Page Elements¶

LaTeX supports standard page elements such as lists, images, and tables. The settings for each of these (for example, the amount of space between items in a bulleted list) can be configured, but here we cover just the basics.

Lists¶

The itemize environment creates a bulleted list, while enumerate creates a numbered list.

Use itemize for a list where the ordering is not very important.
\begin{itemize}
    \item An unordered (bulleted) item.
    \item Another bullet.
\end{itemize}
Use enumerate for a list where the ordering matters or suggests some kind of progression.
\begin{enumerate}
    \item A numbered item.
    \item The next number is automatic.
\end{enumerate}

Problem 8

Under Subsection 2.1 (Lists), make a list of your five favorite foods. If you have a strong ordering of preferences, use numbers; if you only have an unordered “top five,” use bullets.

Images¶

The graphicx package provides tools for inserting an image file into a LaTeX document. On Overleaf, image files are uploaded by opening the file panel in the upper left corner and clicking the upload icon , or with File > New file > Upload.

After uploading an image, insert it into the document by adding \usepackage{graphicx} to the preamble and using \includegraphics{name-of-the-file} in the body. This is enough to include the image, but it is often better to wrap the image in a figure environment, which provides a caption and creates an internal reference so the figure can be referred to later with \ref{}.

\begin{figure}[h]
    \centering
    \includegraphics[width=0.85\textwidth]{cosmo.png}
    \caption{Cosmo the Cougar, the mascot of BYU.}
    \label{fig:cosmo}
\end{figure}

As shown in Figure~\ref{fig:cosmo}, Cosmo is hard to miss.
Note how the width of the figure extends to cover $85\%$
of the horizontal space allotted for text.

The [h] option requests that the figure be placed “here”, the place that the figure environment appears in the source code. A figure is a float, meaning LaTeX may shift its position to avoid awkward gaps. Alternatively, [t] requests placement at the top of a page.
\centering centers the image horizontally.
\includegraphics[width=...]{cosmo.png} inserts the image. The width may be absolute, such as width=5cm, or relative to the text width, such as width=0.5\textwidth for half the text width.
\caption{} prints a numbered caption beneath the image.
\label{fig:cosmo} names the figure so that \ref{fig:cosmo} can print its number in the text. Always place \label after \caption.

Problem 9

Find a publicly available image of something from your hometown, download it to your computer, then upload it to your Overleaf project. Under Subsection 2.2 (Figures), insert a figure with the image. Set the image size to occupy 65% of the text width and add a brief descriptive caption.

Tables¶

Tables in LaTeX are built with the tabular environment, which works like the array environment but outside math mode. Wrap a tabular in a table environment to add a caption and label.

\begin{table}[h]
    \centering
    \begin{tabular}{cl}
        \hline
        Function & Domain \\
        \hline
        $\sin(x)$ & all real numbers \\
        $\ln(x)$  & $x > 0$ \\
        \hline
    \end{tabular}
    \caption{Two common functions and their domains.}
    \label{tab:functions}
\end{table}

Similar to figures, tables have captions and labels that can be referenced.
For example, this is a reference to Table~\ref{tab:functions}.

Problem 10

Recreate the following table under Subsection 2.3 (Tables).

Hint: Use \\[.5em] or \\[.75em], etc., to specify the exact vertical spacing between rows (an em is a unit of measure related to the font size).

Definitions and Theorems¶

The amsthm package provides numbered environments for mathematical writing. Theorem-like environments are declared in the preamble with \newtheorem{}{}.

\usepackage{amsthm}

\theoremstyle{plain}                % \newtheorem{} sets bold headings and italic body text.
\newtheorem{theorem}{Theorem}       % define a "theorem" environment with "Theorem" as the title.

\theoremstyle{definition}           % \newtheorem{} sets bold headings and upright body text.
\newtheorem{definition}{Definition} % define a "definition" environment entitled "Definition".

The theorem and definition environments can then be used in the body of the document.

\begin{definition}
    A number $n \in \mathbb{N}$ is called \emph{even}
    if there exists $j \in \mathbb{N}$ such that $n = 2j$.
\end{definition}

\begin{theorem}
    Every even number greater than $2$ is not prime.
\end{theorem}

\begin{proof}
    Let $n \in \mathbb{N}$ be an even number such that $n > 2$.
    Then there exists $j \in \mathbb{N}$ with $n = 2j$.
    Since $n > 2$, $j \neq 1$, so $n = 2j$ is a factorization of $n$
    and hence $n$ is not prime.
\end{proof}

Theorem-like environments each maintain their own counter by default (Definition 1, Theorem 1, Definition 2, …). To share a counter (Definition 1, Theorem 2, Definition 3, …), use \newtheorem{theorem}{Theorem} as before, but define the next environment with \newtheorem{definition}[theorem]{Definition}.