# HG changeset patch
# User Puneeth Chaganti <punchagan@fossee.in>
# Date 1254486758 -19800
# Node ID 18a010e4caa0d252fb63888b6b0c12c4674041ec
# Parent  cd97cd584f14364fac7f3584309b0b535d85cb7a
Added day2 session1.

diff -r cd97cd584f14 -r 18a010e4caa0 day2/session1.tex
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/day2/session1.tex	Fri Oct 02 18:02:38 2009 +0530
@@ -0,0 +1,757 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Tutorial slides on Python.
+%
+% Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in>
+% Copyright (c) 2005-2008, 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{split}
+  \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[]{Matrices and Arrays\\ \& \\2D Plotting}
+
+\author[Asokan \& Prabhu] {Asokan Pichai\\Prabhu Ramachandran}
+
+\institute[FOSSEE] {FOSSEE Team}
+\date[] {11, October 2009}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%\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}
+}
+
+\AtBeginSection[]
+{
+  \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}
+  \maketitle
+\end{frame}
+
+\begin{frame}
+  \frametitle{Outline}
+  \tableofcontents
+  % You might wish to add the option [pausesections]
+\end{frame}
+
+\section{Matrices and Arrays}
+
+\subsection{Basic \typ{numpy} }
+
+\newcommand{\num}{\texttt{numpy}}
+
+\begin{frame}
+  \frametitle{The \num\ module}
+  \begin{itemize}
+      \item Why?
+  \item What:
+    \begin{itemize}
+    \item An efficient and powerful array type for various common data
+      types
+    \item Abstracts out the most commonly used standard operations on
+      arrays
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Examples of \num}
+\begin{lstlisting}
+# Simple array math example
+>>> from numpy import *
+>>> a = array([1,2,3,4])
+>>> b = array([2,3,4,5])
+>>> a*2 + b + 1 # Basic math!
+array([5, 8, 11, 14])
+# Pi and e are defined.
+>>> x = linspace(0.0, 10.0, 1000)
+>>> x *= 2*pi/10 # inplace.
+# apply functions to array.
+>>> y = sin(x)
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Basic concepts}
+  \begin{itemize}
+  \item fixed size (\typ{arr.size});
+  \item Same type (\typ{arr.dtype}) of data
+  \item arbitrary dimensionality
+  \item \typ{arr.shape}: size in each dimension
+  \item \alert{Note:} \typ{len(arr) != arr.size} in general
+  \item \alert{Note:} By default array operations are performed
+    \alert{elementwise}
+  \item Indices, slicing: just like lists 
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}[fragile]
+  \frametitle{More examples of \num}
+\vspace*{-8pt}
+\begin{lstlisting}
+>>> x = array([1., 2, 3, 4])
+>>> size(x)
+4
+>>> x.dtype # What is a.dtype?
+dtype('float64')
+>>> x.shape
+(4,)
+>>> print rank(x), x.itemsize
+1 8
+>>> x[0] = 10
+>>> print x[0], x[-1]
+10.0 4.0
+\end{lstlisting}
+    
+\inctime{10}
+\end{frame}
+
+\begin{frame}
+    {More Numpy}
+
+    \begin{itemize}
+        \item Multi-dimensional arrays
+        \item Random number generation
+    \end{itemize}
+
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Multi-dimensional arrays}
+\begin{lstlisting}
+>>> a = array([[ 0, 1, 2, 3],
+...            [10,11,12,13]])
+>>> a.shape # (rows, columns)
+(2, 4)
+# Accessing and setting values
+>>> a[1,3] 
+13
+>>> a[1,3] = -1
+>>> a[1] # The second row
+array([10,11,12,-1])
+
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Slicing arrays}
+\begin{lstlisting}
+>>> a = array([[1,2,3], [4,5,6], 
+               [7,8,9]])
+>>> a[0,1:3]
+array([2, 3])
+>>> a[1:,1:]
+array([[5, 6],
+       [8, 9]])
+>>> a[:,2]
+array([3, 6, 9])
+\end{lstlisting}
+\end{frame}
+\begin{frame}[fragile]
+  \frametitle{Striding arrays}
+\begin{lstlisting}
+>>> a[0::2,0::2]
+array([[1, 3],
+       [7, 9]])
+# Slices are references to the 
+# same memory!
