Talk:Mathematics/Archive 2

''This is an archive of topics which have been forgotten or resolved. If a topic still needs to be discussed, move it from this page back to the talk page.''

Capitalization in titles
On the question of capitalization in titles, I find a contradiction between the FAQ and somewhere else I can't remember. Should titles of articles be capitalized throughout, or only at the first word? rchase
 * Contradiction? What contradiction? How could that possibly be, in a collaborative website? :-)

Can I encourage you, mathematicians, to please use lowercase titles? When you use uppercase titles, that forces people to Capitalize Words that Wouldn't Usually be Capitalized in Ordinary Standard English. See naming conventions.

Elementary material
Why isn't there any coverage of K-12 Mathematics? The focus so far is on advanced undergraduate topics.

That's a hell of a good idea. --User:Juuitchan

Greek letters, symbols
What should the policy on Greek letters be? I notice that the symbols on the Mathematical constants page appear as blocks in Opera 5.11. Perhaps it would be better just to write them out as pi, gamma, etc., so that they are at least readable. Zundark, 2001-08-08

I think for now we shouldn't formulate a policy: it should be up to the individual author. If you are interested in widest readability, then spelling out the symbols is best. However, all entities we use (&amp;alpha;, &amp;int;, etc., see Howdoesoneeditapage/Quickreference) are valid HTML 4.0 entities and browsers will sooner or later come around to supporting them. I believe the newest versions of Internet Explorer and Mozilla support almost all of them already; I'm not sure about Konqueror. --AxelBoldt

Yes, you're right. I didn't realise it was valid HTML 4.0. So it's Opera's fault for not understanding it. It works in IE4 anyway, and is at least comprehensible in Netscape 4, so I'll carry on doing it. Zundark


 * Hadn't noticed it, but all the nice math symbols (including &Sigma;, &int;, etc) that work fine w/ NS6.0 on Linux fail utterly w/ Opera 4. Latin-1 works fine with both (of course, latin-1 is the native char set).
 * So how about things like the inverted &Delta; (Del), inverted A, reversed E? Being an engineer, not a mathematician, these would provide all the symbols I am likely to need.
 * --Buz Cory


 * Found a pretty complete set of math symbols on how does one edit a page/Quick reference. For instance &nabla;, &forall;, &exist;.
 * Also did some more browser checking. StarOffice 5.0 fails utterly on the Greek and Math entities, also. --Buz Cory

Chaos
Um has any one thought of putting a chaos page on any where? Like the mandelbrot and the like. I don't know much about it but I would love to learn. Michael (Tas)


 * ''Apparently nobody has. There's a bit about the Mandelbrot set though, and a stub about fractals. I'll put a

link to "Dynamical systems and chaos theory" on the main mathematics home page under "Change", and hopefully someone will bite.'' --AxelBoldt

Trigonometry
Shouldn't there be an article for Trigonometry? I know that we have the Trig Functions article, but general trig is more broad than that.

Also, shouldn't the number sets be combined under the auspices of one article so that they can have a logical overview and venn diagram to describe their structure?


 * A page like Numbers could certainly be put under "Quantity" and then it could have an overview and links to all the various number sets and explain their relationships. I would still want to keep links to the reals, complexes etc. right on the main page, so that they are easily accessible. --AxelBoldt

Transforms
Shouldn't there be a page on transforms? I'm not a mathematician, and can't write it myself. Some transforms I would like to see described are: fourier, cosine, z (used in digital signal processing), laplace, chirp, hilbert, etc. The transforms should be compared regarding their use. --HelgeStenstrom--

Encyclopedias of mathematics
I don't think I have ever seen an encyclopedia of mathematics, so I have a question about encyclopedias of mathematics. Would the entry about elementary group theory in such an encyclopedia consist, as it does here, of a system of group theory? Or would it just discuss such a system? Don't get me wrong--I think we should have mathematical systems in Wikipedia. I am asking whether there might be some other information that mathematicians might expect out of an encyclopedia, that we aren't supplying, in most cases, yet. --LMS

