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.
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.
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Warning: The first edition is seriously out of date about AMS-LaTeX.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.
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}
\newtheoremstyle{note}% name {3pt}% Space above {3pt}% Space below {}% Body font {}% Indent amount (empty = no indent, \parindent = para indent) {\itshape}% Thm head font {:}% Punctuation after thm head {.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.
\newtheoremstyle{note}% name {\topsep}% Space above {\topsep}% Space belowand leave the rest unchanged, and you've got a theorem environment with the default spacing.
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) {\bfseries}% Thm head font {}% Punctuation after thm head {\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