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\usepackage[lined,boxed,commentsnumbered,linesnumbered,ruled]{algorithm2e}

\usepackage{epsfig,graphicx,subfigure}
\usepackage{enumitem,balance,mathtools}
\usepackage{wrapfig}
\usepackage{mathrsfs, euscript}
\usepackage[usenames]{xcolor}
\usepackage{hyperref}
\usepackage{epstopdf}
\usepackage{listings}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{exercise}{Exercise}[section]
\newtheorem*{solution}{Solution}

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\makeatletter \renewenvironment{proof}[1][Proof] {\par\pushQED{\qed}\normalfont\topsep6\p@\@plus6\p@\relax\trivlist\item[\hskip\labelsep\bfseries#1\@addpunct{.}]\ignorespaces}{\popQED\endtrivlist\@endpefalse} \makeatother
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\begin{document}
\noindent

%========================================================================
\noindent\framebox[\linewidth]{\shortstack[c]{
\Large{\textbf{Lab06-Proof}}\vspace{1mm}\\
�������ѧ���ۿκ�ϰ�⣬��ʦ�������h��2016 �＾ѧ��}}
\begin{center}
\footnotesize{\color{red}��ע����\quad ������\_\_\_\_\_\_\_\_\_\_\_\_ \quad ѧ�ţ�\_\_\_\_\_\_\_\_\_\_\_ \quad �༶��\_\_\_\_\_\_\_\_\_\_\_}

\footnotesize{\color{blue}$*$ ���Ӱ���ҵ��ֱ���ϴ����γ���վ}
\end{center}



\begin{enumerate}
\item MATLAB��ͼ��
\begin{enumerate}
    \item ������ʾ���⣬�����һ��˫�亯��$f(x):(0,1)\rightarrow \mathbb{R}$����MATLAB����$f$��ͼ��ͼ����$x$��$f(x)$��ȡֵ��Χ�Զ��� �����$x$��$y$��ı�ע�Լ����⣬�����Զ������ۼ��ɡ�

    \item \label{Lab-Plot} ����ݿ����ϵ�ʾ�����򣨳���ͼƬ��Fig.~\ref{Fig-Projection}��ʾ����������Fig.~\ref{Fig-Linearization}��ͷ�����$\omega \times \omega \rightarrow \omega$���Ի�ͼ��ע�ⷽ�����Ͽ�ʾ���෴����Ҫ��
    \begin{enumerate}
        \item $x+y=m$��$m$ȡֵΪ$30:10:100$����������8���ߣ�
        \item �뽫MATLAB�ű�����Ƕ��Latex��һ���ύ����ʽ�����µ�MatlabԴ������ʾ��
    \end{enumerate}

\begin{figure}[htbp]
\hspace{2cm}
\begin{minipage}[h]{0.4\textwidth}
\centering
\includegraphics[width=\textwidth]{Fig-Projection.pdf}
\caption{Matlabʾ��ͼƬ} \label{Fig-Projection}
\end{minipage}
\hspace{5mm}
\begin{minipage}[h]{0.34\textwidth}
\centering
\includegraphics[width=0.94\textwidth]{Fig-Linearization.pdf}
\caption{$\omega \times \omega \rightarrow \omega$���Ի�����} \label{Fig-Linearization}
\end{minipage}
\end{figure}
\end{enumerate}

\begin{minipage}[c][8cm][t]{0.48\textwidth}
\item ֤����
     \begin{enumerate}
        \item {\color{blue}�����ƶϷ�}��֤�����$n \in \mathbb{Z}^{+}$��������������$n \mod 4 = 2 \mbox{ or } 3$����ô$n$����һ��ƽ����������ƽ����Ϊ������������
        \item {\color{blue}��С������}��֤�����$\forall n \in \mathbb{Z}$��$n>5$����ô$2^n>10n$������
        \item {\color{blue}ǿ��ѧ���ɷ�}��������$\{a_i\}$����
                $$\left\{
                \begin{array}{l}
                a_0=1, \\
                a_1=2, \\
                a_2=3, \\
                a_k=a_{k-1}+a_{k-2}+a_{k-3}, \quad \forall k\geq 3,
                \end{array}
                \right.$$
        ֤��$\forall n \in \mathbb{N}$����$a_n\leq 2^n$��
     \end{enumerate}
\end{minipage}
\hspace{1cm}
\begin{minipage}[c][8cm][t]{0.38\textwidth}
\centering
\ref{Lab-Plot}���е�MatlabԴ����
\begin{lstlisting}[language=Matlab,numbers=left, numberstyle=\tiny,keywordstyle=\color{blue!70},commentstyle=\color{red!50!green!50!blue!50},frame=shadowbox, rulesepcolor=\color{red!20!green!20!blue!20}]
x=0;
y=0;
tick=5;
temp=0;
lim=101;
figure;
hold on;
grid on;
while temp<lim
    x=0;
    while x<temp+1
        y=temp-x;
        plot(x,y,'.');
        x=x+1;
    end
    temp=temp+tick;
end
xlabel('x')
ylabel('y')
\end{lstlisting}
\end{minipage}
\end{enumerate}
%========================================================================
\end{document}
