Wikipedia:WikiProject Mathematics: Difference between revisions

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First, an important note for everyone to remember: some Wikipedians have come together to make some suggestions about how we might organize articles about mathematics.

These are only suggestions, things to give you focus and to get you going, and you shouldn't feel obliged to follow them. This WikiProject is not intended as prescriptive. If you do not yet know what to write, or the guidelines may be helpful. Mainly, we just want you to write articles!

See Wikipedia:How to write a Wikipedia article on Mathematics for a draft manual, with detailed discussion of a number of issues.

Scope

This WikiProject aimed originally to organize articles in the area of mathematics; in its broadest terms, this may include overlap into the areas of physics, computer science, operations research, and other areas.

The initial goals of this WikiProject were to:

provide a standard "bare bones" format for mathematical articles
provide useful links for article writers
provide a location to discuss issues relating to this section of Wikipedia
provide standards for mathematical notation using wikified HTML/TeX.

Update 2005

This project was started in 2002; not surprisingly things have moved on. For example the scope of this project would not now include many physics pages, outside some aspects of theoretical physics. The 'house style' of mathematics articles is now reasonably well established.

The main issues for WP Mathematics are now probably the following.

Keeping track of, by listing and categorising, all relevant articles.

Who knows how many, now? It might be 1% of the English Wikipedia, or around 4000. It depends on how one counts areas such as statistics, cryptography and so on. The overall organisation is pretty much in place, by now.

Bringing stubs up to a reasonable standard.

There are always plenty of pages that are definition-only. It is always good to add motivation and examples.

Developing 'core articles' into good expositions.

As anyone who teaches the subject knows, the gap between stating some true facts, and really putting over a topic, is quite large. Here we can consider also the need to add history and proper attributions.

Expanding coverage to bring the subject up to date.

This is a huge task, so the main requirements are patience, and not to be discouraged. Much of the advanced material is still really from the 1950s.

Hoaxing

There has been some of this; most Wikipedians, naturally enough, don't feel qualified to pronounce on articles purporting to be mathematical. If not us, who?

Charles Matthews 09:59, 20 Jan 2005 (UTC)

Participants

See /Participants for a list. Introduce yourself.

Some issues to think about

Probably the hardest part of writing a mathematical article (actually, any article) is the difficulty of addressing the level of mathematical knowledge on the part of the reader. For example, when writing about a field, do we assume that the reader already knows group theory? A general approach is to start simple, then move toward more abstract and general statements as the article proceeds. The structure described below is one way of achieving this.

When you need to describe a concept in terms of some other concept (for example, explaining rational numbers in terms of integers), be sure to:

Add a (prominent) link to the relevant article (in this case, integer). As for other Wikipedia articles, avoid duplicate links.
If it makes sense, add a very quick (and naive) explanation/description (in this case, "positive or negative whole numbers" might work).

If the relevant article has not been written yet, then create a good stub, and list it on the list of mathematical topics (see below) - the odds are good that someone will expand on it.

Since some terminology varies from author to author in the literature, you can check the Wikipedia article on an ambiguous term (if one exists) to see what usage is established here (or to see if you want to try to change that).

It's worth a bit of time to just peruse what's already in the 'pedia; this will give you a feel for what type of information is already available, and how much detail you need to provide.

Motivation

See discussion at /Motivation.

Diagrams

Diagrams are often a great help in explaining mathematical concepts.

Partial list of articles that need higher-level explanations

How is the above list doing in terms of getting higher-level explanations? ---- Charles Stewart 08:32, 7 Dec 2004 (UTC)

Proofs

See /Proofs for discussion of how and whether to include proofs of results.

Examples

As with proofs, examples should be included where appropriate. Most of the time, they should be put on a separate section or separate page.

Conventions on naming theorems

See Wikipedia:Naming conventions (theorems) and its talk page.

Classification

There is no one single, prescribed method. Both the lists and the categories have grown organically, rather than being imported. See also Wikipedia:Classifications of mathematics topics.

Some useful links and resources

The article List of mathematical topics is used by contributors to keep track of changes to the entire content of mathematics in Wikipedia, in a fashion similar to the more general "Recent Changes" link. If you add new articles which are remotely related to mathematics (including biographies of mathematicians, and so on), please add them to that list, so that everyone can review / add to / mercilessly savage your contributions.

