Wikipedia:WikiProject Mathematics

First, an important note for everyone to remember:

A few Wikipedians have gotten together to make some suggestions about how we might organize data in articles about mathematics. These are only suggestions, things to give you focus and to get you going, and you shouldn't feel obligated in the least to follow them. But if you don't know what to write or where to begin, following the below guidelines may be helpful. Mainly, we just want you to write articles!

Title

WikiProject Mathematics

Scope

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

The goals of this WikiProject are:

• 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.

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 describe below is one way of achieving this.

As you write your article, remember that Wikipedia is constantly growing; and so it may make your job easier to link to definitions of terms used in your article rather than to attempt to define / prove them in-line. If you use a term that you have good reason to think will be used again in another article, by all means create a good stub; if you 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.

Proofs

This is an encyclopedia, not a collection of math texts; but we often want to include proofs, as a way of really exposing the meaning of some theorem, definition, etc. A downside of including proofs is that they may interrupt the flow of the article, whose goal is usually expository. Use your judgement; as a rule of thumb, include proofs when they are part of an explanation; don't include them when they are a justification whose conclusion is merely "... therefore, P is true".

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:

• An introductory paragraph (or two), including the article title in bold, which describes the subject in general terms, and giving the mathematical context in which the term appears; for example
  • In topology and related branches of mathematics, a continuous function is, loosely speaking, a function from one topological space to another which preserves open sets. Continuous functions are the raison d'être of topology itself.
• An exact definition, in mathematical terms; often proceeded by a subheading "==Definition(s)=="; for example:
  • Let S and T be topological spaces, and let f be a function from S to T. Then f is called continuous if, for every open set O in T, the preimage f⁻¹(O) is an open set in S.
• 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.
• 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 = xⁿ; try to use the standard notation (listed below) if you can. If you need to use non-standard notations, or you introduce new notations, define them in your article, and add them to the standard notation.
• 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.
• 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.

Standard notation

We generally use italic text for variables (but not for numbers), and important equations are indented, as in

x_i² + y₅ⁿ = 1

Don't indent using just spaces; you get an ugly mono spaced font like this:

     xi2 + y5n = 1

Commonly used sets of numbers are typeset in boldface, as the set of real numbers R; see Blackboard bold for the types in use.

You may want to have a look at the table of mathematical symbols. Not all of these symbols are displayed correctly on all browsers; sometimes it is better to be conservative in the use of HTML entities in order to reach a larger audience, for example x in Y rather than x ∈ Y.

Diagrams are often a great help in explaining mathematical concepts; User:Chas_zzz_brown (amongst others) would be happy to create them (given time, ability, etc.).

Some Useful Links

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 of topics is also a useful place to check to see what other material on Wikipedia already exists that you can use to link with your material. This helps reduce the effort of defining terms and proving statements; and can help reduce the duplication of definitions and proofs.

Other lists of topics for subdisciplines:

• List of group theory topics
• List of mathematicians

Participants in this WikiProject

• Chas_zzz_brown. My knowledge of topics outside of group theory is a monotonically decreasing function of their relationship to abstract algebra.
• AxelBoldt
• Toby Bartels