Proof template
Author
Diana Davis
Last Updated
5 年前
License
Creative Commons CC BY 4.0
Abstract
Simple template for writing proofs, with formatting that leaves plenty of space for grader comments.
Simple template for writing proofs, with formatting that leaves plenty of space for grader comments.
% ===============================================
% MATH 29: Discrete Mathematics Fall 2018
% hw_template.tex
% ===============================================
% -------------------------------------------------------------------------
% You can ignore this preamble. Go on
% down to the section that says "START HERE"
% -------------------------------------------------------------------------
\documentclass{article}
\usepackage[margin=1.5in]{geometry} % Please keep the margins at 1.5 so that there is space for grader comments.
\usepackage{amsmath,amsthm,amssymb,hyperref}
\newcommand{\R}{\mathbf{R}}
\newcommand{\Z}{\mathbf{Z}}
\newcommand{\N}{\mathbf{N}}
\newcommand{\Q}{\mathbf{Q}}
\newenvironment{theorem}[2][Theorem]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}\hskip \labelsep {\bfseries #2.}]}{\end{trivlist}}
\newenvironment{lemma}[2][Lemma]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}\hskip \labelsep {\bfseries #2.}]}{\end{trivlist}}
\newenvironment{claim}[2][Claim]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}\hskip \labelsep {\bfseries #2.}]}{\end{trivlist}}
\newenvironment{problem}[2][Problem]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}\hskip \labelsep {\bfseries #2.}]}{\end{trivlist}}
\newenvironment{proposition}[2][Proposition]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}\hskip \labelsep {\bfseries #2.}]}{\end{trivlist}}
\newenvironment{corollary}[2][Corollary]{\begin{trivlist}
\item[\hskip \labelsep {\bfseries #1}\hskip \labelsep {\bfseries #2.}]}{\end{trivlist}}
\newenvironment{solution}{\begin{proof}[Solution]}{\end{proof}}
\begin{document}
\large % please keep the text at this size for ease of reading.
\linespread{1.5} % please keep 1.5 line spacing so that there is space for grader comments.
% ------------------------------------------ %
% START HERE %
% ------------------------------------------ %
{\Large Week 2 proofs % Replace with appropriate number -- keep this THE SAME even when you revise and resubmit.
\hfill Math 29, Discrete Mathematics}
\begin{center}
{\Large Author's Name} % Replace "Author's Name" with your name
\end{center}
\vspace{0.05in}
% -----------------------------------------------------
% The following two environments (claim, proof) are
% where you will enter the statement and proof of your
% first problem for this assignment.
%
% In the theorem environment, you can replace the word
% "theorem" in the \begin and \end commands with
% "theorem", "proposition", "lemma", etc., depending on
% what you are proving.
% -----------------------------------------------------
\begin{claim}{(Page P1 $\#$ 2)}
The number $\sqrt{2}$ is irrational.
\end{claim}
\begin{proof}
Replace this text with the details of your proof. You may want to use the symbol $\mathbf{N}$ for the natural numbers. Mathematical symbols go between dollar signs, e.g. $A$, \emph{not} in plain text. If there are more symbols you want, such as $\in$, $\notin$ $\cup$, $\cap$, $\{ \}$, you can find them at \url{http://detexify.kirelabs.org/classify.html}.
\end{proof}
% -----------------------------------------------------
% Second problem
% -----------------------------------------------------
\vspace{1in} % You are welcome to draw figures by hand. This command adds vertical space.
\begin{theorem}{(Page P1 $\#$ 7)}
Replace this text with the statement of the theorem you are proving.
\end{theorem}
\begin{proof}
Replace this text with your proof.
\end{proof}
% ---------------------------------------------------
% Anything after the \end{document} will be ignored by the typesetting.
% ----------------------------------------------------
\end{document}