The list Wikipedia:Requested articles/mathematics is an active forum.

Other lists of topics for subdisciplines (for a more complete listing see list of mathematical topics (lists)):

List of publications in mathematics

There is an effort to organize a list of important publications in many areas of science. Such a list captures the major achievements in each field and might be a valuable asset for one trying to learn a new field. The List of publications in computer science is the oldest and most mature list and might show the goal of the lists. The rest of the list need much more contributions. Please try to improve the mathematics related lists:

Thanks, APH 06:53, 27 Sep 2004 (UTC)

@@ Line 96: / Line 96: @@
 There is no one single, prescribed method. Both the lists and the categories have grown organically, rather than being imported. See also [[Wikipedia:Classifications of mathematics topics]].
-== Suggested structure of a mathematics article ==
-Mathematical articles typically rely highly on an ''exact'' definition of the article title; but in general a definition only begins the process of explaining the idea under consideration.
-A general format that seems to be working well is as follows:
-* Optionally, for articles which beginners might be expected to find difficult, a header line, stating something on the lines of this: <blockquote>''If you are having difficulty understanding this article, you might want to learn more about [[computer programming|function]]s and [[naive set theory]] first'' </blockquote> followed by a horizontal rule to separate it from the rest of the article.
-* An ''introductory paragraph'' (or two), including the field(s) of mathematics this concept belongs to, the '''article title''' in bold, which describes the subject in general terms, and giving the historical motivation and mathematical context in which the term appears, giving names and dates; for example, like the following: <blockquote> In [[topology]] and related branches of [[mathematics]], a '''continuous function''' is, loosely speaking, a function from one [[topological space]] to another which preserves [[open set]]s. Originally, the idea of continuity was a generalization of the informal idea of [[smoothness]], or lack of [[discontinuity]]. The first statement of the idea of continuity was by [[Euler]] in [[1784]], relating to  plane curves. Other mathematicians, including  [[Bernard Bolzano|Bolzano]] and [[Cauchy]], then refined and extended the idea of continuity. Continuous functions are the ''raison d'&ecirc;tre'' of topology itself. </blockquote>
-* Often you will want to then add subheadings for ''applications'' or ''motivations'' which help illuminate the use of the mathematical idea and its connections to other areas of mathematics.
-* Optionally, an ''informal introduction'' to the topic, without rigour, suitable for a school student or first-year undergraduate, as appropriate. This should state that it is informal, and that it is only stated to introduce the formal and correct approach. If a physical or geometric analogy or diagram will help, use one: many of your readers may be non-mathematical scientists.
-* Often, you will need to introduce some ''notation'' (again, often in its own subheading). Remember that not every one understands that, for example, ''x''^''n'' = ''x''**''n'' = ''x''<sup>''n''</sup>; try to use the standard notation (listed below) if you can. If you need to use non-standard notations, or if you introduce new notations, define them in your article.
-* An ''exact definition'', in mathematical terms; often proceeded by a subheading "==Definition(s)=="; for example: <blockquote> Let ''S'' and ''T'' be topological spaces, and let ''f'' be a [[computer programming|function]] from ''S'' to ''T''. Then ''f'' is called ''continuous'' [[iff|if]], [[for every]] open set ''O'' in ''T'', the [[preimage]] ''f''&nbsp;<sup>-1</sup>(''O'') is an open set in ''S''. </blockquote>
-* Some ''examples'' (often proceeded by a header ==Examples==), which serve to both expand on the definition, as well as provide some context as to ''why'' one might want to use the defined entity. You might also want to list non-examples -- things which come close to satisfying the definition but do not -- in order to refine the reader's intution more precisely.
-* A section about the ''history'' of the concept is often useful and can provide additional insight into the motivation.
-* Finally, most mathematical ideas are amenable to some form of ''generalization'' under the subheading ==Generalizations==; for example, multiplication of the rationals can be generalized to other fields, and so on. Given the amount of pretty abstract stuff already on the 'pedia, this is a good place to link out from.
-== Typesetting of mathematical formulas ==
