\documentclass[12pt]{article} %document type
\usepackage{amssymb,amsmath,amsthm,xfrac, mathtools} % for math
\usepackage[margin=1in]{geometry} % margins
\usepackage{tikz}       % for graphics
\usepackage{lastpage}   % for page numbers
\usepackage{lipsum} %dummy text
\usetikzlibrary{shapes.geometric, arrows}

\usepackage{lscape} %for landscape


\usepackage[labelfont=bf]{caption}

%%%%%%%%%%%%%%%%%%%%%%%

\begin{document}


\textbf{Bold Text} \\ %newline character
\textit{Italic Text} \\[0.5cm] %optional height
\textsc{Small Caps Text}

\lipsum[1]

\begin{figure}[h]
\centering
\begin{tikzpicture}
    \draw [->] [ultra thick] [black] (0,0) node[anchor=east, color=black]{$0$} -- (4,0) node[anchor=west, color=black] {$x$};
    \draw [->][ultra thick] [black] (0,0) -- (0,4) node[anchor=south, color=black] {$y$};

    \draw [->, ultra thick, red, domain=0:4] plot (\x, {0.25*\x^2)});
    \draw (2.45,1.35) node[anchor=west, red] {$\frac{x^2}{4}$};
    \draw [help lines] (0,0) grid (4,4);
\end{tikzpicture}
\caption{Plot of $x^2/4$}
\end{figure}

\lipsum[2]












\newpage

\tikzstyle{style1} = [ellipse, minimum width=1cm, minimum height=1cm, text centered, draw=black]
\tikzstyle{empty} = [draw=none]
\tikzstyle{arrow} = [thick, ->, >=stealth]

\begin{tikzpicture}[node distance=2.3cm]

    \node (1) [style1] {$R_H$};
    \node (e1) [empty, left of=1] {$\mu_H$};
    \draw [arrow] (1) -- (e1);
    \node (2) [style1, above of=1] {$I_H$};
    \node (e2) [empty, left of=2] {$\mu_H$};
    \draw [arrow] (2) -- (e2);
    \draw [arrow] (2) -- node[anchor=west]{$\beta_H$} (1);
    \node (3) [style1, above of=2] {$E_H$};
    \node (e3) [empty, left of=3] {$\mu_H$};
    \draw [arrow] (3) -- (e3);
    \draw [arrow] (3) -- node[anchor=west]{$\theta_H$} (2);

    \node (5) [style1, right of=1, xshift=1cm] {$I_N$};
    \draw [arrow] (3) -- (5);

    \node (4) [style1, above of=3] {$S_H$};
    \draw [arrow] (4) -- (5);

\end{tikzpicture}

\newpage









\begin{landscape}


    $$ \begin{pmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \\ 7 & 8 \\ 9 & 10  \end{pmatrix} $$
\vfill %maximum spacing
% \\[0.5cm] %controlled spacing, top-aligned
    $$ \begin{pmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \\ 7 & 8 \\ 9 & 10  \end{pmatrix} $$

\end{landscape}

\newpage

\begin{figure}[h]
\centering
\begin{tabular}{| r || l | c |}
\multicolumn{2}{r}{you have this long this text} & c \\ %multiple column span. arguments: 2 (number of columns to span) r (alignment, right) text
\hline
a long bit of text & 2 & 3 \\
\hline
3 & 4 \\
\hline
5 & 6 \\
\hline
\hline
\end{tabular}
\caption{Table}
\end{figure}

%http://en.wikibooks.org/wiki/LaTeX/Advanced_Mathematics

\begin{align*}
x &= y \\
2x &= 2y \\
\underbrace{x y^z \dfrac{x}{z^3} \sqrt{2x^4} \frac{4}{x} e^{-2x+4}}_{x} &= 0 \\
\overbrace{x}^{y} &= 0 \\
\intertext{My result is:} %text within an align or align* environment that doesn't interrupt the alignment flow
\Aboxed{E &= mc^2} \\ %across alignment character `&', use \Aboxed{} from the `mathtools` package
\text{or you can have} &= \boxed{x=y} %or, when not across an alignment, just use \boxed{}.
\end{align*}

\end{document}