CZ Talk:Mathematics Workgroup

Suggested Plan of attack

I think that the current status of mathematics workgroup is not good. there are two major problems:

• we don't have a plan.
• we don't have enough editors, writers or readers/reviewers

Regarding the first problem. The crop we had from "random suggestions", which is currently on the workgroup wiki, is IMHO total crap. Since I believe it is very important to start with a good "skeleton", I suggest we starts with MSC or ZMATH (which are very similar), and fill all the nodes on the classification tree. Indeed the classification tree does not mention explicitly some classical topics which certainly deserve an article - we just add them in the correct place ( e.g. hyperelliptic curves, Kummer surface, SU(2)->SO)(3) fibration to name some of my personal favorites). I estimate that if we stay close to tree we are talking about 2000 articles. (I know I ignore elementary math, there isn't so much of it).

Regarding the second problem, let us start with the number of writers: It took me about a week to get the hyperelliptic curve article to be more or less ok (it still needs editing, but the content I want is there). I think that this is an average length article. I know that I'll work faster in time, but on the other hand some of the excitement will fade of. Let's assume 20 articles per author per year. If we want to get this thing done in a year we need at least 100 authors. Which means that we need at least 5 editors, and at least 500 readers.

comments ? --dlehavi 22:28, 28 February 2007 (CST)

Good questions. Concerning the number of editors -- it is not up to us. The best we can do is to create a friendly working environment (e.g. to attract new authors). Concerning the "plan of attack" -- I'not sure what I shall think about it. I use WP often as a reference manual to find concrete definitions (or, given the WP's reliability, some hints where to look up). It proves to be extremely useful in this regard. I think I have never read Mathematics article, nor Algebra, Harmonic Analysis etc. These are surely parts of the core skeleton, and of course of the highest importance for an encyclopedia, but I found them hardly of my (selfish) interest. These are also difficult articles to write, aren't they. Besides, while I am all for team working, on wiki it is not easy to make the members do exactly what you want... a kind of anarchy is here, like it or not. A more concrete proposal could attract more brains, however. Consequently, I have the following suggestions/remarks:

• why not move this discussion to the forum (link in the header is for a reason!) and try to design something you proposed. I think it concerns also an approximate structure of envisaged sub-workgroups (someone already posted a proposition). In this regard, we may also benefit from concrete experience of our most active workgroups (Bio, Healing sciences).
• meanwhile, let's continue producing articles dealing with basic --and not so basic-- concrete notions; brand new articles, maybe not exhaustive at the beginning -- but reliable (=let's approve them). More precicely, I think about a "semi-approval" meant for articles that are "not very elaborated", but clearly "containing basic useful informations". Let's imagine a header "This atricle has been revised by an expert (link to the name) who found it correct and containing the most important informations. Still, the article needs to be expanded (link to the draft page)."

This could give us a quick start and make CZ become in not so distant future a useful and reliable source of reference. As far as I can see such "semi-approval" is well adapted for math. The question is whether expanding such "semi-approved" article (instead of writing a complete one from the beginning) would give us much of additional work. Any thoughs? Let's continue on the forum.

--Alex S. 09:32, 1 March 2007 (CST)

PS. I think that Mathematics could be rewritten from scratch. at the moment it is just borrowed from WP (practically untouched) and formally qualifies for BigSpeedyDelete. The only reason to "tolerate" it for a while to have the blue link in the workGroup header...

(Straight) line

Hello. We have an article at line (geometry) and another one at straight line (geometry). However, in elementary geometry, all lines are by definition straight; curved lines are called curves. It may be the case that in some specialized areas, the concept "straight line" is being used and that the articles need to be clarified (I'm not a geometer). However, it seems that the articles are misguided and that straight line (geometry) needs to be deleted. Unfortunately, I've no idea who to do this. Any assistance would be greatly appreciated. Cheers, Jitse Niesen 23:16, 26 March 2007 (CDT)

Agreed. --AlekStos 06:50, 27 March 2007 (CDT)

List of mathematical topics

Is this a worthwhile list or is it redundant to the workgroup page?