I'm only familiar with one Encyclopedia of Mathematics, which is a very large one translated from Russian. The entries usually contain definitions, discuss important results, and give a list of references to the literature. They certainly wouldn't have a article like elementary group theory, since any mathematician should know that anyway. (The article is probably misnamed; proofs of the most basic results in group theory would be more accurate.) Note that we have another article, mathematical group, which discusses group theory. --Zundark

"since any mathematician should know that anyway" isn't that the idea anyway, dictionaries still contain the most basic words. skukok


 * WP has comprehensive definitions, but does not develop most of the most elementary theorems from them. That sort of thorough treatment belongs on Wikibooks. Charles Matthews 22:57, 9 Nov 2004 (UTC)

Thanks for the clarification. skukok

Books
I took the section about Mathematical Books out of the main page. While it would be nice to have a bibliographical listing, right now we don't and it's premature to put it on the main page. --AxelBoldt

Topology
Somebody added that topology focuses on the concepts of continuity and direction. I don't see what topology has to do with direction, but I could be convinced. Generally, when I think "direction", I think "tangent space" and hence "differential geometry". How can you talk about direction in topology? --AxelBoldt


 * perhaps they meant orientable surfaces in algebraic topology. -- Tarquin

Trig functions
What do you think about removing the link to trigonometric functions from the main math page. There's already a link to it under special functions. --Georg Muntingh

Yup, that makes sense. What we really need is a Trigonometry article though. --AxelBoldt

Okay. How can I be sure most people agree? Shall I remove it? (It looks very logical to me.) --Georg Muntingh


 * Just do it - you'll soon find out if someone doesn't agree. :-) --Zundark, 2002 Jan 12

An inequality
A question for you all: is is the inequality
 * u ± v|| &ge; | ||u|| - ||v|| |

(quoted from Normed vector space) known as the Cauchy-Schwartz Inequality, or am I thinking of something else? --Tarquin
 * I've found it in my notes, I'll answer my own question :-) -- The Cauchy-Schwartz Inequality is:
 * || &le; ||u|| . ||v||

Mathematical symbols
I just added the page mathematical symbols. I would like to hear your opinion on the idea of including a link to this page in each article that uses math. symbols and can potentially be made more readable for a mathematical beginner by inserting the link. --Rade

I like the symbols page; I think we don't need links from *all* articles that use math symbols, but certainly from those which are mainly directed at or will be read by beginners. Some articles are completely incomprehensible without some math background, and adding a link to the symbol page wouldn't make them any less so. AxelBoldt 18:14 Aug 20, 2002 (PDT)

Agreed. --Rade

Thematos
I removed the text "2. -thematos" from the etymology part, because it's unclear: what is the two about, what is the hyphen, and because I couldn't verify it in the Oxford English Dictionary or in Merriam Webster. AxelBoldt 22:59 Sep 29, 2002 (UTC)

Formatting
I noticed that the formating for the mathematical topics was changed. I liked the old style because it was more concise and it actually fits on one page. The new style is very cluttered on the screen. Am I the only one who thinks this? -- Ram-Man

I also liked the old style better. AxelBoldt 03:13 Oct 24, 2002 (UTC)

Listings
On the mathematical branch listing: Under "Finite Mathematics", "Basic Set Theory" is coined, but the article itself is called "Naive set theory", shouldn't one of these be changed? (213.8.129.12)

Logically
Going to revert "logically" to "naturally" as "naturally" has a specific meaning in mathematics - PML.

