# How to improve the visual appearance of my document? [closed]

## Introduction

I typed out some definitions from our theoretical computer science lecture for the fun of it. Unfortunately I noticed, that it didn't look very professional and clean . The reason for that should be wrong alignments etc., but I can't really improve it, even though I tried to define theorem/definition-environments and similar stuff. Unfortunately, my definitions still look bad.

## Question

How to improve the visual appearance of my document?

I would like to get suggestions (for packages, environments, spacing, sectioning etc.), which will help me to improve my document.
EDIT: I would like to have real definition environments for every defintion I made in order to label it. Furthermore, some equations are bad aligned (for example the last equations of "formal languages"). Furthermore I would like to get suggestions on how to make the document look more modern (for example by adding colors and changing fonts)

## Code

Note: The file is translated poorly, because English is not my native language. I only translated the document (from german to english), in order that you understand the content and can help with formatting based on it. The file is basically a small list of definitions from the TCS lecture.

Here is my code:

\documentclass{memoir}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}

\title{Computer-Science (Poor translation)}
\date{November 2018}

\begin{document}

\maketitle

\begin{abstract}
Note: The file is translated poorly, because English is not my native language. I only translated the document (from german to english), in order that you understand the content and can help with formatting based on it. The file is basically a small list of definitions from the TCS lecture.
\end{abstract}

\section{Fundamentals}
Definition:
\begin{enumerate}
\item {\em Finite Alphabet:} Finite set $\Sigma := \{a_1,\dots , a_\Delta\}$ with various objects\\ $a_1, \dots , a_\Delta$
\item A {\em word/string} $w=(w_1,\dots , w_n)$ with $w_i\in \Sigma$ for $1\leq i \leq n$ is called a concatenation of letters in $\Sigma$.\\
\emph{The length of} $w$ \emph{is} ${\mid w \mid} := n$\\
Strings with the length of $n$: $\Sigma^n = \underbrace{\Sigma \times \Sigma \dots \times \Sigma}_{n}$\\
The empty string is $\lambda$: ${\mid \lambda \mid} := 0$\\
$\Sigma^* := \bigcup^{\infty}_{n=0} \Sigma^n \text{ is the set of all strings with finite length on } \Sigma.$\\
$\Sigma^* := \{\lambda\}\text{ is not the empty set, because }\lambda\in\Sigma^*$\\
$\Sigma^+ := \Sigma^*\backslash \{\lambda\}$
\item Let $X=(x_1,\dots ,x_n)$, $Y=(y_1,\dots ,y_n)$ then
$X.Y:=(x_1,\dots ,x_n,y_1,\dots ,y_m)$ is called the concatenation of $x$ and $y$. $X$ is called the prefix of $XY$; $Y$ is called the Suffix.\\
Obvious:
\begin{align*}
\mid x.y\mid        &= \mid x\mid +\mid y\mid\\
\mid x.\lambda \mid &= \mid \lambda .x\mid = \mid x\mid
\end{align*}
Notation: $x.y = xy = x_1x_2\dots x_ny_1y_2\dots y_n$
\item Any $L\subseteq \Sigma^*$ is called a "formal language" on $\Sigma$.
\end{enumerate}
Definition: Let $\Sigma$ be a finite alphabet, $L_0,L_1,L_2 \subseteq \Sigma^*$ (free formal languages in the finite alphabet.)
\begin{enumerate}
\item $\overline{L} := \Sigma^*\backslash L \text{ compliment of } L$
\item   $L_1 \cap L_2 := \{ x \in \Sigma^* \mid x \in L_1 \land x \in L_2 \} \text{ Intersection}$\\
$L_1 \cup L_2 := \{ x \in \Sigma^* \mid x \in L_1 \lor x \in L_2 \} \text{ Union}$
\item   $L_1.L_2 := \{ xy \mid x \in L_1 \land y \in L_2 \} \text{ Concatenation of two languages}$
\item   $L^* := \{ w_1 w_2 \dots w_t \mid w_i \in L \lor w_i = \lambda \land t \in N \} \} \text{ Kleene-Star of }L$\\
\emph{Please note:} $\lambda \in L^*$ with $t = 1$, $w_1 = \lambda$\\
$L^+ = L.L^*$\\
$\lambda \in L^+ \Longleftrightarrow \lambda \in L$
\end{enumerate}

\section{Regular Expressions}
Idea: Recursive construction of expressions, which represent the languages.

Definition: Let $\Sigma$ be a finite alphabet. The set of regular expressions on $\Sigma$ and their represented languages are defined in the following way:
\begin{enumerate}
\item $\emptyset$,$\lambda$ and any $a \in \Sigma$ are regular expressions\\

The related languages are:
\begin{align*}
\mathcal{L}(\emptyset)  &:= \emptyset\\
\mathcal{L}(\lambda)    &:= \lambda\\
\mathcal{L}(a)          &:=\{a\} \qquad \forall a \in \Sigma
\end{align*}
\item Let $x,y$ be regular expressions with related languages $\mathcal{L}(x)$, $\mathcal{L}(y)$.
Hence, the following expressions are regular too:
\begin{align*}
& x.y \text{ and } \mathcal{L}(x.y):= \mathcal{L}(x).\mathcal{L}(y)\\
& x\cup y \text{ and } \mathcal{L}(x\cup y):= \mathcal{L}(x)\cup \mathcal{L}(y)\\
& x^* \text{ and } \mathcal{L}(x^*):= \mathcal({L}(x))^*
\end{align*}
\item Everything that can be produced with \em{1.} and \em{2} in finite steps is regular.
\end{enumerate}
The related languages are called regular languages.

\section{Automata}
Definition: The deterministic, finite automaton \emph{(DFA)} $M$ is defined as $M=(K,\Sigma,s,\delta ,F)$ with:
\begin{itemize}
\item $K = K \times \Sigma$ finite set of states
\item $\Sigma$ finite alphabet
\item $s$ initial state
\item $\delta$ transition function
\item $F$ finite set of final states
\end{itemize}
\end{document}


Regards,

• For your first question, please try looking at this resource. As for the equation alignment, please try using \begin{gathered} and \end{gathered} instead. As for making the document more modern, that is a broad question and you may want to do the research with your curiosity. – zyy Nov 8 at 20:36
• You could try gathered to see if you would like it, since you did not give specific requests, what I could say is just try. – zyy Nov 9 at 1:04