If it is good; shouldn't there be a easy-to-find link to it, on the workgroup page?

--David W Gillette 20:15, 30 March 2007 (CDT)

Now I see a link to this list under 00 XX General. --David W Gillette 00:03, 1 April 2007 (CDT)

Level of the introductions in our articles

Judging from my experience, the vast majority of people in the world are very satisfied with keeping their mathematical knowledge at the precalculus level. I also assume that most of those who will be accessing our work in CZ will look to clarify or expand only moderately, their knowledge at this level. In articles that have aspects of both precalculus and advanced math, can we meet this audience where they expect to be, by introducing and beginning these articles on a low level, and then in later sections cover the ‘good’ stuff?

--David W Gillette 17:01, 3 April 2007 (CDT)

I am certainly in favor of writing accessible introductions. Hey, I'm a big fan of the Science Channel, and I think developing accessible accounts of difficult ideas is a real art form. But these are articles about mathematics, after all, and it seems to me that some people have been a little overzealous in "dumbing down" articles, even to the point that they seem condescending (and become factually inaccurate). We need to be a bit careful here, and show respect for the reader. Another question: Is the average reader of Citizendium the average reader of mathematics articles? Greg Woodhouse 17:29, 3 April 2007 (CDT)

More thoughts:

Those articles with titles that sound like something covered in a precalculus class, should not overwhelm our seekers until the basic information that they are looking for is found.

Here is an idea for some upper layer headings

== Introductory material ==
=== Basic notation ===  
=== Basic properties ===
=== Basic operations ===
== Formal coverage ==
===  - - - ===
== Advanced topics ==
=== - - - ===

I would envision a collaborative writing. Some of us are more familiar with how the topics are covered in a precalculus class, and others of you are more familiar with how the topics are covered in a more advanced setting.

I would think that this approach would be used in some more advanced levels as well. There are topics covered in a calculus class at one level, and then in more depth in an analysis class.

In answer to Greg’s question, Obviously not. But if we can put together a useful product for the man on the street, the high school student or the non-math major, we can supply a needed resource.

--David W Gillette 18:41, 3 April 2007 (CDT)

I think it is a very interesting proposition. Concerning the proposed headings, I guess it does not have to be the formal heading structure of every article, since sometimes the notation or operation sections would be _very_ short or empty. But it does express the general idea of the global structure of an 'average' article. So I would propose to put it on the main workgroup's page. Eventually, we could develop there some "author's guide" in math.

My two cents to this end. Introductory part could also mention the general meaning ("where and why is it important"), some historical context ("who, when, what for") and general interactions with other parts of mathematics and/or other sciences applications. All of this is accessible to a wider audience. I do not know the Science Channel, but I agree it is good to begin articles with an intuitive/informal discussion of the subject (yes, it is fun and maybe a form of art too!). --AlekStos 04:06, 4 April 2007 (CDT)

I suppose I look at things a little differently. What makes an encyclopedia different from a dictionary (or in the case of mathematics, a compendium of definitions and theorems). Writing an article for Citizendium ought to be expository writing. But this is really orthogonal to the issue of level or depth. It's pssible to write a good expository article on how to add integers with pen and paper. It's also possible to write a good expository article on, say, the Atiyah-Singer index theorem, or the Langlands program. But a special difficulty with mathematics is that supposedly elementary topics (like prime numbers or map coloring) often lead to very difficult mathematics. (After all, isn't that why mathematicians spend so much time studying "difficult" things? Abstract concepts are generally introduced because they are amenable to analysis!) So, while an article on Artin reciprocity is likely to attract readers with the necessary mathematical background and maturity, articles on arithmetic essentially have to do double duty. They need to provide an accessible introduction for non-experts, but they need to establish a foundation for the introduction of more abstract ideas. Otherwise, we'll end up with a two tiered system: one group of articles will be both understandable and boring, while the other will be technical, sterile, and ultimately unenlightening. Greg Woodhouse 17:01, 4 April 2007 (CDT)

mathematical notation syle

• Don't use \Sigma instead of \sum . Please note:

$\Sigma _{n=1}^{3}a_{n}\,$

$\sum _{n=1}^{3}a_{n}\,$

The former uses \Sigma ; the latter uses \sum . The latter is generally considered correct usage of TeX.