-Wikipedia allows to typeset mathematical [[formula]]s in (a subset of) [[LaTeX]] markup; the formula is normally translated into a PNG image which is included into the text. For the mechanics of this, see [[meta:Help:Formula]].
-The LaTeX formulas work inline (like this: <math>\mathbf{x}\in\mathbb{R}^2</math>) as well as displayed on their own line:
-:<math>\int_0^\infty e^{-x^2}\,dx</math>
-The former inline method is generally discouraged, for several reasons:
-* the font size is somewhat larger than normal, making text containing inline formulas hard to read
-* the download speed of a page is negatively affected if it contains many images
-* HTML (as described below) is adequate for most simple inline formulas and better for text-only browsers.
-When displaying formulas on their own line, we indent the line with one or more colons (:); the above was typeset as
-:<code>:&lt;math&gt;\int_0^\infty e^{-x^2}\,dx&lt;/math&gt;</code>
-If you find an article which indents lines with spaces in order to achieve some formula layout effect, you should convert the formula to LaTeX markup.
-If you plan on editing LaTeX formulas, it is helpful if you leave your preference settings (link in the upper right corner of this page, underneath your user name) in the "rendering math" section at the default "HTML if very simple or else PNG"; that way, you'll see the page like most users will see it.
-The following sections cover the way of presenting simple inline formulas in HTML:
-=== Italicization and bolding ===
-To start with, we generally use italic text for variables (but never for numbers or symbols).
-Most editors prefer to use ''emphasised text'' (with <code><nowiki>''</nowiki></code>, i.e., apostrophe-apostrophe) rather than <i>italic text</i> (with the <code>&lt;i&gt;</code> tag, resembling HTML), since the former is easier to type and read in the edit box. Some prefer using the HTML "variable" tag, <code>&lt;var&gt;</code>, since it provides semantic meaning to the text contained within. Which method you choose is entirely up to you, but in order to keep with convention, we recommend the double-apostrophe emphasis method. Thus we write:
-:<code><nowiki>''x'' = (''y''&lt;sup&gt;2&lt;/sup&gt; + 2)</nowiki></code>
-which results in:
-:''x'' = (''y''<sup>2</sup> + 2)
-Note that the parentheses, equals and plus signs are not emphasized; try to keep them outside of the double-quoted sections.  Also, don't forget that descriptive subscripts should not be in italics, because they are not variables.  For example, ''m''<sub>foo</sub> is the mass of a foo.
-Fixed names for functions, such as sin and cos, are not emphasized, but we emphasize ''f'' when we define the function by ''f''(''x'') = sin(''x'') cos(''x'').
-Sets are usually written in upper case, and emphasized; for example:
-:''A'' = {''x'' : ''x'' > 0}
-would be written:
-:<code><nowiki>''A'' = {''x'' : ''x'' > 0}</nowiki></code>
-Greek letters should not be emphasized; for example, as in <code><nowiki>&amp;lambda; + ''y'' = &amp;pi;''r''<sup>2</sup></nowiki></code>, for the expression "&lambda; + ''y'' = &pi;''r''<sup>2</sup>".
-Commonly used sets of numbers are typeset in boldface, as in the set of real numbers '''R'''; see [[Blackboard bold]] for the types in use. Again, typically we use three apostrophes (<code><nowiki>'''</nowiki></code>) rather than the <code><nowiki><b></nowiki></code> tag for bolding.
-=== Using special symbols ===
-You may want to have a look at the [[table of mathematical symbols]].
-Not all of these symbols are displayed correctly on all browsers; it is generally better to be rather conservative in the use of HTML character entities in order to reach a larger audience, for example by writing "''x'' in ''Y''" rather than "''x'' &isin; ''Y''".
-=== Very simple formulas ===
-If you enter a very simple formula using the math notations like <nowiki><math>L^p</math></nowiki> this will (in the default used by most users) not be displayed using a png but using html, like this <math>L^p</math>. This is ''different'' from typesetting it as <nowiki>''L''<sup>''p''</sup></nowiki>. Compare:
-:Latex: <math>L^p</math> html: ''L''<sup>''p''</sup>
-Both forms are acceptable. Do not change one form to the other in other people's writing. They are likely to get annoyed since this seems to be a highly emotional issue. Changing to make a ''single page'' consistent is acceptable. However, at all costs avoid inline png. Even if you use <nowiki><math>L^p</math></nowiki> throughout the page, use <nowiki>''L''<sup>&amp;infin;</sup></nowiki> to get ''L''<sup>&infin;</sup> rather than the horrid <math>L^\infty</math>.
-If you want to ''force'' a png output for a simple formula, put a \, in its beginning.
-See [[Wikipedia talk:WikiProject Mathematics/Archive4(TeX)|archived discussion]].
-===Punctuation===
