The value of a counter can be changed with a command of the type
\setcounter{equation}{0}
One can achive the reseting of the equation counter at the beginning of
each section and the inclusion of the section number in the equation
numbering with the command
\numberwithin{equation}{section}
To add a label to any of the items which received a number, use
\label{label-name}
One can refer anywhere else in the text to it with one of the following:
\ref{label-name}
\eqref{label-name}
\pageref{label-name}
The meaning is the following:
\ref
gives the "number" to which the
label refers,
\eqref
includes the "number" in
parantheses,
\pageref
gives the page where the reference was
created.
One can adjust the way items are numbered by re-defining some of the
commands (the first example is essentially equivalent to
\numberwithin{equation}{section}
):
\renewcommand{\theequation}{\thesection.\arabic{equation}}
\renewcommand{\thesection}{\arabic{section}}
\renewcommand{\thesubsection}{(\alph{subsection})}
The \newtheorem
command defines a new "theorem-like"
environment. Its syntax is described below. Two arguments are required (as
in the first form), the others are optional.
\newtheorem{env-name}{label-text}
\newtheorem{env-name}[other_env]{label-text}
\newtheorem{env-name}[other_env]{label-text}[within]
where:
env-name
is the name of the new environment
label-text
is the label printed (usually in bold) at the
beginning (e.g., Theorem, Lemma, etc.)
other_env
is the environment whose numbering should be
used by the env-name
(e.g., you might want theorems and lemmas
to be numbered in the same sequence)
within
is a counter (e.g., section
); it
indicates that the numbering should include this counter (and start from 1
each time this counter changes)
\newtheorem{thm}{Theorem}[section]
\newtheorem{lemma}[thm]{Lemma}
\newtheorem{prop}[thm]{Proposition}
\newtheorem{cor}[thm]{Corollary}
\newtheorem{defn}[thm]{Definition}
\newtheorem{examp}[thm]{Example}
\newtheorem{conj}[thm]{Conjecture}
\newtheorem{rmk}[thm]{Remark}}
For more on variations of the fonts used, see this part in the Fancy Stuff Section.