:04, 21 August 2009 (UTC)

Okay, in the same vein however, the dubious notion of an "anonymous function" (as opposed to ??? in lambda calculus) appears at Fixed point combinator as well; see the talk page there. Pcap ping 05:41, 21 August 2009 (UTC)

(Wikimedia) Intersection categories

After having a look at math article alerts, as well as Jitse's activity bot, I concluded that a lot of that stuff could be done by a simple feature in Wikimedia: "intersection categories". Basically to find out if a math article is nominated for whatever, or needs expert input (cleanup and what not) could be done almost trivially if Wikimedia natively supported intersection of categories. I see that there's actually a request for enhancement on bugzilla; somebody even wrote the code, it just needs to be tested and committed. Perhaps you could weigh in on that? Pcap ping 07:28, 23 August 2009 (UTC)

P.S. There's a more generic, but still 3rd party Cat scan. Pcap ping 07:31, 23 August 2009 (UTC)

P.P.S. The {{expert-subject}} template is yet another (special purpose) implementation of intersection categories. Pcap ping 07:40, 23 August 2009 (UTC)

I see that an official extension that supports this does exist. It's called DynamicPageList, but it's only installed on wikinews. Pcap ping 10:32, 23 August 2009 (UTC)

Alas I fear this is one of the many good ideas on wikipedia which have a small chance of ever making it into en-wikipeida. This has been around the block several times Wikipedia:Category intersection was the most recent proposal. There does not seem to be a sufficient number of highly committed people to push this through, and the developers are wary. There are some very real performance issues and some big unanswered questions as to precise method of implementation. For the most part, people seem to work around the problem with various bots creating special purpose categories and third party tools.--Salix (talk): 13:09, 24 August 2009 (UTC)

To hyphenate or not to hyphenate...that is the question

Trend change:

• Ghits (all times): "noncommutative" exclude: "non-commutative" = about 2,200,000
• Ghits (all times): "non-commutative" exclude: "noncommutative" = about 5,440,000
• Ghits (past 1 yr): "noncommutative" exclude: "non-commutative" = about 330,000
• Ghits (past 1 yr): "non-commutative" exclude: "noncommutative" = about 181,000

Henry Delforn (talk) 19:34, 23 August 2009 (UTC)

Short answer: it is a matter of taste, so follow the style of the first main contributor in any given article.

Slightly longer answer: the trend to remove hyphens over time is common in general and in mathematics in particular. When a new combination is introduced, a hyphen is often used so that readers recognise the familiar constituents more easily. However, a hyphen is only really needed if the reader would be led up a mini-garden path without it. I've introduced at least one new term with a hyphen myself, and regretted it (fixing it in subsequent papers) because the hyphen was unnecessary. So if you want to persuade other editors to use noncommutative, instead of non-commutative, then you have a good chance of success in the long run. If you want to argue the other way, you are batting on a sticky wicket. Geometry guy 20:17, 23 August 2009 (UTC)

Agree with G'guy. Love his cricket metaphors --Robin (talk) 00:54, 24 August 2009 (UTC).

yeah, i agree with G'guy G-guy Gguy too. Henry Delforn (talk) 15:02, 25 August 2009 (UTC)

Mathematics deletion sorting list

I've recently been doing quite a bit of deletion sorting, and while many topics have associated deletion sorting lists, mathematics is a notable exception. I find this surprising given that maths is a subject that can be completely impenetrable to someone like me who has no understanding of almost everything above GCSE level. This means that there is often a need for input from someone able to understand the importance (or otherwise) of the subject being nominated.

My question therefore is whether people here feel there would be a benefit in creating such a list? Thryduulf (talk) 20:20, 23 August 2009 (UTC)

Mathematical articles that are proposed for deletion or nominated on AfD are noted in Wikipedia:WikiProject Mathematics/Current activity, which is maintained by a bot. Category:AfD debates (Science and technology) is also useful. I don't see much point to yet another list, but if someone wants to maintain it, then why not. Gandalf61 (talk) 20:44, 23 August 2009 (UTC)

Evenness of zero is under peer review

Comments welcome at Wikipedia:Peer review/Evenness of zero/archive1. (I suppose this'll be picked up on current activity soon enough, but why wait?) Cheers, Melchoir (talk) 03:31, 24 August 2009 (UTC)

Thanking Wikipedia

Just for fun, a quote: "We thank the anonymous referees of the conference and journal versions of the paper for providing useful comments and references, and the anonymous writers of the article on the central limit theorem in Wikipedia for leading us on to the Berry-Esséen theorem." Page 510 of the journal Algorithmica (2009), vol. 55, the paper "Random Measurement Bases, Quantum State Distinction and Applications to the Hidden Subgroup Problem" by Jaikumar Radhakrishnan, Martin Rötteler and Pranab Sen. Boris Tsirelson (talk) 16:03, 24 August 2009 (UTC)

Great find! Thanks for posting it here. --Robin (talk) 16:25, 24 August 2009 (UTC)

Hilbert space gradually moving towards GA

I'm in the process of bringing the Hilbert space article up to scratch for GA. It was delisted by User:Geometry guy last year, but it has progressed substantially since that time. It's almost in a shape that I would consider nominating for relisting as GA, but I thought I should solicit input here somewhat unofficially before doing so. Thanks, Sławomir Biały (talk) 18:11, 27 August 2009 (UTC)

Category:Markov chains and Category:Markov models

There is a naming dispute considering the correct name for the category for the main article Markov chain and related articles, see WP:CFD. 76.66.192.144 (talk) 03:20, 28 August 2009 (UTC)