Princeton University Mathematics Competition Wiki:Guidelines

Article naming
Article titles should be economical, in the sense that they should be the shortest, most straightforward way of referring to the subject matter of the article that still reflects common usage.

Capitalization
Please use "sentence style" for article titles, capitalizing only words that would normally be capitalized in standard English, such as proper nouns (names of people, associations, etc.) and the titles of published works. The purpose of this guideline is to facilitate linking to article titles in running text.

Other considerations:
 * 1) Do not capitalize the names of areas of mathematics.
 * 2) Do not capitalize words like theorem, lemma, etc., even in the names of well known results.
 * 3) The first letter of an article title is interpreted by the MediaWiki software to be capitalized, even if it should be lowercase, and this is how the title will appear in the top-most header of the page. In such cases, the canonical capitalization should be noted as early as is practical in the text of the article.

Examples:
 * elementary algebra &mdash; or, equivalently, Elementary algebra, but not Elementary Algebra
 * Pythagorean theorem &mdash; not Pythagorean Theorem
 * pi &mdash; refers to an article titled Pi

Articles created with nonstandard capitalization may be renamed using the "move" feature.

Please note: In the text that follows, article titles are usually capitalized even though in the running text of a regular article they would not be. This is usually to reinforce the idea that it is the articles or titles themselves that we are talking about. (Thus it is common practice to say: "See Integration by parts for more information." But: "Using integration by parts, we see that....")

Part of speech
Article titles should use the noun form of a mathematical term if one exists. For example, "implication" (a noun) should be used instead of "implies" (a verb). This allows the article to focus on the concept rather than strictly the definition of the operation (i.e., "A implies b when..." should not be the first sentence in the article).

Singular versus plural
Article titles that are nouns should generally be singular when they refer to mathematical objects (i.e., things that have definitions, properties, etc.). Such pages should always begin with a formal definition of the object being addressed. Page names that differ only in terms of pluralization should generally be avoided.

Examples:
 * Triangle &mdash; begins with a definition and figure(s); contains links to articles on different types of triangles (e.g., Right triangle); also links to other articles describing the history of triangles and explaining their applications in different areas of mathematics
 * Triangles &mdash; this page title is not recommended, although it should probably be created as a redirect to Triangle
 * Statistic &mdash; not the subfield of mathematics (see below), but the object called "a statistic"
 * Statistics &mdash; this is the page for the mathematical subfield; this should not, of course, be a redirect to Statistic

This rule should not be taken too far, however. On a page discussing the properties of limits, for example, the page name need not be Property of a limit (or any of the other permutations of singlular and plural in that phrase): Properties of limits is fine. The same thing can be said for many other similar phrases describing the mathematics of certain types of objects.

Examples:
 * Properties of limits &mdash; there are many properties, and they apply to all limits, so the phrasing makes sense
 * Factoring polynomials &mdash; this one is debatable, but it should probably be made a redirect to the page below
 * Factoring a polynomial &mdash; since this singular version makes just as much sense as the one above, it should probably be the preferred form

Some further remarks
One justification for using singular page titles as much as is practical, beyond simple consistency to facilitate linking, is the ambiguity inherent in the plural version of an object name.

Consider two examples:
 * 1) "Let f and g be functions."
 * 2) "Calculus classes generally start by reviewing functions."

In the first example, clearly the word "functions" should be linked to an article describing what a function is (and, in particular, the specific type of function that f and g are supposed to be examples of). In the second example, the word "functions" should probably be linked to a page describing the mathematics of functions that one needs to know to begin the study of calculus (in particular, properties of real-valued functions of a real variable). These are two quite different needs.

The concept of a function is so general as to make the discussion of the mathematics of functions on any single page completely impractical. Therefore, it makes sense to reserve the page Function to address what a function is (i.e., one or more definitions) and link to other pages, with more specific titles, to discuss the mathematics of functions. Having another page called Function s only invites confusion and duplication of effort. Thus almost every page named after a mathematical object should have a singular title and concentrate on defining and illustrating the object, distinguishing special cases, and so forth, leaving it to other pages (to which it links) for descriptions of the mathematics of the object from different perspectives. (Policies on the naming of these other pages needs to be discussed further, but see Disambiguation and Subpages below for two possibilities.)

See also the related policy on categories and the discussion of article content below.

Note: This issue needs to be dicussed further.

Formatting
Do not use single- or double-quotation marks, or any other mechanism, in page titles to indicate published works (and "scare quotes" should never be used in page titles). Such formatting should be accomplished outside of a link, or after a "pipe" character (|) within a link.

Examples:
 * Principia Mathematica
 * Correct:  Principia Mathematica 
 * Incorrect: 
 * Incorrect:  'Principia Mathematica' 
 * Incorrect:  "Principia Mathematica" 
 * Euclid's Elements
 * Correct:  Euclid's Elements|Euclid's Elements 
 * Incorrect:  Euclid's Elements 
 * Incorrect:  Euclid's 'Elements' 
 * Incorrect:  Euclid's "Elements" </tt>

See Help:Editing for more information about wiki syntax.

Synonyms
Duplicate articles can be avoided by creating a redirect from a less common (or more ambiguous) page name, such as Modern algebra, to the more common (or less ambiguous) version, in this case Abstract algebra.

Disambiguation
Even the most carefully chosen page name can cause problems when the same term is used in two or more distinct senses. When such a conflict occurs, the original page should become an "index page" pointing to other, more specific pages that discuss the topic from different points of view, each of which is named using parenthetical "disambiguation text".