+\end{lstlisting}
+\end{frame}
+
+\subsection{Array creation }
+\begin{frame}[fragile]
+  \frametitle{Array creation functions}
+  \begin{itemize}
+  \item \typ{array(object, dtype=None, \ldots)}
+  \item \typ{arange(start, stop=None, step=1 \ldots)}
+  \item \typ{linspace(start, stop, num=50, \ldots)}
+  \item \typ{ones(shape, dtype=None, \ldots)}
+  \item \typ{zeros(shape, dtype=float,\ldots)}
+  \item \typ{identity(n)}
+  \item \typ{empty(shape, dtype=float,\ldots)}
+  \item \typ{ones\_like(x)}, 
+  \item \typ{zeros\_like(x)}, \typ{empty\_like(x)}
+  \end{itemize}
+\end{frame}
+
+\subsection{Array math}
+\begin{frame}[fragile]
+  \frametitle{Array math}
+  \begin{itemize}
+  \item Basic \alert{elementwise} math (given two arrays \typ{a, b}):
+      \typ{+, -, *, /, \%}
+  \item Inplace operators: \typ{a += b}, or \typ{add(a, b,
+      a)} etc.
+  \item Logical operations: \typ{equal (==)}, \typ{not\_equal (!=)},
+    \typ{less (<)}, \typ{greater (>)} etc.
+  \item Trig and other functions: \typ{sin(x), arcsin(x), sinh(x),
+      exp(x), sqrt(x)} etc.
+  \item \typ{sum(x, axis=0), product(x, axis=0)} 
+  \item \typ{dot(a, bp)}
+  \end{itemize}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{2D Plotting}
+\subsection{Getting Started}
+
+\begin{frame}
+    {IPython's \typ{pylab} mode}
+\begin{itemize}
+    \item \typ{pylab}: convenient 2D plotting interface to MPL
+    \item Immediate use: \typ{ipython -pylab}
+    \item Imports all of pylab for you!
+    \item Allows for interactive plotting
+\end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+    \frametitle{Basic 2D plotting}
+
+\begin{lstlisting}
+>>> x = linspace(0, 2*pi, 1000)
+>>> plot(x, sin(x)) 
+>>> plot(x, sin(x), 'ro')
+>>> xlabel(r'$\chi$', color='g')
+# LaTeX markup!
+>>> ylabel(r'sin($\chi$)', color='r')
+>>> title('Simple figure', fontsize=20)
+>>> savefig('/tmp/test.eps')
+\end{lstlisting}
+\begin{itemize}
+  \item Also: PNG, PDF, PS, EPS, SVG, PDF
+\end{itemize}
+\end{frame}
+       
+\subsection{Playing with lines}
+\begin{frame}[fragile]
+  \frametitle{Basic plotting \ldots}
+\begin{lstlisting}
+# Set properties of objects:
+>>> l, = plot(x, sin(x))
+# Why "l,"?
+>>> setp(l, linewidth=2.0, color='r')
+>>> l.set_linewidth(2.0)
+>>> draw() # Redraw.
+>>> setp(l) # Print properties
+>>> clf() # Clear figure.
+>>> close() # Close figure.
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+    \frametitle{Multiple figures}
+
+\begin{lstlisting}
+>>> figure(1)
+>>> plot(x, sin(x))
+>>> figure(2)
+>>> plot(x, tanh(x))
+>>> figure(1)
+>>> title('Easy as 1,2,3')
+\end{lstlisting}
+    
+\end{frame}
+
+\subsection{Handling Text}
+
+\begin{frame}[fragile]
+  \frametitle{Legends and Annotation}
+\begin{lstlisting}
+>>> plot(x, cos(5*x), 'r--', 
+         label='cosine')
+>>> plot(x, sin(5*x), 'g--', 
+         label='sine')
+>>> legend() 
+# Or use:
+>>> legend(['cosine', 'sine'])
+# Annotation:
+>>> text(1,0, '(1,0)')
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+    \frametitle{More commands \ldots}
+    \begin{lstlisting}
+# semilog, loglog 
+>>> x = 10.**(-arange(100)*0.1)
+>>> semilogx(x, x)
+>>> semilogy(x, x)
+>>> loglog(x, x)
+>>> loglog(x, x*x)
+    \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+    \frametitle{More plots \ldots}
+    \begin{lstlisting}
+>>> clf()
+>>> t = arange(0.1, 4, 0.1)
+>>> s = exp(-t)
+>>> e = 0.1*abs(randn(len(s)))