Formatting statements
I have coloured the statements of the theorems in Pythagoras' theorem and Fermat's last theorem. The coloring could make the statements standing out in the article. If this practice is acceptable, I will do it for other theorems and conjectures (with different colour, maybe). -- User:Wshun


 * This seems like the kind of thing that could be very useful for many mathematical articles - does anyone else have suggestions or ideas about what format would be best? One with a white background may be necessary in order to accommodate our TeX markup; it also ensures a maximum amount of contrast for readability. I think a nice colored border would work well. For others who are interested, I have contributed an alternative formatting for theorem/formula highlighting. See Wikipedia talk:TeX markup for another example. (Actually, considering it now, maybe blue is not the best color - too similar to the link color - maybe green or orange or something?) -- Wapcaplet 02:50 17 Jun 2003 (UTC)

I've gone ahead and formatted several of the theorem article with dotted-outline purple boxes. See, for example, Pythagorean theorem, Fundamental theorem of calculus, and Fermat's last theorem. Sticking to traditions I'm familiar with in math textbooks, I've only done this with formal statements of theory (or sometimes hypothesis), and not just any old "suppose such-and-such..." Someone better versed in mathematics should probably take a look at them, since formality is not my strong suit :) I think these look quite a bit better, though. Before, there was a hodge-podge of styles for highlighting important theorems and other statements (bold, italic, indentation, etc.) Comments welcome! -- Wapcaplet 18:56 18 Jun 2003 (UTC)

The "outline" proposal seems to be an acceptable idea. Maybe we should submit a proposal on "styles of mathematics articles" before we proceed...-- Wshun

Something that would be useful to us non-math inclined people would be some sort of pyramid that goes from the building blocks of mathematics to the more advanced concepts. Give people an idea of where to start.--

Road map
I made my own version of a 'distributed roadmap' for mathematics on the page fractional calculus and some of it's subpages (the ones that aren't stubs). Perhaps something like it can be adopted as a conventional practice?

Also, where is this so-called "styles of mathematics articles". I haven't been able to find it. It should be made easier to find. - Kevin Baas

Well, time is becoming too expensive, I've become proactive and decided that there 'is' a Styles of Mathematics Articles page, for the discussion of just that, so that the pages can be more readable and organized. Anyone who wants to discuss the format of mathematics articles, style, presentation, ect., please discuss it there. Thanks. Kevin Baas

History of mathematics
We need more on the history of mathematics. Here is a public domain encycloepdia entry from the Jewish Encyclopedia on this subject. Maybe we can adapt some of this material into an article on the history of math. RK 15:54, 30 Aug 2003 (UTC)


 * History of Mathematics, public domain article


 * I put your suggestion on the History of mathematics in the links section. -- Ap 19:16, 30 Aug 2003 (UTC)

Mathematical education
How come math education is completely absent from the page? It should be listed in one place. I know that math education is a controversial subject, but it should at least be mentioned.

MathWorld
I searched for Eric (of treasure troves/mathworld fame) in this page and the old one, and I couldn't find any references to him. There is a link to his pages at the bottom of the article; shouldn't there be a warning there? Or does everyone know about the events surrounding his website already?

MrJones 19:10, 18 Oct 2003 (UTC)

Labelling angles
I had a question. In law of sines and law of cosines, are the angle measures capital letters (i.e. A, B, C), or greek letters (i.e. &alpha;, &beta;, &gamma;)? Because the formula:

$${\sin A \over a} = {\sin B \over b} = {\sin C \over c}$$

looks kinda tacky. I always learned it as:

$${\sin \alpha \over a} = {\sin \beta \over b} = {\sin \gamma \over c}$$

What should I use in the formulas on the mentioned pages?


 * I don't see anything tacky about using A, B and C, and it's a common notation for this sort of thing. A problem with the Greek letters is that they don't work in some browsers (unless you do them as images, which does look tacky if used everywhere). --Zundark 10:14, 15 Nov 2003 (UTC)

That makes sense... and I have weird senses of things that I think are tacky.


 * The angle A is opposite the side of length a. The angle B is opposite the side of length b. The angle C is opposite the side of length c. Easier just to label them with capital English letters, when we have to label more than 3 angles, so if we do the same with triangles we are being consistent. Brianjd 09:58, Aug 8, 2004 (UTC)

Axiom of countability
I removed the like to "Axiom of Countability" from the list of famous theorems and conjectures. Whatever axioms of countability are, they are not famous theorems or conjectures. Now nothing links to "axiom of countability", which is a really odd little article anyway.