-It is good style to put a period at the end of a formula, if that formula is at the end of a sentence. If the formula is written in LaTeX, that is, surrounded by the <nowiki><math></nowiki> and <nowiki></math></nowiki> tags, then the period must be also inside the tags, because otherwise the period can get badly misaligned.
-== Other special formatting ==
-In many math textbooks, formalized statements, axioms, or theorems are often set apart in a box, perhaps with a colored background. Some Wikipedia editors have experimented with similar formatting in mathematical articles. For example, the [[Continuum hypothesis]], when stated formally, could be formatted using the following Wikipedia code:
-<pre><blockquote style="padding: 1em; border: 2px dotted purple;">
-There is no set whose size is strictly between that of the integers
-and that of the real numbers.
-</blockquote>
-</pre>
-The above is rendered like this in your browser:
-<blockquote style="padding: 1em; border: 2px dotted purple;">
-There is no set whose size is strictly between that of the integers
-and that of the real numbers.
-</blockquote>
-Graphical browsers which support [[Cascading style sheets]] should render the above in an indented box, surrounded by a purple dotted line. This formatting technique helps set apart the most important statements in mathematical articles. Again, whether you do this is entirely up to you; it's just something a few of Wikipedia's editors have found to be helpful in making math articles clearer.
-== Including literature and references ==
-I think that many (all?) math articles require a well-chosen list of references and pointers to the literature. Currently only major articles (sometimes) provide some literature. My reasons are as follows:
-* Wikipedia articles cannot (yet ;-) replace the textbooks. Often one wants to find out more details.
-* Some notions are defined differently depending on context or author. Articles should contain some references that support the given usage.
-* Many theorems come without proof or explanation. There are cases where I really wanted to look up the proofs before believing it...
-* Important theorems should cite historical papers as an additional information (not necessarily for looking them up).
-* Today many research papers or even books are freely available online and thus virtually just one click away from Wikipedia. Newcomers would greatly profit from having an immediate connection to further discussions of a topic.
-* Providing further reading enables other Wikipedians to verify and to extend the given information, as well as to discuss the quality of a particular source.
-Since literature may have different purposes, it is a good idea to add some short comments to the list (preferably in ''italics''), stating whether something is rather an up-to-date undergraduate textbook or a historical research paper. Other than this it could also be a good idea to list websites of influential journals or major research groups that specialize on a given field. Small articles that introduce some standard concept should still have a literature section (readers usually do not know whether a concept is standard): just write something like "''See the literature given in <nowiki>[[</nowiki>Main article on this field]].''" Comments are welcome.
---[[User:Markus Krötzsch|Markus Krötzsch]] 04:53, 19 Jun 2004 (UTC)
-There has been a little discussion of the issues already, on the talk page here.
-[[User:Charles Matthews|Charles Matthews]] 09:15, 19 Jun 2004 (UTC)
-Thanks for the hint. I do not know the current policy on these issues: there seems to be some talk in this article too. Feel free to move my suggestion to the talk page, if you consider it a controversial issue that is not fit for the main article...
-After reading the talk, I feel that I should specify my suggestions: I do not care about citation style, as long as it is precise. I do not suggest putting references within the text (this may work too, but is usually not required). What I recommend is a short -- possibly commented -- section of ''well-chosen'' references to '''back up the claims''' in math articles and to '''provide further reading'''. This should not disturb the article in any way and it could help to spot misconceptions or errors in math articles. So it is not much more than an emphasis of "[[Wikipedia:Cite sources]]" for the particular area of mathematics (where people are usually sceptics that want to have support for any claim ;-). --[[User:Markus Krötzsch|Markus Krötzsch]] 03:28, 20 Jun 2004 (UTC)
-Having read the [[Wikipedia_talk:WikiProject_Mathematics/Archive3#What_to_do_with_references.3F|thread in /Archive3]], I wanted to draw your attention to the article on the [[patience sorting]] that I have recently written for a self-consistent format example of including references. Maybe if you like it, it could be adapted for more articles on the math.&nbsp;(or other sci.)&nbsp;topics. [[User:BACbKA|BACbKA]] 22:48, 1 Dec 2004 (UTC)
 == Some useful links and resources ==