Latex Tricks

Theorems and Proofs

The idea is defining a theorem or other mathematical environment using \newtheorem command, then use the environment later.

% Create a new environment named theorem, which would appear in the PDF as Theorem. The counter of this theorem would be recounted every section
\newtheorem{theorem}{Theorem}[section]
% This corollary environment is recounted after every theorem
\newtheorem{corollary}{Corollary}[theorem]
% This lemma environment uses the same counter as the theorem environment
\newtheorem{lemma}[theorem]{Lemma}

Proof is provided by the amsthm package.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{amsthm}
\begin{document}
\begin{lemma}
Given two line segments whose lengths are $a$ and $b$ respectively there 
is a real number $r$ such that $b=ra$.
\end{lemma}
\begin{proof}
To prove it by contradiction try and assume that the statement is false,
proceed from there and at some point you will arrive to a contradiction.
\end{proof}
\end{document}

Special Characters

When writing mathematical expressions, sometimes, one needs to use special looking alphabets, but not Greek alphabets. Latex supports this with the following fonts:

% All of these must be placed within $$ or equation environment
\mathcal{A}
\mathfrank{A}
\mathrm{A}