+>>> errorbar(t, s, e)
+# Scatter plots
+>>> clf()
+>>> t = randn(len(e))
+>>> scatter(t, e, c=s)
+    \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+    \frametitle{Note: \typ{pylab} in Python scripts}
+\begin{lstlisting}
+import pylab
+x = pylab.linspace(0, 20, 1000)
+pylab.plot(x, pylab.sin(x))
+
+# Can also use:
+from pylab import linspace, sin, plot
+\end{lstlisting}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Types of Plots}
+\begin{frame}[fragile]
+  \frametitle{X-Y plot}
+  \begin{columns}
+    \column{0.5\textwidth}
+    \hspace*{-0.5in}
+    \includegraphics[height=2in, interpolate=true]{data/xyplot}
+    \column{0.45\textwidth}
+    \begin{block}{Example code}
+    \tiny
+\begin{lstlisting}
+t1 = arange(0.0, 5.0, 0.1)
+t2 = arange(0.0, 5.0, 0.02)
+t3 = arange(0.0, 2.0, 0.01)
+subplot(211)
+plot(t1, cos(2*pi*t1)*exp(-t1), 'bo', 
+     t2, cos(2*pi*t2)*exp(-t2), 'k')
+grid(True)
+title('A tale of 2 subplots')
+ylabel('Damped')
+subplot(212)
+plot(t3, cos(2*pi*t3), 'r--')
+grid(True)
+xlabel('time (s)')
+ylabel('Undamped')
+\end{lstlisting}
+    \end{block}
+  \end{columns}
+\end{frame}
+
+\begin{frame}[fragile] \frametitle{Semi-log and log-log plots}
+  \begin{columns}
+    \column{0.5\textwidth}
+    \hspace*{-0.5in}
+  \includegraphics[height=2in, interpolate=true]{data/log}  
+    \column{0.45\textwidth}
+    \begin{block}{Example code}
+    \tiny
+\begin{lstlisting}
+dt = 0.01
+t = arange(dt, 20.0, dt)
+subplot(311)
+semilogy(t, exp(-t/5.0))
+ylabel('semilogy')
+grid(True)
+subplot(312)
+semilogx(t, sin(2*pi*t))
+ylabel('semilogx')
+grid(True)
+# minor grid on too
+gca().xaxis.grid(True, which='minor')  
+subplot(313)
+loglog(t, 20*exp(-t/10.0), basex=4)
+grid(True)
+ylabel('loglog base 4 on x')
+\end{lstlisting}
+  \end{block}
+\end{columns}
+\end{frame}
+
+\begin{frame}[fragile] \frametitle{Errorbar}
+  \begin{columns}
+    \column{0.5\textwidth}
+    \hspace*{-0.5in}
+  \includegraphics[height=2in, interpolate=true]{data/errorbar}  
+    \column{0.45\textwidth}
+    \begin{block}{Example code}
+    \tiny
+\begin{lstlisting}
+t = arange(0.1, 4, 0.1)
+s = exp(-t)
+e = 0.1*abs(randn(len(s)))
+f = 0.1*abs(randn(len(s)))
+g = 2*e
+h = 2*f
+errorbar(t, s, [e,g], f, fmt='o')
+xlabel('Distance (m)')
+ylabel('Height (m)')
+title('Mean and standard error '\
+      'as a function of distance')
+\end{lstlisting}
+  \end{block}
+\end{columns}
+\end{frame}
+
+\begin{frame}[fragile] \frametitle{Histogram}
+  \begin{columns}
+    \column{0.5\textwidth}
+    \hspace*{-0.5in}
+  \includegraphics[height=2in, interpolate=true]{data/histogram}  
+    \column{0.45\textwidth}
+    \begin{block}{Example code}
+    \tiny
+\begin{lstlisting}
+mu, sigma = 100, 15
+x = mu + sigma*randn(10000)
+# the histogram of the data
+n, bins, patches = hist(x, 100, normed=1)
+# add a 'best fit' line
+y = normpdf( bins, mu, sigma)
+l = plot(bins, y, 'r--', linewidth=2)
+xlim(40, 160)
+xlabel('Smarts')
+ylabel('P')
+title(r'$\rm{IQ:}\/ \mu=100,\/ \sigma=15$')
+\end{lstlisting}
+  \end{block}
+\end{columns}
+\end{frame}
+
+\begin{frame}[fragile] \frametitle{Bar charts}
+  \begin{columns}
+    \column{0.5\textwidth}
+    \hspace*{-0.5in}
+  \includegraphics[height=2in, interpolate=true]{data/barchart}  
+    \column{0.45\textwidth}
+    \begin{block}{Example code}
+    \tiny
+\begin{lstlisting}
+N = 5
+menMeans = (20, 35, 30, 35, 27)
+menStd =   ( 2,  3,  4,  1,  2)