Example:
 * Problem: Suppose Intersection is originally created to discuss the intersection of graphs in Cartesian coordinate systems. Someone else wants to discuss the set operation called intersection at the same page.
 * Solution: Instead of addressing such different concepts on the same page we create two different, "disambiguated" pages:
 * A new page called Intersection (sets) is created to address the set operation.
 * The original Intersection page is moved (preserving the edit history) to Intersection (graphs).
 * All of the existing links to Intersection should be checked and updated as necessary to point to the correct pages. Any pages that link to it through a redirect will now link to Intersection (graphs) through a double redirect, which must be fixed. Direct links to Intersection will only be single redirects to the new page, so these can be left as-is, assuming they intend the meaning discussed at Intersection (graphs).
 * Finally, Intersection is re-edited to begin a new "index page" that points to both Intersection (graphs) and Intersection (sets). (It should also, of course, point out how the former is actually just a special case of the latter!)

Note that in cases where the original page is almost always what editors will intend when linking to its page title, only step 1 should be done. For example, it makes no sense to redirect hundreds (let's imagine) of existing links to Integral (in the calculus sense) when someone wants to create Integral (integer) to point out that integral can mean "of or related to an integer".

Pipe trick
The benefit of using parenthetical disambiguation &mdash; rather than, say, subpage (/</tt>) disambiguation &mdash; is that the "pipe trick" can be used in links without slowing down the writing/editing process too much (this is, of course, assuming the parenthetical text has been chosen wisely).

Examples: Note the "pipe" character (|</tt>) before the closing double-brackets (]]</tt>) in these examples. (Again, see Help:Editing for information on wiki syntax.)
 *  intersection (graphs)| </tt> appears as intersection (graphs)|intersection
 *  intersection (sets)| </tt> appears as intersection (sets)|intersection

Additional redirects can be created at pages called Intersection (lines), Intersection (planes), and so forth, all of which point to Intersection (graphs), to make future linking even easier for editors. Of course, if Intersection (graphs) gets too large, these other redirects can be changed into full-fledged pages and Intersection (graphs) made into another index page, in a manner similar to the procedure discussed above.

Choice of disambiguation text
What text is used in the parentheses to disambiguate a page name depends to a great extent on the source of the ambiguity. If a term is used differently in two different areas of mathematics, use the names of the areas of mathematics as the disambigation text; if a term is applied in different senses to two different types of objects, use the name of the objects; and so forth.

Examples:
 * Inverse (function)
 * Inverse (matrix)

Remember that the purpose of this style of disambiguation is to make linking easier in running text. Keep this in mind when choosing the parenthetical text.

Also keep in mind that many disambiguation issues can be solved by careful naming of pages in the first place. The two examples given above should probably actually be redirects to Inverse function and Inverse of a matrix, respectively.

Note: This issue needs to be discussed further.

Subpages
The use of subpages &mdash; separated from the "parent" page by a slash (/</tt>) &mdash; might be useful, but the feature currently doesn't work in the main article namespace.

Note: This issue needs to be discussed further.

Category naming
Category names should generally be plural if they refer to mathematical objects (in contrast to the corresponding article naming convention above). Categories that differ only in pluralization should be avoided.

Examples:
 * :Category:Triangles &mdash; not :Category:Triangle
 * Contains articles such as Triangle (of course), Right triangle and Similar triangles
 * :Category:Geometry
 * Contains articles such as Geometry, Euclidean geometry and Circle &mdash; and also :Category:Triangles as a subcategory
 * Category:Geometries should be avoided because of the existence of the above category

Badly named categories cannot be moved, but may be depopulated and deleted (policy and mechanism yet to come) or a "soft redirect" (text pointing readers to the new category) created. See Help:Category for more information on the MediaWiki Category feature.

Article content
Some considerations for article content:
 * In the interest of quality over quantity, if a topic has a number of closely related subtopics (e.g., linear algebra, linear equations, solving linear equations), those topics may be introduced and addressed in the top-most topic's article if insufficient material exists for each subtopic to be treated in a separate article.

Proof writing
Proofs of propositions should be formal paragraph proofs. Proof outlines should be written into formal paragraph proofs as soon as possible.


 * A statement of the proposition should be succinctly and sufficiently stated.
 * If applicable, before the proof is started, insert a Lemmas section to list important previous proofs that will be used.
 * Always precede the proof with the heading Proof to inform the reader that the proof has begun.
 * Start the proof with a statement of intent. (We will assume that..., and show that...)
 * Conclude the proof with a statement indicating the intent is fulfilled. (This shows that...)
 * Place QED at the bottom to inform the reader the proof is complete.
 * Use first person plural (we, our, us). The idea is that you and the reader are proving a proposition together.
 * Use clear and complete sentences. Avoid run-on sentences.
 * Never start a sentence with a mathematical expression or a number.
 * Each term that appears in the proof should be linked to its own page on the first occurance.
 * Geometric diagrams, if necessary, should be included, in PNG format, at the top of the proof to the right.
 * No Logical Fallacies!!! No Circular Reasoning!!!
 * Please do not plagiarize.

Lesson plans and problem sets
Lesson plans and problem sets are permitted, linked at the bottom(s) of the appropriate page(s), so long as the owner of the lesson plan gives permission and proper credit is given. Please use PDF. Use ZIP where necessary. Please state the title, subject, and grade level.