Misplaced Pages

This is an old revision of this page, as edited by Zundark (talk | contribs) at 19:24, 12 January 2002. The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

Comments at the bottom, please. Eventually, we will have to refactor (probably just delete a lot of stuff from) this page.

Mathematics is one of the strongest areas in the Misplaced Pages,

but we obviously still have a ways to go. Of particular strength is the Probability and Statistics area.

I would disagree here, but then you'd make me fill in the P&S stuff I thought was missing (like more detail about the Bayesians, the Doomsday paradox, more history of gambling and statistics-as-rhetoric, resampling... Damn, I guess I just volunteered. --LDC

Agreeing with LDC...there are strange errors and lapses in clarity in Probability and Statistics that I began to correct, but there is so much material I gave up. Further, the author has glued *his name* to them and I resent correcting what he appears to think is *his* pages- further *his name* link is linked to an educational/commercial site of his, and I see this as advertising and most inappropriate.----

(Note from the author mentioned: The signature is designed to allow me to quickly find the material that I consider unfinished. When I am done with my editing, I will remove the signatures if they are offensive. Dick Beldin)----

Now for my *opinion* - I feel that the other Math pages have been both a more co operative efforts and attempts to single out interesting and fundamental material rather than an attempt at writing a text book by one author. This will naturally result in occassional failure to link and some incomplete entries, so far. I do think that eventually these will be corrected. Most impotantly, in these pages the math is correct. Further certain areas of math are almost impossible to explain here, due to the lack of symbols, ability to show diagrams and graphs, etc. How does one properly explain the Integral without being able to draw a graph, Limits with no proper notation, classic functions without the ability to show graphs (trig, exponential, natural logarithm, conic sections- need I go on.) Submitting graphs and symbol images to wikipedia to upload for every entry is a little much. Within the constraints of this media I think the Abstact Algebra is fine as far as it goes, and the Analysis nearly impossible.) Finally, I think it is very hard for a non-Math person to assess the value of the higher level math pages.-RP

RP, what I, seriously, suggest that you do is simply go in and remove every instance of the offending name, or, if you don't want to do this, ask the person bearing the name to remove them. I very much suspect that he won't do it without being asked. If you don't, I might myself, or someone else might.

My own philosophy pages are pasted with Larrys Text, but at least I invite people to change them; and today I decided to remove the Larrys Text pointer from pages that I've wikified.

I totally agree with the assessment of the accessibility of the higher-level math pages. I have the impression that the mathematicians are simply showing off :-) which is just fine, and actually great because so much has been done, but it sure would be nice (and actually, even more impressive) if they would make an effort also to explain the concepts, insofar as this can be done, in a way that intelligent nonmathematicians can understand, or start to understand. This won't be easy, but in many cases it can be done. The simpler explanations needn't replace the more precise formulations, of course! --LS

My pages all have conctrete examples and diagrams as much as posible, in this medium and so do a number of others, as well as an attmept ot explain the importance or place of the material within the field of math. See {{Ptyhagorean Theorem]], Vector Space, Mathematical Group, Fieldand more. I am a teacher in this field and realize that pure high level theory will not do. But, say, in Vector Space adding the matrices took hours, and now I suppose I should mark-up, the maybe 100+ subscripts in this entry, which became available after this was wriiten. Well not today...friends...:-).

emacs regular expressions are your friends...

Don't know what to do with the <pre> matrices though...Gareth Owen----

I don't either because if you remove them you lose the alignment. If you leave them you can't put in subscripts. Just another little obstacle.RoseParks

But more math talk would help and that I will try to add. Math is a subject, that after a certain level, you do not read, but you rework it through, and try examples. This makes math somewhat different than other subjects. "Reading" a math text can take literally hours per page. Knowing math involves a unique set of skills, because you can not progress until you have integrated the material you are studying into your brain to the extent that you can "use" it in the next development. This is really hard to explain and I am in a hurry. I will return and try to do better. I am not saying here that math requires higher level skills than another subject, just different ones.