+# the x locations for the groups
+ind = arange(N) 
+# the width of the bars
+width = 0.35       
+p1 = bar(ind, menMeans, width, 
+         color='r', yerr=menStd)
+womenMeans = (25, 32, 34, 20, 25)
+womenStd =   ( 3,  5,  2,  3,  3)
+p2 = bar(ind+width, womenMeans, width, 
+         color='y', yerr=womenStd)
+ylabel('Scores')
+title('Scores by group and gender')
+xticks(ind+width, 
+       ('G1', 'G2', 'G3', 'G4', 'G5'))
+xlim(-width,len(ind))
+yticks(arange(0,41,10))
+legend((p1[0], p2[0]), 
+       ('Men', 'Women'), shadow=True)
+\end{lstlisting}
+  \end{block}
+\end{columns}
+\end{frame}
+
+\begin{frame}[fragile] \frametitle{Pie charts}
+  \begin{columns}
+    \column{0.5\textwidth}
+    \hspace*{-0.4in}
+  \includegraphics[height=2.0in, interpolate=true]{data/piechart}  
+    \column{0.45\textwidth}
+    \begin{block}{Example code}
+    \tiny
+\begin{lstlisting}
+# make a square figure and axes
+figure(1, figsize=(8,8))
+ax = axes([0.1, 0.1, 0.8, 0.8])
+labels = 'Frogs', 'Hogs', 'Dogs', 'Logs'
+fracs = [15,30,45, 10]
+explode=(0, 0.05, 0, 0)
+pie(fracs, explode=explode, labels=labels, 
+    autopct='%1.1f%%', shadow=True)
+title('Raining Hogs and Dogs', 
+      bbox={'facecolor':'0.8', 'pad':5})
+\end{lstlisting}
+  \end{block}
+\end{columns}
+\end{frame}
+
+\begin{frame}[fragile] \frametitle{Scatter plots}
+  \begin{columns}
+    \column{0.5\textwidth}
+    \hspace*{-0.4in}
+  \includegraphics[height=2in, interpolate=true]{data/scatter}  
+    \column{0.45\textwidth}
+    \begin{block}{Example code}
+    \tiny
+\begin{lstlisting}
+N = 30
+x = 0.9*rand(N)
+y = 0.9*rand(N)
+# 0 to 10 point radiuses
+area = pi*(10 * rand(N))**2 
+volume = 400 + rand(N)*450
+scatter(x,y,s=area, marker='o', c=volume, 
+        alpha=0.75)
+xlabel(r'$\Delta_i$', size='x-large')
+ylabel(r'$\Delta_{i+1}$', size='x-large')
+title(r'Volume and percent change')
+grid(True)
+colorbar()
+savefig('scatter')
+\end{lstlisting}
+  \end{block}
+\end{columns}
+\end{frame}
+
+\begin{frame}[fragile] \frametitle{Polar}
+  \begin{columns}
+    \column{0.5\textwidth}
+    \hspace*{-0.5in}
+  \includegraphics[height=2in, interpolate=true]{data/polar}  
+    \column{0.45\textwidth}
+    \begin{block}{Example code}
+    \tiny
+\begin{lstlisting}
+figure(figsize=(8,8))
+ax = axes([0.1, 0.1, 0.8, 0.8], 
+          polar=True, 
+          axisbg='#d5de9c')
+r = arange(0,1,0.001)
+theta = 2*2*pi*r
+polar(theta, r, color='#ee8d18', lw=3)
+# the radius of the grid labels
+setp(ax.thetagridlabels, y=1.075) 
+title(r"$\theta=4\pi r", fontsize=20)
+\end{lstlisting}
+  \end{block}
+\end{columns}
+\end{frame}
+
+\begin{frame}[fragile] \frametitle{Contours}
+  \begin{columns}
+    \column{0.45\textwidth}
+    \hspace*{-0.5in}
+  \includegraphics[height=2in, interpolate=true]{data/contour}  
+    \column{0.525\textwidth}
+    \begin{block}{Example code}
+    \tiny
+\begin{lstlisting}
+x = arange(-3.0, 3.0, 0.025)
+y = arange(-2.0, 2.0, 0.025)
+X, Y = meshgrid(x, y)
+Z1 = bivariate_normal(X, Y, 1.0, 1.0, 0.0, 0.0)
+Z2 = bivariate_normal(X, Y, 1.5, 0.5, 1, 1)
+# difference of Gaussians
+Z = 10.0 * (Z2 - Z1)
+im = imshow(Z, interpolation='bilinear', 
+            origin='lower',
+            cmap=cm.gray, extent=(-3,3,-2,2))
+levels = arange(-1.2, 1.6, 0.2)
+# label every second level
+clabel(CS, levels[1::2],  inline=1,
+       fmt='%1.1f', fontsize=14)
+CS = contour(Z, levels,
