LaTeX document compile error

Sounds as though reading up on some basics would be a good idea. http://www.dickimaw-books.com/latex/novices/ might be good place to start.

Very briefly though, every LaTeX document needs a document class first, which is selected with

\documentclass{<name of class>} 

This sets up the basic features of the document. After that you can add customizations, and packages, which give you additional features.

The text itself should be written in a document environment, i.e. between \begin{document} and \end{document}. Everything before \begin{document} is called the preamble.

The code you show appears to be written for the exam class, so if you make the changes as seen in the code below it works fine.

\documentclass{exam} \pagestyle{headandfoot} \firstpageheader{MAT 577/777: Fall 2016}{Quiz 1}{Name:~~~~~~~~~~~~~~~~~~~~~~~~~~~~} \begin{document} \begin{questions} \question Who is considered the father of modern communications? \begin{solution} \end{solution} \question What is redundancy? \begin{solution} \end{solution} \question Explain how to convert a binary symmetric channel with probability of transmission $p_1$ where $0<p_1\leq{1\over 2}$ into a binary symmetric channel with probability of transmission $p_2$ where ${1\over 2}\leq p_2<1$. \begin{solution} \end{solution} \question Let $A=\{0,1\}$ and $C=\{001,101\}$, a $3$-length binary code. Assume we are using a binary symmetric channel with a probability of transmission greater than ${1\over 2}$. If $001$ is sent, for which of the 8 possible received words, will CMLD make the correct guess? \begin{solution} \end{solution} \question In the error correcting code example of the class notes ``Introduction to Codes'', how would the information word 1011 get encoded and how would the received word 1010101 get decoded? If IMLD is used, (considering a symmetric channel with ${1\over q-1}<p<1$), would there ever be a case where retransmission was necessary? Explain. \begin{solution} \end{solution} \end{questions} \end{document}