Help:Editing
You should feel welcome to contribute, even if you think what you write doesn't match the 'house style'.
In that case, this page is more to explain the meaning behind any minor changes that may be applied to your work after it has been submitted.
Over the course of prolonged contribution, it is considered both polite and very desirable that contributors put effort in mastering and adhering to house style, which is located at Help:House Style.
Should there be any questions, Help:Questions is the place to raise issues.
Contents
 1 Page Editing
 2 Creating a Page
 3 Deleting a page
 4 Page Naming
 5 Tips to choose a good name
 6 Naming conventions
 7 Things named after a mathematician
 8 Multiple Names
 9 Special Characters
 10 Page Structure
 11 Introduction
 12 General Format
 13 Sections
 14 Categories
 15 Wiki Editing
 16 $\LaTeX$ Editing
 17 Aligned Equations
 18 Specific Topics
 19 External references and manuals
Page Editing
This reference provides the general outline on creating pages and instructions for specific sections; for the rest, see Help:House Style. Furthermore, this page does not dwell on details pertaining to the MediaWiki architecture; the reference for such things is Help:Wiki Editing.
Creating a Page
After searching, you may conclude that the page you're looking for does not exist yet. There are several ways to create it.
By Searching
Search for the page name which you would like to create. As you have found out by now, the page has not already been created. You will see something that looks like this:
 Create the page "Proof name" on this wiki!
Clicking on Proof name will open the page editing window, and you can start writing.
By following a red link
All you have to do is click the red link and start writing.
By entering a direct URL
If you know for sure that the proof is not on the site, then simply type that name into the URL. For example, if you wanted to prove the Riemann Hypothesis, you would type:
http://www.proofwiki.org/wiki/Riemann Hypothesis
If this page does not exist then, you will get a single line saying:
 There is currently no text in this page. You can search for this page title in other pages, search the related logs, or create this page.
Clicking create this page will open the editing page where you can edit the page.
Deleting a page
Don't do this. Only trusted users can delete pages in any event; but this website has a strict nondeletion policy. Hence, deletions on this website happen very rarely.
Page Naming
Choosing a good page title is important for multiple reasons:
 It makes the page easier to search for.
 The title gives a first impression of what the page is about. A good title adds to the understanding.
 The title is what is used in links. It's always nice to know what a page is about before clicking the link.
 A descriptive title avoids name conflicts.
Some pages are subject to specific naming conventions. See the corresponding help pages for instructions:
Page titles that do not meet the standards can be flagged for renaming.
Tips to choose a good name
Be specific
There's no such thing as being too specific! In particular, page names consisting of a single word should generally be avoided: you never know if there are other concepts in mathematics with the same name. That is:
 not Definition:Prime Ideal but Definition:Prime Ideal of Ring
 not Definition:Supremum or Definition:Supremum of Set but Definition:Supremum of Subset of Real Numbers
The word "of" comes in handy here.
In the same spirit, it is a good practice to always include at least one noun in the title. That is:
 not Definition:Differentiable but Definition:Differentiable Mapping
 not Definition:Simple but Definition:Simple Group
Note how the shorter page names are always disambiguation pages.
For theorems, the same philosophy applies:
Redundant words
Page names should not be started with articles such as "A" or "The", as this makes it significantly harder to find pages alphabetically in their categories. For example: Pythagorean Theorem, not The Pythagorean Theorem.
Similarly, is not necessary to begin the name with "Proof of ...", and this should be avoided. Since $\mathsf{Pr} \infty \mathsf{fWiki}$ is a collection of proofs, it is assumed that each page is going to be a proof of something. This also makes searching for articles much easier.
In general, the words "the", "a" or "an" are strongly discouraged in page names, as they make the name longer than necessary and rarely add clarity to the concept being defined.
The main exception to this rule is for concepts split into subtypes named along the lines "of the $n$th kind" , for example: Definition:Elliptic Integral of the First Kind.
Descriptiveness
A good page title describes the content accurately. Because theorems are linked to using their exact page title, when reading a proof it is useful when you can guess what a theorem is about without having to visit the page. In particular, if a theorem contains an equivalence proof, the title should makes this clear, by using "iff".
Don't blindly trust literature
Books, thanks to their limited scope, can afford to use simplified terminology without running into ambiguity problems. At $\mathsf{Pr} \infty \mathsf{fWiki}$ we can not. Thus it is a good idea to check if there is a danger for name conflicts by doing some research. Alternatively, make the name overly specific.
As for theorems, books may call a theorem "Fundamental Property of Homomorphisms" or "Continuity Property". This does not mean that the theorem is everywhere known by that name. While at $\mathsf{Pr} \infty \mathsf{fWiki}$ we do prefer to use as a title the name of a theorem rather than a description of the result, we do so only if there is no ambiguity.
Naming conventions
Namespaces
When you would like to create a page for a definition, all you have to do different from naming a proof is to add Definition:
in front of the name. So for example if you wanted to create a page for the definition of calculus you would name the page:
Definition:Calculus
Also, after you create the page, be sure to add the definition to the appropriate "Definitions" categories (see Category:Definitions).
The same method that is used for Definitions is also used to name and categorize axiom and symbols pages. Simply substitute Symbol
or Axiom
for Definition:
in the page name and, mutatis mutandis, in the category name. See Help:Categories.
Capitalizing