+             origin='lower',
+             linewidths=2,
+             extent=(-3,3,-2,2))
+# make a colorbar for the contour lines
+CB = colorbar(CS, shrink=0.8, extend='both')
+title('Lines with colorbar')
+hot(); flag()
+\end{lstlisting}
+  \end{block}
+\end{columns}
+\end{frame}
+
+\begin{frame}[fragile] \frametitle{Velocity vectors}
+  \begin{columns}
+    \column{0.5\textwidth}
+    \hspace*{-0.5in}
+  \includegraphics[height=2in, interpolate=true]{data/quiver}  
+    \column{0.45\textwidth}
+    \begin{block}{Example code}
+    \tiny
+\begin{lstlisting}
+X,Y = meshgrid(arange(0,2*pi,.2),
+               arange(0,2*pi,.2) )
+U = cos(X)
+V = sin(Y)
+Q = quiver(X[::3, ::3], Y[::3, ::3], 
+           U[::3, ::3], V[::3, ::3],
+           color='r', units='x', 
+           linewidths=(2,), 
+           edgecolors=('k'), 
+           headaxislength=5 )
+qk = quiverkey(Q, 0.5, 0.03, 1, '1 m/s', 
+               fontproperties=
+               {'weight': 'bold'})
+axis([-1, 7, -1, 7])
+title('triangular head; scale '\
+      'with x view; black edges')
+\end{lstlisting}
+  \end{block}
+\end{columns}
+\end{frame}
+
+\begin{frame}[fragile] \frametitle{Maps}
+  \includegraphics[height=2.5in, interpolate=true]{data/plotmap}  
+  \begin{center}
+    \tiny
+    For details see \url{http://matplotlib.sourceforge.net/screenshots/plotmap.py}
+  \end{center}
+\end{frame}
+
+
+\begin{frame}
+  \frametitle{More information}
+  \begin{itemize}
+  \item More information here: \url{http://matplotlib.sf.net}
+  \item \url{http://matplotlib.sf.net/tutorial.html}
+  \item \url{http://matplotlib.sf.net/screenshots.html}
+  \end{itemize}
+
+  \inctime{25}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Problem set 1.0}
+  \begin{enumerate}
+      \item Write a function that plots any n-gon given \typ{n}.
+      \item Consider the logistic map, $f(x) = kx(1-x)$, plot it for
+          $k=2.5, 3.5$ and $4$
+\end{enumerate}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Problem set 1.1}
+  \begin{enumerate}
+      \item Consider the iteration $x_{n+1} = f(x_n)$ where $f(x) =
+          kx(1-x)$.  Plot the successive iterates of this process.
+      \item Plot this using a cobweb plot as follows:
+          \begin{enumerate}
+              \item Start at $(x_0, 0)$
+              \item Draw line to $(x_i, f(x_i))$; 
+              \item Set $x_{i+1} = f(x_i)$
+              \item Draw line to $(x_i, x_i)$
+              \item Repeat from 2 for as long as you want 
+          \end{enumerate}
+    \end{enumerate}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Problem set 1.2}
+  \begin{enumerate}
+
+      \item Plot the Koch snowflake.  Write a function to generate the
+          necessary points given the two points constituting a line.
+          \pause
+          \begin{enumerate}
+              \item Split the line into 4 segments.
+              \item The first and last segments are trivial.
+              \item To rotate the point you can use complex numbers,
+                  recall that $z e^{j \theta}$ rotates a point $z$ in 2D
+                  by $\theta$.
+              \item Do this for all line segments till everything is
+                  done.
+          \end{enumerate}
+      \item Show rate of convergence for a first and second order finite
+          difference of sin(x)
+\end{enumerate}
+\inctime{30}
+\end{frame}
+\end{document}