This is a list of common TeX/LaTeX errors that I see when reviewing manuscripts. Also some shortcuts are given to make math equations more readable (and easier to edit).
Note the \def (or \newcommand) should appear at the beginning of your tex file (before \begin{document} in LaTeX).
If you look carefully at math writing, variables are printed in the italics or slanted font. However something like the exp or log function is not a variable, so it is in standard font, even within math mode. That is, \exp, \log, \sin etc are used for math and trigonometric functions. For statistics, \Pr is a definition for probability of an event, but \E for expectation and \Var for variance, etc, are not defined.
However, you can define these yourself with something like
\def\Var{\mathop{\rm Var}}
or
\def\Var{{\rm Var}\,}
\def\E{{\rm E}\,}
The first version does not work well for E.
- Math expressions with subscripts and superscripts should also be put in math mode, e.g., $a$, $x=1$, $-1$. In non-math mode, - is a hyphen (shorter than minus sign, -- is an en dash (e.g. for pp. 34--43), and --- is an em dash — for use in a middle of a sentence.
- Unless you are in displayed math mode, fractions should usually be expressed with a solidus, for example $x_i/n$ and not $\frac{x_i}{n}$ or ${x_i\over n}$.
Use a definition for any math symbol with a 'hat', 'bar', 'tilde' etc. This will make equations easier to read in TeX. Same thing for symbols for equal in distribution, convergence in probability, etc. Examples are:
\def\phat{{\hat p}}
\def\Fbar{{\overline F}}
\def\atil{{\tildealpha}}
\def\inprob{\rightarrow_p}
\def\eqd{\,{\buildrel d \over =}\,}
\def\law{\rightarrow_d}
boldface Greek in scriptsize: LaTeX may not automatically resize a symbol when it is a subscript of superscript. Hence def are needed for scriptsize characters, e.g.
\def\thbf{\mbox{\boldmath $\theta$}
\def\thbfs{\mbox{\scriptsize \boldmath $\theta$}}
$$f(\thbf) =2^{\thbfs}$$
Alternatively, use the ams packages amsmath and amssymb
\def\dbfams{\boldsymbol{\delta}}
\def\mubfams{\boldsymbol{\mu}}
labelling of equations, and theorems, lemmas, corollary:
To get the section number to appear in an equation, add (to the beginning):
\renewcommand{\theequation}{\thesection\.\arabic{\equation}}
and add
\setcounter{\equation}{0}
at the beginning of each section.
To get Theorems, Lemmas, Corollaries to be on the same numbering scheme, by section, add:
\newtheorem{\theorem}{Theorem}[section]
\newtheorem{\lemma}[theorem]{Lemma}
\newtheorem{\corollary}[theorem]{Corollary}
larger brackets[], braces{}, parentheses(): these should be used around summations, fractions etc. It is simplest to use \left[, \right] etc, but left and right only work if your equation is not split into more than one line. In the latter case, use one of \bigl, \Bigl, \bbigl, \Biggl (and corresponding \bigr on the right).
Sometimes one needs a larger '/' or '|'. For '/', use \bigm, \Bigm etc. For '|', use \bigl, \bigm, \bigr etc depending on whether it is left, middle or right.