Weekly Homework X
作者:
Dana Ernst
最近上传:
9 年前
许可:
Creative Commons CC BY 4.0
摘要:
This is the homework my students use for typing up their weekly homework in LaTeX.
\begin
Discover why 18 million people worldwide trust Overleaf with their work.
\begin
Discover why 18 million people worldwide trust Overleaf with their work.
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% This is all preamble stuff that you don't have to worry about.
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\documentclass[12pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath,amsthm,amssymb}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\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{exercise}[2][Exercise]{\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{question}[2][Question]{\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}
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% Start here
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\title{Weekly Homework X}%replace X with the appropriate number
\author{Tony Stark\\ %replace with your name
Foundations of Mathematics} %if necessary, replace with your course title
\maketitle
\begin{theorem}{x.yz} %You can use theorem, exercise, problem, or question here. Modify x.yz to be whatever number you are proving
Delete this text and write theorem statement here.
\end{theorem}
\begin{proof} %You can also use solution in place of proof.
Blah, blah, blah. Here is an example of the \texttt{align} environment:
%Note 1: The * tells LaTeX not to number the lines. If you remove the *, be sure to remove it below, too.
%Note 2: Inside the align environment, you do not want to use $-signs. The reason for this is that this is already a math environment. This is why we have to include \text{} around any text inside the align environment.
\begin{align*}
\sum_{i=1}^{k+1}i & = \left(\sum_{i=1}^{k}i\right) +(k+1)\\
& = \frac{k(k+1)}{2}+k+1 & (\text{by inductive hypothesis})\\
& = \frac{k(k+1)+2(k+1)}{2}\\
& = \frac{(k+1)(k+2)}{2}\\
& = \frac{(k+1)((k+1)+1)}{2}.
\end{align*}
\end{proof}
\begin{theorem}{x.yz}
Let $n\in \Z$. Then yada yada.
\end{theorem}
\begin{proof}
Blah, blah, blah. I'm so smart.
\end{proof}
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\end{document}