RoseParks

Just notice that I did say "insofar as this can be done." :-) --LS

I am a student studying to be a mathematician. The mathematics section of Misplaced Pages looks like it could eventually be a good replacement for Mathworld. I think that MathML should be considered for the math section. Yes, I know that not many browsers other than Mozilla can render it, but someone could make a CGI script that converts pages that use MathML into pages that express mathematical expressions in plain text form. There are some things that cannot be easily expressed in plain text form and the alternative of using gifs for mathematical expressions is rather unappealing.----

This present scheme is developing problems. I just entered Linear Algebra under Structure and Space, I think. This should be more like a diagram where you can show subjects that

cross two fields. I give up. RoseParks

Since this is your own project, just bear in mind that whenever you say "I give up," what you really mean is "I don't have the time and energy to do personally what I think needs to be done, and I'm not going to try to persuade other people to do it." That's understandable, sure. But note, you cannot mean, "I'm giving up on you: you are to be blamed because you have failed my expectations, but there's nothing I can do about it because I'm not responsible." Since you can change any page on Misplaced Pages, you could change it as you see fit, if you wanted to. So you personally are just as responsible as anyone else here is. :-) --LMS----

I am not the one who created this scheme, nor the one that chose it above the other/others. In fact, I wish I did know who put this particular scheme up above the other/others. You can fault me for being reluctant to radically change anothers work and, yes, of not having a great deal of time for this--other than that, well...:-). I CALL ALERNATIVE SCHEMES TO ORGANIZE THE MATH PAGES!!!

Alternative schemes, makes sense to me, but in any case, can we make sure that the table isn't so wide? It's wider than my screen.

By the way, when you say, "I call alternative schemes..." you seem to be inviting public support for a radical change to the Mathematics page. Y'know, the best way to get that support, I'll bet, is just to change the Mathematics page and invite comment/further changes. --LMS

I'll have additional comments in a few minutes addressing several comments on this talk page, but

for the moment I'm requesting that anyone hold off adding to the Mathematics or Talk pages until I've

done some more editing. Please give me about half an hour ... ok, I'm done.

1.

I've reorganized the Mathematics page, changing the table to a more conventional layout, primarily because the table wouldn't resize (it scrolled off the right hand side of my window). This also

gives the page a similar look and feel to other "portal" pages in Misplaced Pages. Finally, it will make

it much easier (I believe) for anyone else to edit the page.

2.

Signing pages. I understand the desire to "track down" pages one has a vested interest in for further

work. I offer a couple alternatives to signing: set up a "To-Do" list on your personal page, as

several others have already done; put an inocuous marker (I've used "To-Do" without the hyphen) which

can be easily searched for. Try searching for it right now; there aren't that many pages that match

and it might encourage someone else to work on them. If you really want to stake out some territory,

I'd suggest creating a "Talk" page and signing comments there.

3.

Editing "owned" pages. As a former coworker used to say, "Get over it!". Yes, I'm reluctant to

modify pages that someone else has put a lot of work into, but we all knew when we started using

Misplaced Pages that any page is subject to complete revision--that's one of the key features

of Misplaced Pages.

4.

Misplaced Pages is not a textbook, it's an encyclopedia. Keep in mind that most viewers of these articles

will likely not have a deep background in mathematics, so the tone, depth, and in-line "handholding"

gloss should be appropriate for that level of reader.

5.

Presentation. Wow. This discussion has been going on in several locations. I think that these

discussions should be consolidated in one place, perhaps a subpage on presentation;

say /HowToPresent.

I don't have the time right now to do that, but if no one else does it first, I'll try to merge

and summarize the comments to date.

Ok, flame away. --loh (2001-06-20)

I added this to the main page, then decided to put it here!

Oh please. Applied math pays the bills, and does a darn good job of it. And its fun. Its just really, really, hard (consider a horse, a perfectly spherical horse...). As a first topic here, I propose Mechanics?, which one might say is the queen of applied math. I will also state that without a thorough steeping in Lie Groups and Lie Algebras, you ain't going anywhere fast in mechanics. So the rigor is there, always has been, but the problems we can solve are getter more and more interesting!

An Applied Mathematics page already exists (I didn't know that when I reformatted the table). I'll add that link, but perhaps someone who knows more about the field will decide whether to add items here or just refer to the separate A/M page. (cf Finite Mathematics) --loh (2001-06-22)

There is a link to "computation" lost all by itself at the bottom of the page. Where should we move it? AxelBoldt

I stuck that link there when I added the article. I had no idea where to put it -- Simon J Kissane

I'll put it under Finite Math for now. It doesn't quite fit, but I think it's the best choice short of starting a new toplevel hierarchy. AxelBoldt

Taxonomy of mathematical disciplines, like classification of all knowledge, should use multi-dimensional Venn diagrams.

On the other hand, wiki doesn't do Venn diagrams.

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.

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.html----

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 (&alpha;, &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 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 Misplaced Pages. 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

"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, Misplaced Pages'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