Formal looking Symbols, Operators and Abbreviations section for thesis?

Question

I have 3 tabular environments for symbols, operators and abbreviations where each tabular environment gets to its own page. Also spacing between each row is too narrow and some mathematical signs actually cross each other such as the brackets below. And long sentences go over the page. I am using a template CLS file of my university that may interfere with something but try to answer as generally as possible.

Fig. 1 Contents of the page which looks too informal, Fig. 2 Example of Problem

How can you make Fig. 2's Math more LaTeX? How can you show Mathematical formulee in the page better in Fig. 1?

MWE demonstrating the 3 sections for symbols, operators and abbreviations

\documentclass[english]{article}
\usepackage{amsmath}

\section{Symbols and abbreviations}
%
\subsection*{Symbols}
%
\begin{tabular}{ll}
$\triangle$             &   triangle graph  oeuaua euaeouaoeuaoe uaoeu aoeu aou aoeu aoeu aoeu aou aou aoeu ae u        \\
$\triangle$             &   simplicial complex  aoeuauaou au au eaeu aoeu aoeu aoeu aoeu aoue auoe oeua au au           \\
$K[x_1,\ldots,x_n]$     &   polynomial ring                                         \\
$K[x_1,\ldots,x_n]/I$   &   quotient ring   \\
$\mathbb L^2$           &   lattice                             \\ 
$\mathcal R$            &   quotient ring f                 \\
\end{tabular}
%
\subsection*{Operators}
%
\begin{tabular}{ll}
$P\left[G(n;p)\models H\right]$     &   probability     \\
                            &   random graph                                                        \\
$P\left[\Lambda^s_p\models H\right]$    &   probability     \\
$P\left[G^s_p\models H\right]$      &   probability for the induced     \\
\end{tabular}
%
\subsection*{Abbreviations}
%
\begin{tabular}{ll}
cut                     &   cut-vertex set                                                          \\
DAG                     &   directed acyclic graph                  \\
digraph                 &   directed graph                                                          \\
network                 &   two-terminal graph                                                      \\
sp                      &   series-parallel                                                         \\
\end{tabular}

\end{document}

Answer 1

I would do the tables with the tabularx environment: a first column as p{2.5cm}, and a second X column, the whole table linewidth wide.. Theqe are cells in paragraph mode, hence they can be several line long. For the problem of too tight rows – a well-known problem of the default parameters of LaTeX, you can use the cellspace package, which lets you define a minimal vertical spacing of cells in columns with specifier prefixed with the letter S (or C if you load siunitx):

\documentclass[english]{article}
\usepackage{amsmath, amsfonts}
\usepackage{tabularx, cellspace} %
\setlength\cellspacetoplimit{3pt}
\setlength\cellspacebottomlimit{3pt}

\begin{document}

\section{Symbols and abbreviations}
%
\subsection*{Symbols}
%
\begin{tabularx}{\linewidth}{@{}SlX@{}}
$\triangle$ & triangle graph oeuaua euaeouaoeuaoe uaoeu aoeu aou aoeu aoeu aoeu aou aou aoeu ae u \\
$\triangle$ & simplicial complex aoeuauaou au au eaeu aoeu aoeu aoeu aoeu aoue auoe oeua au au \\
$K[x_1,\ldots,x_n]$ & polynomial ring \\
$K[x_1,\ldots,x_n]/I$ & quotient ring \\
$\mathbb L^2$ & lattice \\
$\mathcal R$ & quotient ring f \end{tabularx}
%
\subsection*{Operators}
%
\begin{tabularx}{\linewidth}{@{}S{p{2.5cm}}X@{}}
$P\left[G(n;p)\models H\right]$ & probability \newline random graph \\
$P\left[\Lambda^s_p\models H\right]$ & probability \\
$P\left[G^s_p\models H\right]$ & probability for the induced \end{tabularx}
%
\subsection*{Abbreviations}
%
\begin{tabularx}{\linewidth}{@{}S{p{2.5cm}}X@{}}
cut & cut-vertex set \\
DAG & directed acyclic graph \\
digraph & directed graph \\
network & two-terminal graph \\
sp & series-parallel \end{tabularx}

\end{document} 

Answer 2

A comment suggested to use the package glossaries -- perhaps it could be used here but for me a bit overkill I think. The glossaries package helps you with something a bit like generating dictionaries. You can get something like this

A|B|C|D|F|G|I|M|O|R|S|C|D|G|M|P
A
A First term 
   Has some long description 7, 9
B
Barely missed first 
   Has some long description 7, 9

as outlined in the instructions and Ctan on glossaries. I feel glossaries is more appropriate for writing books instead of thesis.