Page titles are casesensitive. For all types of pages, major words in the title of the page should be capitalized. For example: Subring Generated by Unity of Ring with Unity. So as to promote consistency, be informed that in particular, the following words are not considered to be "major" and ought to be used in their lowercase form when naming a page:
 Prepositions, pronouns and conjunctions:
 and, around, as, between, by, for, from, if, iff, in, its, minus, no, not, of, on, or, over, plus, such that, that, the, then, to, under, with, with respect to, which, whose
 Short verbs, such as:
 are, can, cannot, does, equals, form, has, have, implies, is
These lists are not exhaustive.
Variables in formulas are not capitalized. See #Names with Formulas.
Names with Formulas
If the name of a page contains mathematical statements, the following formatting practices should be adhered to:
 Put no spaces between numbers/elements that are added, subtracted, divided, or multiplied together.
 Example:
(1+2)x3
 Example:
 Do, however, put spaces between elements that are put into equality or inequality with one another. Use
!=
to signify inequality. Example:
1 = 3/3 != 3/4
 Example:
 Variables appearing in the formulas need not be capitalized.
 Example:
Primitive of x squared over a x + b
 Example:
 A page name is no place for $\LaTeX$ commands.
Things named after a mathematician
A theorem that is named after a Mathematician gets a call of the Namedfor template. When done properly, the page is then automatically placed in a corresponding category in Named Theorems, which itself has to be created manually.
Similarly, for named definitions there is the NamedforDef template.
Disambiguation pages are treated in the same way. Note that theorem disambiguations do not otherwise get categories. See Help:Disambiguation.
A page whose name contains a word named after a Mathematician does not fall under this category. For example, not every theorem about Krull dimension needs a call of Namedfor.
Multiple Names
Some mathematical concepts have several names, according to the sources you consult. Which of these names is used in $\mathsf{Pr} \infty \mathsf{fWiki}$ is largely a matter of happenstance.
However, if one of the names of a concept is for a particular mathematician, that name is to be used in preference.
An example of this is Definition:Chebyshev Distance, which is otherwise known as the Definition:Maximum Metric or the Definition:Chessboard Metric.
See also Help:Also known as.
Special Characters
Disallowed Characters
The following characters should not be used in page names:
# < > [ ]  { } * & $ @
Accented Characters
A theorem named after someone gets this exact name, including accented characters.
For search convenience, a redirect can be set up. See Help:Redirects#Accented characters
Page Structure
The purpose of this page is to describe the general structure that the various sections most used on $\mathsf{Pr} \infty \mathsf{fWiki}$ are to adhere to. While this naturally intersects with House Style at some points, an attempt is made to separate the global editing instructions and sectionspecific instructions.
Introduction
On all pages (except for talk and user pages), the House Style applies.
This page gives the general structure that applies to all pages. Click on the links below for the more precise expected format, which depends on the type of page:
General Format
Generally, pages follow this format:
== Theorem == State the theorem here. == Proof == State the proof here. == Also see == * List of (internal) links to closely related material. == Sources == Add citations here. [[Category:The Category]]
Sections
Below, various recurring sections on $\mathsf{Pr} \infty \mathsf{fWiki}$ pages and their particular rules are explained. All of these should have a type 2 heading.
The sections should be placed in the following order, with this exact capitalization:
 Definition / Theorem
 Proof(s)
 Also known as
 Also defined as
 Also see
 Named for
 Historical Note
 Linguistic Note
 Technical Note
 Sources
Other optional sections include:
and more, such as remarks, comments, notations, for which there are no written guidelines yet.
Definitions and Theorems
These are in practice split into two parts (which is made visual by extra blank lines separating them).
Namely, first there is a series of lines, typically starting with "Let", introducing all names and concepts needed for stating the actual definition or theorem.
Then, separated by two blank lines, the definition or theorem itself is stated. Thus, we obtain the following structure (analogous for Theorems):
== Definition == Let ... ... Let ... Then '''what is to be defined''' is defined as ...
The concept that is to be defined is to be displayed in bold (i.e., with three apostrophes, '
, on either side) throughout the page to make it stand out.
Proofs
Besides adhering to house style, it is a good idea to separate different stages of the proof by subsections or whitespace. Other than that, rigour is the only real prerequisite for proofs.
If you would like other contributors to check your proof, please use the proofread template.
Notes (avoid)
Try to avoid having a general "Notes" section on a page you create or edit. Instead, try to put any remarks you want to add into one of the sections listed next.
Explanation
This section can be used to explain concepts, in particular on pages that give definitions or describe types of proofs. To give context, consider using an "Also see" section.
Also known as
Use this section when a concept or result is referred to in multiple ways; this is most commonly used for definitions.
All names should appear in bold. Should an alternative name coincide with the $\mathsf{Pr} \infty \mathsf{fWiki}$ name of something else, it is good to draw the reader's attention to this by including a link and a comment.
Also defined as
Use this section when a single name is used in the literature for multiple definitions. Typically, it is to be used mainly when these definitions are in the same field of mathematics. In other cases, a disambiguation is usually more appropriate. See Help:Disambiguation for instructions on that.
It is advisable to create a synthesis of this and the "Also known as" section. That is, to place "Also known as" sections on pages that are referred to in this section.
Also see
The "Also see" section is intended to contain references to closely related concepts and/or results. These are entered as a bulleted list:
== Also see == * [[Check This Out 1]] * [[Check This Out 2]] * Etc.
