# AMS-LaTeX

### What is AMS-LaTeX?

AMS-LaTeX is a set of LaTeX packages for mathematics, which was developed by the American Mathematical Society so that mathematicians could produce beautiful mathematics in LaTeX, mathematics acceptible for publication in the society's journals.

Originally AMS-LaTeX was separate from LaTeX, but in the new version of LaTeX, called LaTeX2e, introduced 10 years ago, all such separate programs became LaTeX packages. So now AMS-LaTeX is just a set of LaTeX packages.

### Why AMS-LaTeX?

If you are using LaTeX for a document that contains math of any complexity, you should be using AMS-LaTeX. Among the wonderful features that all math heads want (quoted from the AMS-LaTeX documentation) are
• A convenient way to define new operator name' commands analogous to \sin and \lim, including proper side spacing and automatic selection of the correct font style and size (even when used in sub- or superscripts).
• Multiple substitutes for the eqnarray environment to make various kinds of equation arrangements easier to write.
• Equation numbers automatically adjust up or down to avoid overprinting on the equation contents (unlike eqnarray).
• Spacing around equals signs matches the normal spacing in the equation environment (unlike eqnarray).
• A way to produce multiline subscripts as are often used with summation or product symbols.
• An easy way to substitute a variant equation number for a given equation instead of the automatically supplied number.
• An easy way to produce subordinate equation numbers of the form (1.3a) (1.3b) (1.3c) for selected groups of equations.
• A \boldsymbol command for printing bold versions of individual symbols, including things like \infty and lowercase Greek letters.
• An amsthm package that provides a useful proof environment and some enhancements to the \newtheorem command: support for multiple theorem styles in a single document and for unnumbered theorem types.

The AMS-LaTeX people are too polite about the defects of the LaTeX eqnarray environment; eqnarray is so brain-damaged that it is impossible to use it to produce non-ugly mathematics. AMS-LaTeX provides six different replacements to do a variety of jobs, all of which must be done and done poorly by eqnarray when you use plain LaTeX. All six of the AMS-LaTeX replacements work beautifully.

They also don't say enough about the amsthm. It also provides a newtheoremstyle environment that allows you to change the style of theorem environments so that they have the look you want. You can also use different theorem styles for different theorem environments, one style for theorem and corollary, another style for remark, and yet another style for example.

### Getting the Documentation.

The documentation can be found on the web at http://www.ams.org/tex/amslatex.html.

The LaTeX Companion, 2nd Edition by Mittelbach, Goossens, Braams, Carlisle, and Rowley is a really cool book, having lots of information about all aspects of LaTeX.

Warning: The first edition is seriously out of date about AMS-LaTeX. Use the second edition only.

### Using AMS-LaTeX.

AMS-LaTeX is now just a set of LaTeX2e packages. So use \documentclass instead of \documentstyle to get LaTeX2e and use any of the following packages
amsmath
Defines extra environments for multiline displayed equations, as well as a number of other enhancements for math (includes the amstext, amsbsy, and amsopn packages).
amstext
Provides a \text command for typesetting a fragment of text inside a display.
amsbsy
Defines \boldsymbol and \pmb poor man's bold' commands.
amsopn
Provides \DeclareMathOperator for defining new operator names' like \sin and \lim.
amsthm
Provides a proof environment and extensions for the \newtheorem command.
amsintx
Provides more descriptive command syntax for integrals and sums.
amscd
Provides a CD environment for simple commutative diagrams (no support for diagonal arrows).
amsxtra
Provides certain odds and ends such as \fracwithdelims and \accentedsymbol.
upref
Makes \ref print cross-reference numbers always in an upright/roman font regardless of context.
amsfonts
Loads extra fonts and symbols, including boldface (\mathbf), blackboard boldface (\mathbb), and fractur (\mathfrac).
amssymb

So the typical AMS-LaTeX document looks something like

   \documentclass{article}
\usepackage{amsmath}
\usepackage{amsfonts}   % if you want the fonts
\usepackage{amssymb}    % if you want extra symbols
\begin{document}

Blah, blah, blah (the document).

\end{document}


### Undocumented stuff about the newtheoremstyle environment.

The newtheoremstyle environment allows you to define new theoremstyles that can be used with a theoremstyle command to change the style for a theorem environment. For example, thmtest.tex defines a note theoremstyle by
   \newtheoremstyle{note}% name
{3pt}%      Space above
{3pt}%      Space below
{}%         Body font
{}%         Indent amount (empty = no indent, \parindent = para indent)
{.5em}%     Space after thm head: " " = normal interword space;
%       \newline = linebreak
{}%         Thm head spec (can be left empty, meaning normal')

then
   \theoremstyle{note}
\newtheorem{note}{Note}

defines a note theorem environment that uses this style.

Great! But your humble author found two questions with answers found only in the source code amsthm.dtx.

• Suppose I don't want to set a specific space above'' and space below'' like in the example. What I want is the same space as the default theorem environments. Answer: \topsep. Make the first three lines in the example
   \newtheoremstyle{note}% name
{\topsep}%      Space above
{\topsep}%      Space below

and leave the rest unchanged, and you've got a theorem environment with the default spacing.

• How do I take apart the bits of the theorem header to make a theorem header in my favorite style? Answer
The [Thm head spec] argument follows a special convention: it is interpreted as the replacement text for an internal three-argument function \thmhead, i.e., as if you were defining
   \renewcommand{\thmhead}[3]{...#1...#2...#3...}

but omitting the initial \renewcommand{\thmhead}[3]. The three arguments that will be supplied to \thmhead are the name, number, and optional note components. Within the replacement text you can (and normally will want to) use other special functions \thmname, \thmnumber, and \thmnote. These will print their argument if and only if the corresponding argument of \thmhead is nonempty. For example
   {\thmname{#1}\thmnumber{ #2}\thmnote{ (#3)}}

This would cause the theorem note #3 to be printed with a preceding space and enclosing parentheses, if it is present, and if it is absent, the space and parentheses will be omitted because they are inside the argument of \thmnote.

Putting both together, here's an example of an example environment I use for lecture notes.

   \newtheoremstyle{example}{\topsep}{\topsep}%
{}%         Body font
{}%         Indent amount (empty = no indent, \parindent = para indent)
{\newline}%     Space after thm head (\newline = linebreak)
{\thmname{#1}\thmnumber{ #2}\thmnote{ #3}}%         Thm head spec

\theoremstyle{example}
\newtheorem{example}{Example}[subsection]

This empty body font argument sets the body in the normal (roman) font. This theorem head spec makes
   \begin{example}[Normal Distributions]

produce
Example 1.1.1 Normal Distributions

Written by Charles Geyer (charlie@stat.umn.edu) Dec 8, 1996. Revised July, 1, 2004.