3201.sagews

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\usepackage[margin=1in]{geometry} 
\usepackage{amsmath,amsthm,amssymb}

\newcommand{\N}{\mathbb{N}}
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\begin{document}

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\title{Weekly Write-up 1}
\author{Jessica Lamb\\ %replace with your name
Abstract Algebra} %if necessary, replace with your course title

\maketitle

\begin{theorem}{8} %You can use theorem, exercise, problem, or question here.  Modify x.xx to be whatever number you are proving
Let G be a group with identity $e$, and let $a$ be an element of G with inverse $b$. If $c /in G$ and either $a*c=e$ or $c*a=e$, then $c=b$. In particular, $a$ only has one inverse.
\end{theorem}

\begin{proof}
Blah, blah, blah.  Here is an example of the \texttt{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.xx}
Let $n\in \Z$.  Then yada yada.
\end{theorem}

\begin{proof}
Blah, blah, blah.  I'm so smart.
\end{proof}

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