\documentclass[11pt]{article} % you can replace with 10pt (smaller) or 12pt (larger)
% Packages %
\usepackage{geometry}
%\geometry{a4paper}
%\geometry{margin=1in} % remove "%" symbol in front of \geometry to make 1 inch margins
\usepackage{amsmath} % this package allows you to use math symbols, you can look up what other packages do via google
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{latexsym}
\usepackage{titlesec}
\usepackage{graphicx} % this package lets you insert images into your file
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\begin{center} % centers
\Large{Sample Homework} % Large makes the font larger, put title inside { }
\end{center}
\begin{center}
Victoria Kala \\
Math 117 \\
August 2, 2016
\end{center}
\begin{enumerate} % this makes a numbered list
%%%%%
\item Statement of problem 1
\begin{enumerate} % this makes a numbered list within the numbered list, starts with (a) by default
\item Statement of part (a) of problem
\begin{proof}
Here I type the proof of my problem. Notice that LaTeX will automatically place ``Proof" at the beginning of the proof and an open square at the end of the proof.
\end{proof}
\item Statement of (b) of problem
\begin{proof}[Solution]
Maybe I am not proving something but want to state a solution. I can still use the``Proof" environment, just use `[ ]' symbols to rename ``Proof" to ``Solution". \\ % the double \ with an extra return will automatically create a new paragraph
Notice that I must use the ` symbol to make left apostrophe or use it twice to make left quotation marks, otherwise I only get right apostrophes or quotation marks like so:
"look at these weird 'quotation' marks". % didn't use \\ here so I only get a new line, not a new paragraph
\end{proof}
\end{enumerate} % ends the numbered list we were using earlier
%%%%%
\item[200.] Statement of problem 200 % You can rename items with [ ]
\begin{proof}
Use the dollar symbol to enter math mode: $5x^2 + 100 \frac{e}{\pi} + \ln{500}$.\\
Use square brackets and backslash to enter math mode, but on a centered new line:
\[ \forall \varepsilon > 0, \exists ~ n \in \mathbb{N} ~ \text{s.t.} ~ n, m \geq N \Rightarrow |a_n - a_m| < \varepsilon. \]
% the ~ symbol puts spaces inbetween math characters
Use equation environment to write an equation on a centered new line with a number next to it:
\begin{equation}
\frac{d}{dx} \arctan{x} = \frac{1}{1+x^2}
\end{equation}
You can also rename equations:
\begin{equation}\tag{105}
\lim_{x \to 0} e^x = 1
\end{equation}
\end{proof}
%%%%%
\item Statement of problem 2
\begin{proof}[Solution]
Maybe I have a set of steps I want to show, I can use the align environment:
\begin{align*}
\int_0^{\pi} \sin{x} dx & = - \cos{x} \Big|_0^{\pi} \\
& = - \cos{\pi} - (-\cos{0}) \\
& = - (-1) - (-1) \\
& = 1 + 1 \\
& = 2
\end{align*}
\end{proof}
\end{enumerate} % ends the numbered list we made earlier
\end{document}