templates.tex

\begin{frame}[allowframebreaks]{  \insertframenumber}
\begin{itemize}
\item  
\end{itemize}
\end{frame}

\begin{frame}[allowframebreaks,fragile]{ Java  \insertframenumber}
\begin{lstlisting}
 public 
\end{lstlisting}
\end{frame}


 { %local background frame, enclose frames
 \usebackgroundtemplate{\includegraphics[width=1.0\paperwidth]{../NeilsHarbourLight2.jpg}}
 \begin{frame}{ Random Process  \insertframenumber}
  If we roll two fair dice and add the result, is that a random process?
 \begin{itemize}
 \item [A]  Yes
 \item [B]  No
 \item [C]  It depends
 \end{itemize}
 \end{frame}
 \begin{frame}{ Random Process  \insertframenumber}
  If we roll two fair dice and add the result, is that a random process?
 \begin{itemize}
 \item [\textbf{A}]  Yes, \textbf{because} we cannot predict the result with certainty.
 \item [B]  No
 \item [C]  
 \end{itemize}
 \end{frame}
 }
 
 { %local background frame, enclose frames
 \usebackgroundtemplate{\includegraphics[width=1.0\paperwidth]{../NeilsHarbourLight2.jpg}}
 \begin{frame}{   \insertframenumber}
 ?
 \begin{itemize}
 \item [A]  Yes
 \item [B]  No
 \item [C]  It depends
 \end{itemize}
 \end{frame}
  
 }
 
 
 
  { %local background frame, enclose frames
  \usebackgroundtemplate{\includegraphics[width=1.0\paperwidth]{../NeilsHarbourLight2.jpg}}
  }
  
  \begin{frame}[fragile,allowframebreaks]{What happens when we execute this code?  \insertframenumber}
  \begin{algorithm}[H] 
  factorization(n)\;
  \KwData{an integer $\geq 2$, which becomes bound to the variable n}
  \KwResult{a prime factorization of n}
  \eIf{$prime(n)$}{
    return n
    }{
   (factor1, factor2) = getFactors(n)\;
    return factorization(factor1) $\times$  factorization(factor2)
  }  
    \caption{pseudocode for obtaining factorization }
   \end{algorithm}
   If we want to factor a negative number, we just divide out -1, and factor the rest.
  \end{frame}
  
  
  \begin{frame}{Contradictions \insertframenumber}
  A statement, $A$, implies a contradiction, $c$.\\
  $A \rightarrow c$\\
  It must be that $A$ is false.
  
  \begin{algorithm}[H]
  \begin{algorithmic}[1]
  \IF{$A \rightarrow false$}
  \STATE $A = false$ \\
  \ENDIF
  \end{algorithmic}
  \end{algorithm}
  \end{frame}
  
  \begin{frame}[fragile]{Modus Tollens in code \insertframenumber}
  We are given that:\\
  1. $A \rightarrow B$\\
  2. $B$ is false\\
  so, using this form, we conclude that, $\therefore A$ is false\\
  \begin{algorithm}[H]
  \begin{algorithmic}[1]
  \IF{$\neg B$}
  %\FOR{$j=1$ to $JJJJ$}
  \STATE $A = false$ \\
  %$ interpolate(AAA[i*JJJ+j], ZZZ)$
  %\ENDFOR
  \ENDIF
  \end{algorithmic}
  \caption{pseudocode for modus tollens }
   
  \end{algorithm}
  \end{frame}
  
  \begin{frame}{Valid Argument Forms Are Helpful. \insertframenumber}
  \begin{figure}[tbph]
  \centering
  \includegraphics[height=0.6\textheight]{YodaPuppet}
  \caption{The forms be with you}
  \label{fig:YodaPuppet}
  \end{figure}
  \end{frame}