Mathematics is Not...
In the article, what is the purpose of the single member list (which BTW is not in standard Wikipedia form for a trivially populated list) captioned "Mathematics is Not..." ?  Is there supposed to be any difference between this presentation of information and just a simple sentence that says the same thing? Bevo 18:32, 23 Feb 2004 (UTC)

Formula pages/tables
I was just thinking, isn't it a nice idea to have a link on the main mathematics page, to a page which is an index for the various formula pages? --Georg Muntingh 13:59, 10 Apr 2004 (UTC)

North America is not a country
"Mathematics is often abbreviated to math in North America and maths in other English-speaking countries." seems to suggest that North America is a country, which it isn't. Or maybe I'm being nitpicky. Elektron 09:15, 1 May 2004 (UTC)


 * Be bold, pitch in and change it if you feel strongly about it :) Dysprosia 09:17, 1 May 2004 (UTC)


 * I assume nobody has objections to changing it to "math (American English) and maths (British English)". Elektron 16:36, 1 May 2004 (UTC)


 * What about Australian, New Zealand, South African, Canadian, etc. English?


 * If there's a particular spelling which was not 'imported' from Britain or the US, feel free to add it. For the record, Canadians are supposed to spell 'Colour', but a lot of people skip the u (I don't know if it's even standardised). And signing always helps. Elektron 18:52, 2004 Nov 1 (UTC)

Lateral thinking
Why should a link for Lateral thinking be in this page? KRS 17:26, 20 May 2004 (UTC)


 * Because it shows what mathematics can't solve? --Elektron 16:23, 2004 May 24 (UTC)

Descriptions
I added some descriptions of the categories of topics in mathematics. I know the categories are not rigid, and are meant as guidance, but they deserved some small explanation of why they were categorized so. I don't think these should be expanded too much (but certainly edited as needed!) - siroxo 11:36, Jun 11, 2004 (UTC)

Is there a reason that shouldn't just go on Wikipedia? Although not a wiki, Planet Math seems to have that basic idea already.

Mathematical abilities and gender issues
I think the whole Mathematical abilities and gender issues section (which was mostly created on Jul 23) should be split off into a separate article. Comments ? Gandalf61 09:14, Jul 30, 2004 (UTC)


 * No comments after more than a week, so I just went ahead and did it. Mathematical abilities and gender issues is now a separate article. For the moment, I just copied the text as was, without trying to improve it. Gandalf61 14:23, Aug 9, 2004 (UTC)

Pseudo-mathematics
Is there a section, or entire article, on pseudo-mathematics? (I don't know if there is a formal name for this phenomenon.) By this I mean the long-standing problem of amateur mathematicians (and occasionally real scholars) getting hooked into solving provably unsolvable problems, or hooked into thinking that they have found a proof for a theoretically solvable problem, even though in fact they have not.

One of the characteristics of this pseudo-mathematics is the tendency to phrase complex problems in an overly simplified fashion. People who advocate pseudo-mathematics live in a closed system of faulty mathematical assumptions and premises, and depend on a faulty interpretation of the rules of that system. While pseudosciences have merely failed to prove themselves true, pseudo-mathematical results can actually be proven incorrect and impossible. The ancient geometric problems of trisecting an angle using only a straightedge and compass, and of drawing a square with the same area as a given circle (or "squaring the circle") are examples of this kind of problem.

So we do we have anything on this topic? If not, would anyone like to take a crack at it? RK 16:22, Aug 25, 2004 (UTC)


 * Well, we have an article on squaring the circle, and we can start from there... -- The Anome 16:43, 25 Aug 2004 (UTC)


 * Well, hello! I just found an article on Pseudomathematics! RK 21:05, Aug 25, 2004 (UTC)