It is understood that definitions should be referenced in this section directly, without providing a reader view. This is to make it easy to see which entries are definitions and which are proofs.
Thus:
* [[Definition:Increasing Sequence of Sets]]
is a correct entry.
In addition to the above, when a definition has an associated category, this category is to be referenced as well.
For example, Definition:Set Union refers to Category:Set Union. This is accomplished by the LinkToCategory template, entered as:
{{LinkToCategorySet Unionset union}}
More documentation for this template can be found on its page: Template:LinkToCategory.
Source of Name
This section is exclusively created by the Namedfor template.
It is entered as:
{{NamedforName of mathematiciancat = Surname of mathematician}}
where Surname of mathematician
is actually the name of the mathematician's subcategory of Category:Named Theorems  multiple notable mathematicians with identical surnames exist.
If some page is named for multiple mathematicians (e.g. CayleyHamilton Theorem) they should all be listed, via:
{{NamedforName 1cat = Surname 1name2 = Name 2cat2 = Surname 2}} {{NamedforName 1cat = Surname 1name2 = Name 2cat2 = Surname 2name3 = Name 3cat3 = Surname 3}}
A similar technique is used for definitions.
If a definition is named for a particular mathematician, then the NamedforDef template is used:
{{NamedforDefName of mathematiciancat = Surname of mathematician}}
and again for axioms:
{{NamedforAxiomName of mathematiciancat = Surname of mathematician}}
The same extensions apply for multiple mathematicians.
Historical Note
The Historical Note section is intended as a relatively freeform section in which any interesting information about the concept can be elaborated on.
If there is already a "Source of Name" section, then if what you want to say consists of a sentence or two, it may be better just to add it to directly after your invocation of the namedfor template. See Fermat's Little Theorem for a simple example. On the other hand, see Fermat's Two Squares Theorem for an example of where the author has considered it appropriate to create a separate section.
If you have a great deal to say about the subject in question, then it is worth considering whether to write it as a separate transcluded page.
Indeed, if you have a strong interest and expertise in the history of mathematics and wish to impart that knowledge on this website, then it may be a worthwhile future task setting up a properly structured category for the history of mathematics, into which we may find it worthwhile to migrate, for example, our Mathematicians space into.
This is one area of $\mathsf{Pr} \infty \mathsf{fWiki}$ whose evolution is in progress.
Linguistic Note
If a term being defined is not a common word in natural language, then it may be appropriate to give an indication of various linguistic characteristics of that word.
Examples of this are:
 Its pronunciation (for example: see Definition:Integer)
 Its plural form (for example: see Definition:Continuum (Topology))
 Its etymology (for example: see Definition:Summand)
Boldface is used for all words which directly relate to the term being defined.
The pronunciation is given in simple, phonetic English, with syllables separated by hyphens.
Stressed syllables are indicated in italics, hence the rendering: syllable.
Note that the Linguistic Note section is not mandatory for any page; it is created only when there is a need.
It needs to be remembered that $\mathsf{Pr} \infty \mathsf{fWiki}$ is accessed by users worldwide, to whom English is not their first language, and may not be familiar with many aspects of mathematical language which may be taken for granted by a native English speaker.
Also note that if there are differences between UK and US English forms of the spelling, the pronunciation or the plural form of any term, then this is the section to document it.
Technical Note
On definitions pages, typically some notation is introduced.
When rendering this notation using $\LaTeX$ requires some involved trickery, the code for achieving this may be explained in a section named "Technical Note".
See Definition:Convergence in Measure for an example.
Sources
This section serves to list the sources backing up a certain page. Because this section is of paramount importance for the reliability of $\mathsf{Pr} \infty \mathsf{fWiki}$, it and its constituents are discussed in detail on a dedicated page, Help:Sources.
Categories
At the very bottom of the page, categories have to be added. See Help:Categories for documentation.
Wiki Editing
The definitive reference on wiki editing is of course MediaWiki's own site, in particular the MediaWiki Help Pages.
The below gives an overview of the wiki functionality that is most frequently used on $\mathsf{Pr} \infty \mathsf{fWiki}$.
Text styles
Text you would like to be bold should be enclosed in three single quotes. For example:
'''Bold text'''
creates: Bold text.
Italic font is produced with two single quotes, for example:
''Italic text''
creates: Italic text
To produce bold, italicised writing, use five consecutive single quotes:
'''''Bold and italic text'''''
creates: Bold and italic text.
Fixed width text:
<code> Fixed width text</code>
creates: Fixed width text
Note that while:
<tt> Fixed width text </tt>
produces the same result, the tt
tag is known to be badly behaved in combination with MediaWiki, creating rendering issues.
Therefore, the code
tag is to be used universally on $\mathsf{Pr} \infty \mathsf{fWiki}$ to generate fixed width text.
Line breaking
Breaking a line in the editor does not break a line in the displayed text. For example:
''I will continue this'' ''on the next line''
displays as:
I will continue this on the next line.
To break a line, space the text with a single blank line:
''I will continue this'' ''on the next line''
Sections and subsections
A section heading is produced by enclosing the desired title between two equals (=
) signs. For example:
== Definition ==
will produce a section entitled "Definition".
A subsection should be enclosed between three equals signs, for example:
=== Subsection ===
will produce a subsection within the section that it is located.
One can continue making subsubsections etc. with four or more equals signs.
For documentation of the accepted house style regarding sections, see Help:House Style.
Inclined to move the below to referenced Help:House Style.
