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\begin{document}

\title{Mathematical Scratchpad }

\section*{Smith \hfill Math 290\hfill Spring 2010}

\subsubsection*{Proof LT-1}

\textbf{Accepted}\hfill \textbf{Not Accepted} $\hfill $

\vspace{1pt}

\vspace{1pt}

$\hfill $

\vspace{1pt}I affirm this work abides by the university's Academic Honesty
Policy.

$\vspace{1pt}$

$\vspace{1pt}$ $\vspace{1pt}\hfill \overline{\text{\ \ \ \ \ \ \ \thinspace
\thinspace \thinspace \thinspace \thinspace \thinspace \thinspace \thinspace
\thinspace \thinspace\ \ \ \ \ \ \textbf{Print \thinspace Name, then Sign}%
\thinspace\ \ \ \thinspace \thinspace \thinspace \thinspace \thinspace
\thinspace \thinspace \thinspace \thinspace \thinspace \thinspace \thinspace
\thinspace\ \ \ \ \ \ }}$ \vspace{1pt}

\begin{itemize}
\item First due date \textbf{Thursday, April }$22$.

\item Turn in your work on a separate sheet of paper with this page stapled
in front.

\item Do not include scratch work in your submission.

\item There is to be \textbf{no collaboration} on any aspect of developing
and presenting your proof. Your only resources are: you, the course
textbook, me, and pertinent discussions that occur \textbf{during class. }

\item Follow the Writing Guidelines of the Grading Rubric in the course
information sheet.

\item Retry:\ Only use material from the relevant section of the text or
earlier.

\item Retry:\ Start over using a new sheet of paper.

\item Retry:\ Re-staple with new attempts first and this page on top.
\end{itemize}

\vspace{1pt}

Ignoramus, n. A person unacquainted with certain kinds of knowledge familiar
to yourself, and having certain other kinds that you know nothing about. --
Ambrose Bierce, 1890

\rule{7in}{0.02in}

LT-1 (You may \textbf{ONLY }use material up to, but not including, Theorem
LTLC)\ 

\vspace{1pt}

Given vector spaces $U\ $and $V,$ prove that a function $T:U\rightarrow V$
is a linear transformation if and only if $T\left( \alpha \mathbf{u}_{1}+%
\mathbf{u}_{2}\right) =\alpha T\left( \mathbf{u}_{1}\right) +T\left( \mathbf{%
u}_{2}\right) $ for all vectors $\mathbf{u}_{1},\mathbf{u}_{2}\in U$ and all
scalars $\alpha \in \mathbf{C.}$

\rule{7in}{0.02in}

\vspace{1pt}

\end{document}
