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Here are some tips on TeX.
Use the commands below if you would like parentheses etc. bigger than $\Biggl(\Biggr)$. An example is $\bigggl(\bigggr)$. I referred to the definitions of \big etc. in the TeXbook.
\makeatletter
\newcommand{\biggg}[1]{{\hbox{$\left#1\vbox to 20.5pt{}\right.\n@space$}}}
\newcommand{\Biggg}[1]{{\hbox{$\left#1\vbox to 23.5pt{}\right.\n@space$}}}
\newcommand{\bigggg}[1]{{\hbox{$\left#1\vbox to 26.5pt{}\right.\n@space$}}}
\newcommand{\Bigggg}[1]{{\hbox{$\left#1\vbox to 29.5pt{}\right.\n@space$}}}
\newcommand{\biggggg}[1]{{\hbox{$\left#1\vbox to 32.5pt{}\right.\n@space$}}}
\newcommand{\Biggggg}[1]{{\hbox{$\left#1\vbox to 35.5pt{}\right.\n@space$}}}
\newcommand{\bigggggg}[1]{{\hbox{$\left#1\vbox to 38.5pt{}\right.\n@space$}}}
\newcommand{\Bigggggg}[1]{{\hbox{$\left#1\vbox to 41.5pt{}\right.\n@space$}}}
\makeatother
\newcommand{\bigggl}{\mathopen\biggg}
\newcommand{\bigggm}{\mathrel\biggg}
\newcommand{\bigggr}{\mathclose\biggg}
\newcommand{\Bigggl}{\mathopen\Biggg}
\newcommand{\Bigggm}{\mathrel\Biggg}
\newcommand{\Bigggr}{\mathclose\Biggg}
\newcommand{\biggggl}{\mathopen\bigggg}
\newcommand{\biggggm}{\mathrel\bigggg}
\newcommand{\biggggr}{\mathclose\bigggg}
\newcommand{\Biggggl}{\mathopen\Bigggg}
\newcommand{\Biggggm}{\mathrel\Bigggg}
\newcommand{\Biggggr}{\mathclose\Bigggg}
\newcommand{\bigggggl}{\mathopen\biggggg}
\newcommand{\bigggggm}{\mathrel\biggggg}
\newcommand{\bigggggr}{\mathclose\biggggg}
\newcommand{\Bigggggl}{\mathopen\Biggggg}
\newcommand{\Bigggggm}{\mathrel\Biggggg}
\newcommand{\Bigggggr}{\mathclose\Biggggg}
\newcommand{\biggggggl}{\mathopen\bigggggg}
\newcommand{\biggggggm}{\mathrel\bigggggg}
\newcommand{\biggggggr}{\mathclose\bigggggg}
\newcommand{\Biggggggl}{\mathopen\Bigggggg}
\newcommand{\Biggggggm}{\mathrel\Bigggggg}
\newcommand{\Biggggggr}{\mathclose\Bigggggg}
Use \arc if you would like to put a symbol similar to \frown over something in order to indicate that it is an arc. An example is $\arc{AB}$. It poses no problems to use a long argument such as ABCDEF.
\usepackage{amsmath}
\usepackage{graphicx}
\newcommand{\arc}[1]{%
\settowidth{\dimen0}{\ensuremath{#1}}%
\divide\dimen0 by 2%
\overset{\rotatebox{-90}{\ensuremath{\left(\rule{0pt}{\dimen0}\right.}}}{#1}%
}
Use \hooklongrightarrow and \twoheadlongrightarrow if you would like \hookrightarrow and \twoheadrightarrow as long as \longrightarrow and \longmapsto. An example is $f\colon X\hooklongrightarrow Y$. I referred to the definition of \longmapsto in the TeXbook.
\newcommand{\hooklongrightarrow}{\lhook\joinrel\longrightarrow}
\newcommand{\twoheadlongrightarrow}{\relbar\joinrel\twoheadrightarrow}
Mathematicians use italics in the statement of a theorem by convention, but in my opinion italic punctuation marks are not very beautiful. Use cmtiup package if you would like upright punctuation marks in the statement of a theorem. You can find this package at /fonts/cm/cmtiup/ in CTAN.
I prefer slanted fonts to italic fonts in theorems because I think using slanted fonts makes it easier to distinguish, for example, an indefinite article `a' and a variable $a$. For those who prefer slanted fonts use cmslup package, which can be found at /fonts/cm/cmslup/ in CTAN.
If you are unsatisfied with the position of a QED symbol when your proof ends with a displayed formula, I ams sure that ntheorem.sty is the best solution.
If you use dviout, you can let dviout know the size of the paper by writing, for example,
\AtBeginDvi{\special{papersize=a4}}
right after \begin{document}.
Starting dviout with the command
dviout -Set=!m
maximises dviout.