As a general rule on spacing, each section or subsection heading should be preceded by two blank lines and followed by a single blank line.
Each sentence should appear on a separate line, with a single blank line above and below. For example:
This line precedes the section. == Section heading == Line one of the section. Line two of the section.
Indenting and bullet points
To indent a sentence or equation, add a colon (:
) at the start of the line. For example:
:Indented material
will produce:
 Indented material
For a larger indent use two or more colons.
For example, it is required by house style that each displayed equation be preceded with a single colon.
To produce a list of bullet points, write each point on a line beginning with an asterisk (*
). For example:
* Bullet point 1 * Bullet point 2
produces:
 Bullet point 1
 Bullet point 2
As a notable discrepancy in house style, the empty lines guideline does not apply to successive items of lists.
This is because doing so results in a slight spacing issue, as seen in:
* Bullet point 1 * Bullet point 2 * Bullet point 3
which renders as:
 Bullet point 1
 Bullet point 2
 Bullet point 3
On $\mathsf{Pr} \infty \mathsf{fWiki}$, these lists are mainly used in the Also see and Sources sections.
Link to internal page
To link to another page on $\mathsf{Pr} \infty \mathsf{fWiki}$, you must enclose the page name in double square brackets.
For example, to link to Pythagoras's Theorem, you would type:
[[Pythagoras's Theorem]]
To change the text to say something different and still link to that page you need to use a pipe character (
).
For example to link here you would type:
[[Pythagoras's Theoremhere]]
To link to a particular section on a page, append a octothorpe (#
) to the page name followed by the subsection.
For example, to link here you would type:
[[Pythagoras's Theorem#The Classic Proofhere]]
This means of reference is generally going out of fashion on $\mathsf{Pr} \infty \mathsf{fWiki}$ due to the advent of the transclusion method.
In the above example, it would be more correct to refer to the subpage containing the "Classic Proof", viz here:
[[Pythagoras's Theorem/Classic Proofhere]]
There may be instances though where its use will be continued, for example to link to particular sections of the main wiki talk page in discussions.
For more information on the house style stipulations regarding internal reference, see Help:House Style.
Redirecting a page
See also Help:Redirects
If a theorem or definition is commonly known by more than one name, rather than create two separate pages just one page should be created, and the second redirected to the first.
This should be done with the command:
#Redirect [[Page Name]]
For example, to redirect a page to Pythagoras's Theorem enter:
#Redirect [[Pythagoras's Theorem]]
See Help:Redirects for more information on redirecting pages and the associated house style.
Link to external page
Linking to an external page is almost the same as linking to an internal page.
You need to enclose the page name in square brackets, []
.
To add text the link, you just have to add what you want to name the link inside the brackets.
For example:
[http://www.google.com Google]
would create a link that looked like this: Google
References
See also Help:Citations
References can easily be created by enclose the reference inside a <ref></ref> tag in the area you would like referenced. Then near the end of your article include this: <references/> . This will be where the references are actually listed. For an example see the below:
According to scientists, the Sun is pretty big.^{[1]} The Moon, however, is not so big.^{[2]}
Notes
The code for this:
According to scientists, the Sun is pretty big.<ref>E. Miller, The Sun, (New York: Academic Press, 2005), 235.</ref> The Moon, however, is not so big.<ref>R. Smith, "Size of the Moon", Scientific American, 46 (April 1978): 446.</ref> '''Notes''' <references/>
Typically, it is desirable to collect the references under a designated 'type2' header named 'References', whose code is:
== References ==
This section is best placed directly above the "Sources" section. For more information on page structuring, see Help:Page Editing.
Transclusion
Transclusion is a MediaWiki feature that allows (part of) a page to be displayed verbatim on another.
Since the construct is rather involved, it is explained on its own page, Help:Transclusion.
The $\mathsf{Pr} \infty \mathsf{fWiki}$ extension
The $\mathsf{Pr} \infty \mathsf{fWiki}$ extension is an amendment of MediaWiki's code that enables certain sitespecific constructs.
See Help:ProofWiki Extension for documentation on this feature.
$\LaTeX$ Editing
In general, contributors are assumed to be up to speed with some form of $\LaTeX$; a web search should be sufficient to find ample reference on how to get started with it, should you still need to.
The "External references" section below may also be consulted.
The $\LaTeX$ interpreter used on this site is brought to you by MathJax.
This produces an experience different from that produced by the MediaWiki interpreter which is (at time of writing) the one used by Wikipedia and other places.
It also has a subtly different syntax in places. Specific instances will be detailed where relevant.
$\LaTeX$ delimiters
To display an equation in line with some text, the equation should be enclosed in single dollar signs: $ ... $
Note that \( ... \)
also works, but takes more effort to type and so is less recommended.
There may (but we hope not) still be some pages with <math> ... </math>
in them. This is a holdover from when MediaWiki was the interpreter used for $\LaTeX$ commands. It still works in MathJax after a fashion but on transcluded pages, such enclosed $\LaTeX$ will not be converted to mathematical symbols.
If you see any, then feel free to change them to $
signs, as they should not be there.
No longer supported
The following $\LaTeX$ commands are not supported in MathJax, but may still be present in some pages. When found they need to be replaced.
 For $\lor$:
\or
to be replaced by\lor
 For $\land$:
\and
to be replaced by\land
 For $\R$:
\reals
to be replaced by\R
 For $\varnothing$:
\O
to be replaced by\varnothing
 For $\exists$:
\exist
to be replaced by\exists
 For producing fixed width text in math mode:
\texttt
needs to be replaced by\mathtt
.
If you find any more examples, add them here.
New commands
New commands can be requested and discussed at Symbols:LaTeX Commands/ProofWiki Specific, transcluded here:
\(\AA\)  $\quad:\quad$\AA