• Note this difference:

$a_{1}+...+a_{n}\,$

$a_{1}+\dots +a_{n}\,$

$a_{1}+\cdots +a_{n}\,$

I think the last should be adopted as standard, and the lower dots in the second display above should be used between commas.

I don't know about anyone else, but the use of centered dots with sums (not products) looks very wrong to me. consider the following (more or less random) example from Wolfram Mathworld [1]. Greg Woodhouse 04:12, 12 April 2007 (CDT)

I always use centred dots in sums. I looked in some books on my shelf and found that seven use centred dots in sums and only one (on quantum physics) lower dots. Donald Knuth write in the TeXbook (p. 172) that "in general, it is best to use \cdots between + and − and × signs, and also between = signs or ≤ signs or ⊂ signs or other similar relations. Low dots are used between commas, and when things are juxtaposed with no signs between them at all." -- Jitse Niesen 04:31, 12 April 2007 (CDT)

The American Mathematical Monthly's style manual precribes \cdots between two occurrences of "+", if I'm not mistaken. Michael Hardy 16:00, 20 April 2007 (CDT)

Hmm...Well, I don't have TeXbook handy, so I looked in Guide to LaTeX (Kopka and Daly). They, too, use \cdots, but add (p. 125) "The command \ldots is available in normal text mode, whereas the other three are only available in math mode. In text mode, the command \dots may be used in place of \ldots to the same effect." So, I'm sure you're right here, it just looks wrong to me. Greg Woodhouse 04:53, 12 April 2007 (CDT)

a + b = c

a+b=c

I think the first style above should be adopted as standard in non-TeX mathematical notation.

Does Citizendium have a manual of style for mathematical notation? Michael Hardy 14:46, 11 April 2007 (CDT)

Also note that you can add "\textstyle": $\textstyle \sum _{n=1}^{3}a_{n}$. There's no such manual of style yet; I suppose that for the moment we could just follow the Wikipedia manual of style. Nice to see you here, Michael. Fredrik Johansson 02:06, 12 April 2007 (CDT)

Formatting

Right:

<math>\int_0^\infty \frac{dx}{x}.</math>

Wrong:

<math>\int_0^\infty \frac{dx}{x}</math>.

I.e. I propose this convention. When TeX is used in the NORMAL way, this wouldn't matter, but when it's used the way it's used HERE, it does. Putting the period or comma OUTSIDE of TeX causes bad misalignments and sometimes may cause the period to appear at the beginning of the next line.

Also, it is lunacy to write anything like this (Wrong):

<math>\begin{cases} blah blah \end{cases}. </math>

or this (Wrong):

<math>\begin{cases} blah blah \end{cases} </math>.

The periods or commas need to go at the ends of the appropriate lines WITHIN the "cases" environment. Michael Hardy 16:39, 17 April 2007 (CDT)

---

Another proposal:

Right:

<math> \int f(x) \, dx </math>

<math> \int \int f(x,y) \, dx \, dy </math>

Wrong:

<math> \int f(x) dx </math>

<math> \int \int f(x) dx dy </math>

Compare and contrast the two:

Right:

$\int \int f(x,y)\,dx\,dy$

Wrong:

$\int \int f(x,y)dxdy\,$

Michael Hardy 16:50, 17 April 2007 (CDT)

I always use \iint for double integral signs, as in <math> \iint f(x,y) \, dx \, dy </math> which renders as

$\iint f(x,y)\,dx\,dy$

The symbol \iint was introduced for this purpose. -- Jitse Niesen 21:24, 17 April 2007 (CDT)

If your talking about a double integral over a region D in the plane, then certainly I'd use \iint, thus:

$\iint _{D}f(x,y)\,dA.$

But what about iterated integrals, thus:

$\int _{-1}^{1}\int _{0}^{\sqrt {1-x^{2}\,}}f(x,y)\,dy\,dx.$

Michael Hardy 16:03, 20 April 2007 (CDT)