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-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%Tutorial slides on Python.
-%
-% Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in>
-% Copyright (c) 2005-2009, Prabhu Ramachandran
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\documentclass[14pt,compress]{beamer}
-%\documentclass[draft]{beamer}
-%\documentclass[compress,handout]{beamer}
-%\usepackage{pgfpages} 
-%\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm]
-
-% Modified from: generic-ornate-15min-45min.de.tex
-\mode<presentation>
-{
-  \usetheme{Warsaw}
-  \useoutertheme{infolines}
-  \setbeamercovered{transparent}
-}
-
-\usepackage[english]{babel}
-\usepackage[latin1]{inputenc}
-%\usepackage{times}
-\usepackage[T1]{fontenc}
-
-% Taken from Fernando's slides.
-\usepackage{ae,aecompl}
-\usepackage{mathpazo,courier,euler}
-\usepackage[scaled=.95]{helvet}
-
-\definecolor{darkgreen}{rgb}{0,0.5,0}
-
-\usepackage{listings}
-\lstset{language=Python,
-    basicstyle=\ttfamily\bfseries,
-    commentstyle=\color{red}\itshape,
-  stringstyle=\color{darkgreen},
-  showstringspaces=false,
-  keywordstyle=\color{blue}\bfseries}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Macros
-\setbeamercolor{emphbar}{bg=blue!20, fg=black}
-\newcommand{\emphbar}[1]
-{\begin{beamercolorbox}[rounded=true]{emphbar} 
-      {#1}
- \end{beamercolorbox}
-}
-\newcounter{time}
-\setcounter{time}{0}
-\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\tiny \thetime\ m}}
-
-\newcommand{\typ}[1]{\texttt{#1}}
-
-\newcommand{\kwrd}[1]{ \texttt{\textbf{\color{blue}{#1}}}  }
-
-%%% This is from Fernando's setup.
-% \usepackage{color}
-% \definecolor{orange}{cmyk}{0,0.4,0.8,0.2}
-% % Use and configure listings package for nicely formatted code
-% \usepackage{listings}
-% \lstset{
-%    language=Python,
-%    basicstyle=\small\ttfamily,
-%    commentstyle=\ttfamily\color{blue},
-%    stringstyle=\ttfamily\color{orange},
-%    showstringspaces=false,
-%    breaklines=true,
-%    postbreak = \space\dots
-% }
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Title page
-\title[Exercises]{Exercises}
-
-\author[FOSSEE] {FOSSEE}
-
-\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
-\date[] {12 January, 2010\\Day 2}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%\pgfdeclareimage[height=0.75cm]{iitmlogo}{iitmlogo}
-%\logo{\pgfuseimage{iitmlogo}}
-
-
-%% Delete this, if you do not want the table of contents to pop up at
-%% the beginning of each subsection:
-\AtBeginSubsection[]
-{
-  \begin{frame}<beamer>
-    \frametitle{Outline}
-    \tableofcontents[currentsection,currentsubsection]
-  \end{frame}
-}
-
-
-% If you wish to uncover everything in a step-wise fashion, uncomment
-% the following command: 
-%\beamerdefaultoverlayspecification{<+->}
-
-%\includeonlyframes{current,current1,current2,current3,current4,current5,current6}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% DOCUMENT STARTS
-\begin{document}
-
-\begin{frame}
-  \titlepage
-\end{frame}
-
-\begin{frame}{Problem 1.1}
-  The aliquot of a number is defined as: the sum of the \emph{proper} divisors of the number. For example:\\
-aliquot(12) = 1 + 2 + 3 + 4 + 6 = 16.\\
-  Write a function that returns the aliquot number of a given number. 
-\end{frame}
-
-\begin{frame}{Problem 1.2}
-  Pair of numbers (a, b) is said to be \alert{amicable} if aliquot number of a is b and aliquot number of b is a.\\
-  Example: \texttt{220, 284}\\
-  Write a program that prints all four digit amicable pairs.
-  
-\inctime{20}
-\end{frame}
-
-%% \begin{frame}{Problem 2}
-%%   Given an empty chessboard and one Bishop placed in any s%quare, say (r, c), generate the list of all squares the Bi%shop could move to.
-
-%% \end{frame}
-
-\begin{frame}[fragile]
-  \frametitle{Problem 2}
-  Given a string of numbers like, ``1, 3-7, 12, 15, 18-21'', produce the following list \\
-  \begin{lstlisting}
-    [1,3,4,5,6,7,12,15,18,19,20,21]
-  \end{lstlisting}
-\inctime{10}
-\end{frame}
-
-\begin{frame} 
-  \frametitle{Problem 3}
-  Count frequencies of words in a file.
-\inctime{25}
-\end{frame}
-
-\begin{frame}[fragile]
-  \frametitle{Problem set 4}
-  Central difference
-  \begin{equation*}
-  \frac{sin(x+h)-sin(x-h)}{2h}
-  \end{equation*}
-  \begin{lstlisting}
-  In []: x = linspace(0, 2*pi, 100)
-  In []: y = sin(x)
-  In []: deltax = x[1] - x[0]
-  \end{lstlisting}
-  \pause
-    \begin{enumerate}
-      \item Given this, get the finite difference of sin in the range 0 to 2*pi
-    \end{enumerate}
-\end{frame}
-
-\begin{frame}
-  \frametitle{Problem Set 5}
-  \begin{itemize}
-      \item[5.1] Write a function that plots any regular n-gon given \typ{n}.
-      \item[5.2] Consider the logistic map, $f(x) = kx(1-x)$, plot it for
-          $k=2.5, 3.5$ and $4$ in the same plot.
-\end{itemize}
-\end{frame}
-
-\begin{frame}[fragile] 
-\frametitle{Problem Set 5}
-  \begin{columns}
-    \column{0.6\textwidth}
-    \small{
-    \begin{itemize}
-      \item[3] Consider the iteration $x_{n+1} = f(x_n)$ where $f(x) = kx(1-x)$.  Plot the successive iterates of this process as explained below. 
-    \end{itemize}}
-    \column{0.35\textwidth}
-    \hspace*{-0.5in}
-  \includegraphics[height=1.6in, interpolate=true]{data/cobweb}  
-\end{columns}
-\end{frame}
-
-\begin{frame}
-  \frametitle{Problem Set 5.3}
-  Plot the cobweb plot as follows:
-  \begin{enumerate}
-    \item Start at $(x_0, 0)$ ($\implies$ i=0)
-    \item Draw a line to $(x_i, f(x_i))$
-    \item Set $x_{i+1} = f(x_i)$
-    \item Draw a line to $(x_{i+1}, x_{i+1})$
-    \item $(i\implies i+1)$ 
-    \item Repeat from 2 for as long as you want 
-  \end{enumerate}
-\inctime{20}
-\end{frame}
-
-\end{document}