$\qquad$that is: \mathcal A


\(\Add\)  $\quad:\quad$\Add

$\qquad$Addition as a Primitive Recursive Function  
\(\adj {\mathbf A}\)  $\quad:\quad$\adj {\mathbf A}

$\qquad$Adjugate Matrix  
\(\arccot\)  $\quad:\quad$\arccot

$\qquad$Arccotangent  
\(\arccsc\)  $\quad:\quad$\arccsc

$\qquad$Arccosecant  
\(\arcsec\)  $\quad:\quad$\arcsec

$\qquad$Arcsecant  
\(\Area\)  $\quad:\quad$\Area

$\qquad$Area of Plane Figure  
\(\Arg z\)  $\quad:\quad$\Arg z

$\qquad$Principal Argument of Complex Number  
\(\Aut {S}\)  $\quad:\quad$\Aut {S}

$\qquad$Automorphism Group  
\(\BB\)  $\quad:\quad$\BB

$\qquad$that is: \mathcal B


\(\Bernoulli {p}\)  $\quad:\quad$\Bernoulli {p}

$\qquad$Bernoulli Distribution  
\(\BetaDist {\alpha} {\beta}\)  $\quad:\quad$\BetaDist {\alpha} {\beta}

$\qquad$Beta Distribution  
\(\bigintlimits {\map f s} {s \mathop = 0} {s \mathop = a}\)  $\quad:\quad$\bigintlimits {\map f s} {s \mathop = 0} {s \mathop = a}

$\qquad$Limits of Integration  
\(\bigvalueat {\delta x} {x \mathop = x_j} \)  $\quad:\quad$\bigvalueat {\delta x} {x \mathop = x_j}


\(\Binomial {n} {p}\)  $\quad:\quad$\Binomial {n} {p}

$\qquad$Binomial Distribution  
\(\braket {a} {b}\)  $\quad:\quad$\braket {a} {b}

$\qquad$Dirac Notation  
\(\bsDelta\)  $\quad:\quad$\bsDelta

$\qquad$a vector '$\Delta$'  
\(\bsone\)  $\quad:\quad$\bsone

$\qquad$vector of ones  
\(\bst\)  $\quad:\quad$\bst

$\qquad$a vector 't'  
\(\bsv\)  $\quad:\quad$\bsv

$\qquad$a vector 'v'  
\(\bsw\)  $\quad:\quad$\bsw

$\qquad$a vector 'w'  
\(\bsx\)  $\quad:\quad$\bsx

$\qquad$a vector 'x'  
\(\bsy\)  $\quad:\quad$\bsy

$\qquad$a vector 'y'  
\(\bsz\)  $\quad:\quad$\bsz

$\qquad$a vector 'z'  
\(\bszero\)  $\quad:\quad$\bszero

$\qquad$vector of zeros  
\(\map \Card {S}\)  $\quad:\quad$\map \Card {S}

$\qquad$Cardinality  
\(\card {S}\)  $\quad:\quad$\card {S}

$\qquad$Cardinality  
\(\Cauchy {x_0} {\gamma}\)  $\quad:\quad$\Cauchy {x_0} {\gamma}

$\qquad$Cauchy Distribution  
\(\CC\)  $\quad:\quad$\CC

$\qquad$that is: \mathcal C


\(\Cdm {f}\)  $\quad:\quad$\Cdm {f}

$\qquad$Codomain of Mapping  
\(\ceiling {11.98}\)  $\quad:\quad$\ceiling {11.98}

$\qquad$Ceiling Function  
\(30 \cels\)  $\quad:\quad$30 \cels

$\qquad$Degrees Celsius  
\(\Char {R}\)  $\quad:\quad$\Char {R}

$\qquad$Characteristic of Ring, etc.  
\(\Ci\)  $\quad:\quad$\Ci

$\qquad$Cosine Integral Function  
\(\cis \theta\)  $\quad:\quad$\cis \theta

$\qquad$$\cos \theta + i \sin \theta$  
\(\cl S\)  $\quad:\quad$\cl S

$\qquad$Closure (Topology)  
\(\closedint {a} {b}\)  $\quad:\quad$\closedint {a} {b}

$\qquad$Closed Interval  
\(\cmod {z^2}\)  $\quad:\quad$\cmod {z^2}

$\qquad$Complex Modulus  
\(\conjclass {x}\)  $\quad:\quad$\conjclass {x}

$\qquad$Conjugacy Class  
\(\cont {f}\)  $\quad:\quad$\cont {f}

$\qquad$Content of Polynomial  
\(\ContinuousUniform {a} {b}\)  $\quad:\quad$\ContinuousUniform {a} {b}

