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Talk:Mathematics

Comments at the bottom, please. Eventually, we will have to refactor (probably just delete a lot of stuff from) this page. Some old talk has been moved to Mathematics/Old_Talk. See also Mathematics/Schemes.

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.
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. --Juuitchan


I have a suggestion for a slight reorganization of the main page:
  • "Methods" becomes "Foundations"
  • "Miscellanea" becomes "History and Miscellanea"
  • "History of Mathematics" (to be created) goes into "History and Miscellanea"
  • "Special Functions" moves to "Change"
  • "Fermat's little theorem" goes on a "Number theory" page (to be created under "Structure")
  • Links to "Symbolic Logic" and "Set Theory" are placed under "Foundations and History" (Set Theory also remains under Finite Math)
  • "Finite Math" moves down the list, after "Space"
  • "Discrete Math" moves under "Finite Math"

What do you guys and gals think? --AxelBoldt


An alternative well thought out classification scheme for math is at http://www.math-atlas.org/index/beginners---- As one of the original autors of Math entries here, like Group, Field, Linear algebra, Trigonometric Functions, I think that the new group of articles, are too high level for the average reader, particularly without examples. Many college grads get out of college with a general math course. I think we have to begin to fill in the lower levels. In regard to your placement of Finite Mathematics under Space, I do not agree. We also need people to draw graphics for some of these entries, not to mention a way to do matrices. RoseParks
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 (α, ∫, 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 Σ, ∫, 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 Δ (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 ∇, ∀, ∃.
Also did some more browser checking. StarOffice 5.0 fails utterly on the Greek and Math entities, also. --Buz Cory


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
It's a shame the mathematics page still lacks a good general article about mathematics. With so many mathematicians about, you'd think a general discussion and characterization of mathematics would be forthcoming. --LMS
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


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--


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


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


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


"Arithmetic does not count as a "foundation for mathematics"; it is part of elementary algebra"--AxelBoldt

Then why does the elementary algebra article begin: "For this introduction, knowledge of arithmetic (including the use of parentheses) is assumed." --BlackGriffen

No substantive knowledge, except of the English language common to an intelligent high school graduate, should be assumed--unless an exposition of the subject really does require such assumptions. In this case, since we introduce school children to arithmetic all the time, I should think we need a simpler article about arithmetic... In other words, Wikipedia's math articles should, while being maximally useful for mathematicians, also be very useful for non-mathematicians. --LMS

Yes, the elementary algebra article is incomplete and should start out very gently with introducing the order of operations, parentheses, commutativity and associativity etc. (or factor out to an arithmetic article and add a link to elementary algebra if that seems preferable). --AxelBoldt


Should there be a page for arithmetic? There's a page for modular arithmetic, defining it as "a modified system of arithmetic", without any definition of that term. Is it considered to be such a simple concept as to require only a dictionary definition? - Stuart Presnell

See the above discussion. I think we should have a separate article on arithmetic, but I'm not really sure how to write elementary stuff like this, so I haven't attempted it. --Zundark, 2002 Jan 5


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


A question for you all: is is the inequality

||u ± v|| ≥ | ||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:
|<u , v>| ≤ ||u|| . ||v||


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


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)
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)


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)


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


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



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