Most of the answer was extracted from the Introduction sections of the documentation of
amsmath provides miscellaneous enhancements for improving the information structure and printed output of documents containing mathematical formulas. Some of the features provided by this package are:
\DeclareMathOperator command (through the auxiliary package
amsopn) to define new "operator name" commands analogous to
\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
- Spacing around equals signs matches the normal spacing in the
- A way to produce multiline subscripts as are often used with summation
or product symbols.
tag command, 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.
\text command (through the auxiliary package
amstext) for typesetting a fragment of text inside a display.
eqref command, which provides formatting for equation references
amsthm helps to define theorem-like structures; the introduction to the documentation gives a nice concise description of the package:
amsthm package provides an enhanced version of LaTeX's
\newtheorem command for defining theorem-like environments. The
\newtheorem recognizes a
\theoremstyle specification (as
theorem package) and has a
* form for defining
unnumbered environments. The
amsthm package also defines a
environment that automatically adds a QED symbol at the end. AMS
document classes incorporate the
amsthm package, so everything
described here applies to them as well.
amsthm package is used with a non-AMS document class and with
amsthm must be loaded after
amssymb provides an extended symbol collection. For example, after loading
amssymb you have the following additional binary relation symbols:
\Cup (and many more), the arrow
\leadsto, and some other symbols such as
\Diamond. Another useful feature is the
\mathbb command to produce blackboard bold characters
amssymb internally loads
amsfonts, it's enough to load the former.
As far as I know, there's not a single package loading
amssymb so all three of them will have to be loaded when using the standard classes (
If one of the document classes of the AMS-collection (
amsart) is being used, there's no need to load
amssymb will have to be explicitly loaded.