$\qquad$Continuous Uniform Distribution  
\(\cosec\)  $\quad:\quad$\cosec

$\qquad$Cosecant (alternative form)  
\(\Cosh\)  $\quad:\quad$\Cosh

$\qquad$Hyperbolic Cosine  
\(\Coth\)  $\quad:\quad$\Coth

$\qquad$Hyperbolic Cotangent  
\(\cov {X, Y}\)  $\quad:\quad$\cov {X, Y}

$\qquad$Covariance  
\(\csch\)  $\quad:\quad$\csch

$\qquad$Hyperbolic Cosecant  
\(\Csch\)  $\quad:\quad$\Csch

$\qquad$Hyperbolic Cosecant  
\(\curl\)  $\quad:\quad$\curl

$\qquad$Curl Operator  
\(\DD\)  $\quad:\quad$\DD

$\qquad$that is: \mathcal D


\(\dfrac {\d x} {\d y}\)  $\quad:\quad$\dfrac {\d x} {\d y}

$\qquad$Roman $\d$ for Derivatives  
\(30 \degrees\)  $\quad:\quad$30 \degrees

$\qquad$Degrees of Arc  
\(\Dic n\)  $\quad:\quad$\Dic n

$\qquad$Dicyclic Group  
\(\DiscreteUniform {n}\)  $\quad:\quad$\DiscreteUniform {n}

$\qquad$Discrete Uniform Distribution  
\(a \divides b\)  $\quad:\quad$a \divides b

$\qquad$Divisibility  
\(\Dom {f}\)  $\quad:\quad$\Dom {f}

$\qquad$Domain of Mapping  
\(\dr {a}\)  $\quad:\quad$\dr {a}

$\qquad$Digital Root  
\(\E\)  $\quad:\quad$\E

$\qquad$Euler's number  
\(\EE\)  $\quad:\quad$\EE

$\qquad$that is: \mathcal E


\(\Ei\)  $\quad:\quad$\Ei

$\qquad$Exponential Integral Function  
\(\empty\)  $\quad:\quad$\empty

$\qquad$Empty Set  
\(\eqclass {x} {\mathcal R}\)  $\quad:\quad$\eqclass {x} {\mathcal R}

$\qquad$Equivalence Class  
\(\erf\)  $\quad:\quad$\erf

$\qquad$Error Function  
\(\erfc\)  $\quad:\quad$\erfc

$\qquad$Complementary Error Function  
\(\expect {X}\)  $\quad:\quad$\expect {X}

$\qquad$Expectation  
\(\Exponential {\beta}\)  $\quad:\quad$\Exponential {\beta}

$\qquad$Exponential Distribution  
\(\Ext {\gamma}\)  $\quad:\quad$\Ext {\gamma}

$\qquad$Exterior  
\(\F\)  $\quad:\quad$\F

$\qquad$False  
\(30 \fahr\)  $\quad:\quad$30 \fahr

$\qquad$Degrees Fahrenheit  
\(\family {S_i}\)  $\quad:\quad$\family {S_i}

$\qquad$Indexed Family  
\(\FF\)  $\quad:\quad$\FF

$\qquad$that is: \mathcal F


\(\Fix {\pi}\)  $\quad:\quad$\Fix {\pi}

$\qquad$Set of Fixed Elements  
\(\floor {11.98}\)  $\quad:\quad$\floor {11.98}

$\qquad$Floor Function  
\(\fractpart {x}\)  $\quad:\quad$\fractpart {x}

$\qquad$Fractional Part  
\(\Frob {R}\)  $\quad:\quad$\Frob {R}

$\qquad$Frobenius Endomorphism  
\(\Gal {S}\)  $\quad:\quad$\Gal {S}

$\qquad$Galois Group  
\(\Gaussian {\mu} {\sigma^2}\)  $\quad:\quad$\Gaussian {\mu} {\sigma^2}

$\qquad$Gaussian Distribution  
\(\gen {S}\)  $\quad:\quad$\gen {S}

$\qquad$Generator  
\(\Geometric {p}\)  $\quad:\quad$\Geometric {p}

$\qquad$Geometric Distribution  
\(\GF\)  $\quad:\quad$\GF

$\qquad$Galois Field  
\(\GG\)  $\quad:\quad$\GG

$\qquad$that is: \mathcal G


\(\GL {n, \R}\)  $\quad:\quad$\GL {n, \R}

$\qquad$General Linear Group  
\(\grad {p}\)  $\quad:\quad$\grad {p}

$\qquad$Gradient  
\(\hav \theta\)  $\quad:\quad$\hav \theta

$\qquad$Haversine  
\(\hcf\)  $\quad:\quad$\hcf

$\qquad$Highest Common Factor  
\(\H\)  $\quad:\quad$\H

$\qquad$Set of Quaternions  
\(\HH\)  $\quad:\quad$\HH

$\qquad$Hilbert Space  
\(\hointl {a} {b}\)  $\quad:\quad$\hointl {a} {b}

$\qquad$Left HalfOpen Interval  
\(\hointr {a} {b}\)  $\quad:\quad$\hointr {a} {b}

$\qquad$Right HalfOpen Interval  
\(\ideal {a}\)  $\quad:\quad$\ideal {a}

$\qquad$Ideal of Ring  
\(\II\)  $\quad:\quad$\II

$\qquad$that is: \mathcal I


\(\map \Im z\)  $\quad:\quad$\map \Im z

$\qquad$Imaginary Part  
\(\Img {f}\)  $\quad:\quad$\Img {f}

$\qquad$Image of Mapping  
\(\index {G} {H}\)  $\quad:\quad$\index {G} {H}

$\qquad$Index of Subgroup  
\(\inj\)  $\quad:\quad$\inj

$\qquad$Canonical Injection  
\(\Inn {S}\)  $\quad:\quad$\Inn {S}

$\qquad$Group of Inner Automorphisms  
\(\innerprod {x} {y}\)  $\quad:\quad$\innerprod {x} {y}

$\qquad$Inner Product  
\(\Int {\gamma}\)  $\quad:\quad$\Int {\gamma}

$\qquad$Interior  
\(\intlimits {\dfrac {\map f s} s} {s \mathop = 1} {s \mathop = a}\)  $\quad:\quad$\intlimits {\dfrac {\map f s} s} {s \mathop = 1} {s \mathop = a}

$\qquad$Limits of Integration  
\(\invlaptrans {F}\)  $\quad:\quad$\invlaptrans {F}

$\qquad$Inverse Laplace Transform  
\(\JJ\)  $\quad:\quad$\JJ

$\qquad$that is: \mathcal J


\(\KK\)  $\quad:\quad$\KK

$\qquad$that is: \mathcal K


\(\laptrans {f}\)  $\quad:\quad$\laptrans {f}

$\qquad$Laplace Transform  
\(\lcm \set {x, y, z}\)  $\quad:\quad$\lcm \set {x, y, z}

$\qquad$Lowest Common Multiple  
\(\leadstoandfrom\)  $\quad:\quad$\leadstoandfrom


\(\leftset {a, b, c}\)  $\quad:\quad$\leftset {a, b, c}

$\qquad$Conventional set notation (left only)  
\(\leftparen {a + b + c}\)  $\quad:\quad$\leftparen {a + b + c}

$\qquad$Parenthesis (left only)  
\(\len {AB}\)  $\quad:\quad$\len {AB}

$\qquad$Length Function: various  
\(\LL\)  $\quad:\quad$\LL

$\qquad$that is: \mathcal L


\(\Ln\)  $\quad:\quad$\Ln

$\qquad$Principal Branch of Complex Natural Logarithm  
\(\Log\)  $\quad:\quad$\Log

$\qquad$Principal Branch of Complex Natural Logarithm  
\(\map {f} {x}\)  $\quad:\quad$\map {f} {x}

$\qquad$Mapping or Function  
\(\MM\)  $\quad:\quad$\MM

$\qquad$that is: \mathcal M


\(\Mult\)  $\quad:\quad$\Mult

$\qquad$Multiplication as a Primitive Recursive Function  
\(\NegativeBinomial {n} {p}\)  $\quad:\quad$\NegativeBinomial {n} {p}

$\qquad$Negative Binomial Distribution  
\(\Nil {R}\)  $\quad:\quad$\Nil {R}

$\qquad$Nilradical of Ring  
\(\nint {11.98}\)  $\quad:\quad$\nint {11.98}

$\qquad$Nearest Integer Function  
\(\NN\)  $\quad:\quad$\NN

$\qquad$that is: \mathcal N


\(\norm {z^2}\)  $\quad:\quad$\norm {z^2}

$\qquad$Norm  
\(\O\)  $\quad:\quad$\O

$\qquad$Empty Set  
\(\OO\)  $\quad:\quad$\OO

$\qquad$that is: \mathcal O


\(\On\)  $\quad:\quad$\On

$\qquad$Ordinal Class  
\(\openint {a} {b}\)  $\quad:\quad$\openint {a} {b}

$\qquad$Open Interval  
\(\Orb S\)  $\quad:\quad$\Orb S

$\qquad$Orbit  
\(\Ord {S}\)  $\quad:\quad$\Ord {S}

$\qquad$$S$ is an Ordinal  
\(\order {G}\)  $\quad:\quad$\order {G}

$\qquad$Order of Structure, and so on  
\(\Out {G}\)  $\quad:\quad$\Out {G}

$\qquad$Group of Outer Automorphisms  
\(\paren {a + b + c}\)  $\quad:\quad$\paren {a + b + c}

$\qquad$Parenthesis  
\(\Poisson {\lambda}\)  $\quad:\quad$\Poisson {\lambda}

$\qquad$Poisson Distribution  
\(\polar {r, \theta}\)  $\quad:\quad$\polar {r, \theta}

$\qquad$Polar Form of Complex Number  
\(\pounds\)  $\quad:\quad$\pounds

$\qquad$Pound Sterling  
\(\powerset {S}\)  $\quad:\quad$\powerset {S}

$\qquad$Power Set  
\(\PP\)  $\quad:\quad$\PP

$\qquad$that is: \mathcal P


\(\Preimg {f}\)  $\quad:\quad$\Preimg {f}

$\qquad$Preimage of Mapping  
\(\map {\pr_j} {F}\)  $\quad:\quad$\map {\pr_j} {F}

$\qquad$Projection  
\(\PV\)  $\quad:\quad$\PV

$\qquad$Cauchy Principal Value  
\(\QQ\)  $\quad:\quad$\QQ

$\qquad$that is: \mathcal Q


\(\radians\)  $\quad:\quad$\radians

$\qquad$Radian  
\(\displaystyle \int \map f x \rd x\)  $\quad:\quad$\displaystyle \int \map f x \rd x

$\qquad$Roman $\d$ for use in Integrals  
\(\rD\)  $\quad:\quad$\rD

$\qquad$Differential Operator  
\(y \rdelta x\)  $\quad:\quad$y \rdelta x

$\qquad$$\delta$ operator for use in sums  
\(\map \Re z\)  $\quad:\quad$\map \Re z

$\qquad$Real Part  
\(\relcomp {S} {A}\)  $\quad:\quad$\relcomp {S} {A}

$\qquad$Relative Complement  
\(\rem\)  $\quad:\quad$\rem

$\qquad$Remainder  
\(\Res {f} {z_0}\)  $\quad:\quad$\Res {f} {z_0}

$\qquad$Residue  
\(\rightparen {a + b + c}\)  $\quad:\quad$\rightparen {a + b + c}

$\qquad$Parenthesis (right only)  
\(\rightset {a, b, c}\)  $\quad:\quad$\rightset {a, b, c}

$\qquad$Conventional set notation (right only)  
\(\Rng {f}\)  $\quad:\quad$\Rng {f}

$\qquad$Range of Mapping  
\(\RR\)  $\quad:\quad$\RR

$\qquad$that is: \mathcal R


\(\sech\)  $\quad:\quad$\sech

$\qquad$Hyperbolic Secant  
\(\Sech\)  $\quad:\quad$\Sech

$\qquad$Hyperbolic Secant  
\(\sequence {a_n}\)  $\quad:\quad$\sequence {a_n}

$\qquad$Sequence  
\(\set {a, b, c}\)  $\quad:\quad$\set {a, b, c}

$\qquad$Conventional set notation  
\(\ShiftedGeometric {p}\)  $\quad:\quad$\ShiftedGeometric {p}

$\qquad$Shifted Geometric Distribution  
\(\Si\)  $\quad:\quad$\Si

$\qquad$Sine Integral Function  
\(\Sinh\)  $\quad:\quad$\Sinh

$\qquad$Hyperbolic Sine  
\(\size {x}\)  $\quad:\quad$\size {x}

$\qquad$Absolute Value, and so on  
\(\SL {n, \R}\)  $\quad:\quad$\SL {n, \R}

$\qquad$Special Linear Group  
\(\Spec {R}\)  $\quad:\quad$\Spec {R}

$\qquad$Spectrum of Ring  
\(\sqbrk {a} \)  $\quad:\quad$\sqbrk {a}


\(\SS\)  $\quad:\quad$\SS

$\qquad$that is: \mathcal S


\(\Stab x\)  $\quad:\quad$\Stab x

$\qquad$Stabilizer  
\(\stratgame {N} {A_i} {\succsim_i}\)  $\quad:\quad$\stratgame {N} {A_i} {\succsim_i}

$\qquad$Strategic Game  
\(\struct {G, \circ}\)  $\quad:\quad$\struct {G, \circ}

$\qquad$Algebraic Structure  
\(\StudentT {k}\)  $\quad:\quad$\StudentT {k}

$\qquad$Student's tDistribution  
\(\SU {n}\)  $\quad:\quad$\SU {n}

$\qquad$Unimodular Unitary Group  
\(\Succ\)  $\quad:\quad$\Succ

$\qquad$Successor Function  
\(\Syl {p} {N}\)  $\quad:\quad$\Syl {p} {N}

$\qquad$Sylow $p$Subgroup  
\(\T\)  $\quad:\quad$\T

$\qquad$True  
\(\Tanh\)  $\quad:\quad$\Tanh

$\qquad$Hyperbolic Tangent  
\(\tr\)  $\quad:\quad$\tr

$\qquad$Trace  
\(\TT\)  $\quad:\quad$\TT

$\qquad$that is: \mathcal T


\(\tuple {a, b, c}\)  $\quad:\quad$\tuple {a, b, c}

$\qquad$Ordered Tuple  
\(\UU\)  $\quad:\quad$\UU

$\qquad$that is: \mathcal U


\(\valueat {\dfrac {\delta y} {\delta x} } {x \mathop = \xi} \)  $\quad:\quad$\valueat {\dfrac {\delta y} {\delta x} } {x \mathop = \xi}


\(\var {X}\)  $\quad:\quad$\var {X}

$\qquad$Variance  
\(\vers \theta\)  $\quad:\quad$\vers \theta

$\qquad$Versed Sine  
\(\VV\)  $\quad:\quad$\VV

$\qquad$that is: \mathcal V


\(\WW\)  $\quad:\quad$\WW

$\qquad$that is: \mathcal W


\(\XX\)  $\quad:\quad$\XX

$\qquad$that is: \mathcal X


\(\YY\)  $\quad:\quad$\YY

$\qquad$that is: \mathcal Y


\(\ZZ\)  $\quad:\quad$\ZZ

$\qquad$that is: \mathcal Z

Aligned Equations
To include aligned equations, a set of templates has been written: begineqn, eqn and endeqn.
For more explanation, see Template:eqn.
Known issues
See Problem with Eqn template.
Specific Topics
Commutative diagrams
External references and manuals
It may not be exactly the same version of $\LaTeX$, but I always find this page helpful as a first, quick overview:
This is also a good reference page, pertaining to MediaWiki $\LaTeX$:
but be aware that not all commands are supported.
This is a link of all the currently supported commands available: