Branches merged.

5 files changed, 1006 insertions, 308 deletions

diff --git a/day2/handout.tex b/day2/handout.tex
new file mode 100644
index 0000000..d7df544
--- /dev/null
+++ b/day2/handout.tex
@@ -0,0 +1,423 @@
+\documentclass[12pt]{article}
+\usepackage{amsmath}
+\title{Python Workshop\\Problems and Exercises}
+\author{Asokan Pichai\\Prabhu Ramachandran}
+\begin{document}
+\maketitle
+
+\section{Matrices and Arrays \& 2D Plotting}
+\subsection{Matrices and Arrays}
+\begin{verbatim}
+# Simple array math example
+>>> import numpy as np
+>>> a = np.array([1,2,3,4])
+>>> b = np.arange(2,6)
+>>> b
+array([2,3,4,5])
+>>> a*2 + b + 1 # Basic math!
+array([5, 8, 11, 14])
+
+# Pi and e are defined.
+>>> x = np.linspace(0.0, 10.0, 1000)
+>>> x *= 2*np.pi/10 # inplace.
+# apply functions to array.
+>>> y = np.sin(x)
+>>> z = np.exp(y)
+
+>>> x = np.array([1., 2, 3, 4])
+>>> np.size(x)
+4
+>>> x.dtype # What is a.dtype?
+dtype('float64')
+>>> x.shape
+(4,)
+>>> print np.rank(x), x.itemsize
+1 8
+>>> x[0] = 10
+>>> print x[0], x[-1]
+10.0 4.0
+
+>>> a = np.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])
+
+>>> b=np.array([[0,2,4,2],[1,2,3,4]])
+>>> np.add(a,b,a)
+>>> np.sum(x,axis=1)
+
+>>> np.greater(a,4)
+>>> np.sqrt(a)
+
+>>> np.array([2,3,4])  
+array([2, 3, 4])
+
+>>> np.linspace(0, 2, 4)   
+array([0.,0.6666667,1.3333333,2.])
+
+>>>np.ones([2,2])
+array([[ 1.,  1.],
+     [ 1.,  1.]])
+
+>>>a = np.array([[1,2,3],[4,5,6]])
+>>>np.ones_like(a)
+array([[1, 1, 1],
+       [1, 1, 1]])
+
+>>> a = np.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])
+>>> a[...,2]
+array([3, 6, 9])
+
+>>> a[0::2,0::2]
+array([[1, 3],
+       [7, 9]])
+# Slices are references to the 
+# same memory!
+
+>>> np.random.rand(3,2)
+array([[ 0.96276665,  0.77174861],
+       [ 0.35138557,  0.61462271],
+       [ 0.16789255,  0.43848811]])
+>>> np.random.randint(1,100)
+42
+\end{verbatim}
+
+\subsection{Problem Set}
+\begin{verbatim}
+    >>> from scipy import misc
+    >>> A=misc.imread(name)
+    >>> misc.imshow(A)
+\end{verbatim}
+\begin{enumerate}
+  \item Convert an RGB image to Grayscale. $ Y = 0.5R + 0.25G + 0.25B $.
+  \item Scale the image to 50\%.
+  \item Introduce some random noise.
+  \item Smooth the image using a mean filter.
+  \\\small{Each element in the array is replaced by mean of all the neighbouring elements}
+  \\\small{How fast does your code run?}
+\end{enumerate}
+
+\subsection{2D Plotting}
+\begin{verbatim}
+$ ipython -pylab
+>>> 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')
+
+# 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.
+
+>>> w = arange(-2,2,.1)
+>>> plot(w,exp(-(w*w))*cos)
+>>> ylabel('$f(\omega)$')
+>>> xlabel('$\omega$')
+>>> title(r"$f(\omega)=e^{-\omega^2}
+            cos({\omega^2})$")
+>>> annotate('maxima',xy=(0, 1), 
+             xytext=(1, 0.8), 
+             arrowprops=dict(
+             facecolor='black', 
+             shrink=0.05))
+
+>>> x = linspace(0, 2*np.pi, 1000)
+>>> plot(x, cos(5*x), 'r--', 
+         label='cosine')
+>>> plot(x, sin(5*x), 'g--', 
+         label='sine')
+>>> legend() 
+# Or use:
+>>> legend(['cosine', 'sine'])
+
+>>> figure(1)
+>>> plot(x, sin(x))
+>>> figure(2)
+>>> plot(x, tanh(x))
+>>> figure(1)
+>>> title('Easy as 1,2,3')
+
+\end{verbatim}
+
+\subsection{Problem Set}
+  \begin{enumerate}
+    \item Write a function that plots any regular n-gon given n.
+    \item Consider the logistic map, $f(x) = kx(1-x)$, plot it for
+          $k=2.5, 3.5$ and $4$ in the same plot.
+
+  \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}
+
+\section{Advanced Numpy}
+
+\subsection{Broadcasting}
+\begin{verbatim}
+>>> a = np.arange(4)
+>>> b = np.arange(5)
+>>> a+b
+>>> a+3
+>>> c=np.array([3])
+>>> a+c
+>>> b+c
+
+>>> a = np.arange(4)
+>>> a+3
+array([3, 4, 5, 6])
+
+>>> x = np.ones((3, 5))
+>>> y = np.ones(8)
+>>> (x[..., None] + y).shape
+(3, 5, 8)
+
+\end{verbatim}
+
+\subsection{Copies \& Views}
+\begin{verbatim}
+>>> a = np.array([[1,2,3],[4,5,6]])
+>>> b = a
+>>> b is a
+>>> b[0,0]=0; print a
+>>> c = a.view()
+>>> c is a
+>>> c.base is a
+>>> c.flags.owndata
+>>> d = a.copy()
+>>> d.base is a
+>>> d.flags.owndata
+
+>>> a = np.arange(1,9)
+>>> a.shape=3,3
+>>> b = a[0,1:3]
+>>> c = a[0::2,0::2]
+>>> a.flags.owndata
+>>> b.flags.owndata
+>>> b.base
+>>> c.base is a
+
+>>> b = a[np.array([0,1,2])]
+array([[1, 2, 3],
+       [4, 5, 6],
+       [7, 8, 9]])
+>>> b.flags.owndata
+>>> abool=np.greater(a,2)
+>>> c = a[abool]
+>>> c.flags.owndata
+
+\end{verbatim}
+
+\section{Scipy}
+\subsection{Linear Algebra}
+\begin{verbatim}
+>>> import scipy as sp
+>>> from scipy import linalg
+>>> A=sp.mat(np.arange(1,10))
+>>> A.shape=3,3
+>>> linalg.inv(A)
+>>> linalg.det(A)
+>>> linalg.norm(A)
+>>> linalg.expm(A) #logm
+>>> linalg.sinm(A) #cosm, tanm, ...
+
+>>> A = sp.mat(np.arange(1,10))
+>>> A.shape=3,3
+>>> linalg.lu(A)
+>>> linalg.eig(A)
+>>> linalg.eigvals(A)
+\end{verbatim}
+
+\subsection{Solving Linear Equations}
+
+\begin{align*}
+  3x + 2y - z  & = 1 \\
+  2x - 2y + 4z  & = -2 \\
+  -x + \frac{1}{2}y -z & = 0
+\end{align*}
+To Solve this, 
+\begin{verbatim}
+>>> A = sp.mat([[3,2,-1],[2,-2,4]
+              ,[-1,1/2,-1]])
+>>> B = sp.mat([[1],[-2],[0]])
+>>> linalg.solve(A,B)
+\end{verbatim}
+
+\subsection{Integrate}
+\subsubsection{Quadrature}
+Calculate the area under $(sin(x) + x^2)$ in the range $(0,1)$
+\begin{verbatim}
+>>> def f(x):
+        return np.sin(x)+x**2
+>>> integrate.quad(f, 0, 1)
+\end{verbatim}
+
+\subsubsection{ODE Integration}
+Numerically solve ODEs\\
+\begin{align*}
+\frac{dx}{dt} &=-e^{-t}x^2\\ 
+         x(0) &=2    
+\end{align*}
+\begin{verbatim}
+>>> def dx_dt(x,t):
+...     return -np.exp(-t)*x**2
+>>> x=integrate.odeint(dx_dt, 2, t)
+>>> plt.plot(x,t)
+\end{verbatim}
+
+\subsection{Interpolation}
+\subsubsection{1D Interpolation}
+\begin{verbatim}
+>>> from scipy import interpolate
+>>> interpolate.interp1d?
+>>> x = np.arange(0,2*np.pi,np.pi/4)
+>>> y = np.sin(x)
+>>> fl = interpolate.interp1d(
+            x,y,kind='linear')
+>>> fc = interpolate.interp1d(
+             x,y,kind='cubic')
+>>> fl(np.pi/3)
+>>> fc(np.pi/3)
+\end{verbatim}
+
+\subsubsection{Splines}
+Plot the Cubic Spline of $sin(x)$
+\begin{verbatim}
+>>> x = np.arange(0,2*np.pi,np.pi/4)
+>>> y = np.sin(x)
+>>> tck = interpolate.splrep(x,y)
+>>> X = np.arange(0,2*np.pi,np.pi/50)
+>>> Y = interpolate.splev(X,tck,der=0)
+>>> plt.plot(x,y,'o',x,y,X,Y)
+>>> plt.show()
+\end{verbatim}
+
+\subsection{Signal \& Image Processing}
+Applying a simple median filter
+\begin{verbatim}
+>>> from scipy import signal, ndimage
+>>> from scipy import lena
+>>> A=lena().astype('float32')
+>>> B=signal.medfilt2d(A)
+>>> imshow(B)
+\end{verbatim}
+Zooming an array - uses spline interpolation
+\begin{verbatim}
+>>> b=ndimage.zoom(A,0.5)
+>>> imshow(b)
+\end{verbatim}
+
+\section{3D Data Visualization}
+\subsection{Using mlab}
+\begin{verbatim}
+>>> from enthought.mayavi import mlab
+
+>>> mlab.test_<TAB>
+>>> mlab.test_contour3d()
+>>> mlab.test_contour3d??
+\end{verbatim}
+
+\subsubsection{Plotting Functions}
+\begin{verbatim}
+>>> from numpy import *
+>>> t = linspace(0, 2*pi, 50)
+>>> u = cos(t)*pi
+>>> x, y, z = sin(u), cos(u), sin(t)
+
+>>> x = mgrid[-3:3:100j,-3:3:100j]
+>>> z = sin(x*x + y*y)
+>>> mlab.surf(x, y, z)
+\end{verbatim}
+
+\subsubsection{Large 2D Data}
+\begin{verbatim}
+>>> mlab.mesh(x, y, z)
+
+>>> phi, theta = numpy.mgrid[0:pi:20j, 
+...                         0:2*pi:20j]
+>>> x = sin(phi)*cos(theta)
+>>> y = sin(phi)*sin(theta)
+>>> z = cos(phi)
+>>> mlab.mesh(x, y, z, 
+...           representation=
+...           'wireframe')
+\end{verbatim}
+
+\subsubsection{Large 3D Data}
+\begin{verbatim}
+>>> x, y, z = ogrid[-5:5:64j, 
+...                -5:5:64j, 
+...                -5:5:64j]
+>>> mlab.contour3d(x*x*0.5 + y*y + 
+                   z*z*2)
+
+>>> mlab.test_quiver3d()
+\end{verbatim}
+
+\subsection{Motivational Problem}
+Atmospheric data of temperature over the surface of the earth. Let temperature ($T$) vary linearly with height ($z$)\\
+$T = 288.15 - 6.5z$
+
+\begin{verbatim}
+lat = linspace(-89, 89, 37)
+lon = linspace(0, 360, 37)
+z = linspace(0, 100, 11)
+\end{verbatim}
+
+\begin{verbatim}
+x, y, z = mgrid[0:360:37j,-89:89:37j,
+                0:100:11j]
+t = 288.15 - 6.5*z
+mlab.contour3d(x, y, z, t)
+mlab.outline()
+mlab.colorbar()
+\end{verbatim}
+
+\subsection{Lorenz equation}
+\begin{eqnarray*}
+\frac{d x}{dt} &=& s (y-x)\\
+\frac{d y}{d t} &=& rx -y -xz\\
+\frac{d z}{d t} &=& xy - bz\\
+\end{eqnarray*}
+
+Let $s=10,$
+$r=28,$ 
+$b=8./3.$
+
+\begin{verbatim}
+x, y, z = mgrid[-50:50:20j,-50:50:20j,
+                -10:60:20j]
+
+\end{verbatim}
+
+\end{document}
diff --git a/day2/session1.tex b/day2/session1.tex
index 53ee07a..1d80bd4 100644
--- a/day2/session1.tex
+++ b/day2/session1.tex
@@ -146,16 +146,25 @@
   \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])
+>>> import numpy as np
+>>> a = np.array([1,2,3,4])
+>>> b = np.arange(2,6)
+>>> b
+array([2,3,4,5])
 >>> a*2 + b + 1 # Basic math!
 array([5, 8, 11, 14])
+\end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Examples of \num}
+\begin{lstlisting}
 # Pi and e are defined.
->>> x = linspace(0.0, 10.0, 1000)
->>> x *= 2*pi/10 # inplace.
+>>> x = np.linspace(0.0, 10.0, 1000)
+>>> x *= 2*np.pi/10 # inplace.
 # apply functions to array.
->>> y = sin(x)
+>>> y = np.sin(x)
+>>> z = np.exp(y)
 \end{lstlisting}
 \inctime{5}
 \end{frame}
@@ -178,14 +187,14 @@ array([5, 8, 11, 14])
   \frametitle{More examples of \num}
 \vspace*{-8pt}
 \begin{lstlisting}
->>> x = array([1., 2, 3, 4])
->>> size(x)
+>>> x = np.array([1., 2, 3, 4])
+>>> np.size(x)
 4
 >>> x.dtype # What is a.dtype?
 dtype('float64')
 >>> x.shape
 (4,)
->>> print rank(x), x.itemsize
+>>> print np.rank(x), x.itemsize
 1 8
 >>> x[0] = 10
 >>> print x[0], x[-1]
@@ -196,7 +205,7 @@ dtype('float64')
 \begin{frame}[fragile]
   \frametitle{Multi-dimensional arrays}
 \begin{lstlisting}
->>> a = array([[ 0, 1, 2, 3],
+>>> a = np.array([[ 0, 1, 2, 3],
 ...            [10,11,12,13]])
 >>> a.shape # (rows, columns)
 (2, 4)
@@ -206,78 +215,85 @@ dtype('float64')
 >>> a[1,3] = -1
 >>> a[1] # The second row
 array([10,11,12,-1])
-
 \end{lstlisting}
 \end{frame}
+
 \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 \typ{sum(x, axis=0)}, 
-        \typ{product(x, axis=0)},
-        \typ{dot(a, bp)}   
+  \item Inplace operators: \typ{a += b}, or \typ{np.add(a, b, a)} etc. 
+  \item \typ{np.sum(x, axis=0)}, 
+        \typ{np.product(x, axis=0)},
+        \typ{np.dot(a, bp)}   
   \end{itemize}
+\begin{lstlisting}
+>>> b=np.array([[0,2,4,2],[1,2,3,4]])
+>>> np.add(a,b,a)
+>>> np.sum(x,axis=1)
+\end{lstlisting}
 \end{frame}
 
 \begin{frame}[fragile]
   \frametitle{Array math cont.}
   \begin{itemize}
-  \item Logical operations: \typ{equal (==)}, \typ{not\_equal (!=)},
-    \typ{less (<)}, \typ{greater (>)} etc.
-  \item Trig and other functions: \typ{sin(x),}
-        \typ{arcsin(x), sinh(x),}
-      \typ{exp(x), sqrt(x)} etc.
+  \item Logical operations: \typ{np.equal (==)}, \typ{np.not\_equal (!=)},
+    \typ{np.less (<)}, \typ{np.greater (>)} etc.
+  \item Trig and other functions: \typ{np.sin(x),}
+        \typ{np.arcsin(x), np.sinh(x),}
+      \typ{np.exp(x), np.sqrt(x)} etc.
   \end{itemize}
+\begin{lstlisting}
+>>> np.greater(a,4)
+>>> np.sqrt(a)
+\end{lstlisting}
 \inctime{10}
 \end{frame}
 
 \subsection{Array Creation \& Slicing, Striding Arrays}
 \begin{frame}[fragile]
   \frametitle{Array creation functions}
-  \begin {block}{\typ{array(object, dtype=None, ...)}}
-  \begin{lstlisting}
-  >>> array( [2,3,4] )  
-  array([2, 3, 4])
-  \end{lstlisting}
-  \end {block}
-  \begin{block}{\typ{linspace(start, stop, num=50, ...)}}
-  \begin{lstlisting}
-  >>> linspace( 0, 2, 4 )   
-  array([0.,0.6666667,1.3333333,2.])
-  \end{lstlisting}
-  \end{block}
   \begin{itemize}
-  \item also try \typ{arange} command
+    \item {\typ{np.array(object,dtype=None,...)}
+    \begin{lstlisting}
+>>> np.array([2,3,4])  
+array([2, 3, 4])
+    \end{lstlisting}
+    \item \typ{np.linspace(start,stop,...)}
+    \begin{lstlisting}
+>>> np.linspace(0, 2, 4)   
+array([0.,0.6666667,1.3333333,2.])
+    \end{lstlisting}
+    \item Also try \typ{np.arange}
   \end{itemize}
 \end{frame}
 
 \begin{frame}[fragile]
   \frametitle{Array creation functions cont.}
   \begin{itemize}  
-  \item \typ{ones(shape, dtype=None, ...)}  
+  \item \typ{np.ones(shape, dtype=None, ...)}  
   \begin{lstlisting} 
-  >>>ones([2,2])
-  array([[ 1.,  1.],
-       [ 1.,  1.]])
+>>>np.ones([2,2])
+array([[ 1.,  1.],
+     [ 1.,  1.]])
   \end{lstlisting}  
-  \item \typ{identity(n)} 
-  \item \typ{ones\_like(x)}  
+  \item \typ{np.identity(n)} 
+  \item \typ{np.ones\_like(x)}  
   \begin{lstlisting} 
-  >>>a = array([[1,2,3],[4,5,6]])
-  >>>ones_like(a)
-    array([[1, 1, 1],
-           [1, 1, 1]])
+>>>a = np.array([[1,2,3],[4,5,6]])
+>>>np.ones_like(a)
+array([[1, 1, 1],
+       [1, 1, 1]])
   \end{lstlisting}
-  \item check out \typ{zeros, zeros\_like, empty}
+  \item Also try \typ{zeros, zeros\_like, empty}
   \end{itemize}
 \end{frame}
 
 \begin{frame}[fragile]
   \frametitle{Slicing arrays}
 \begin{lstlisting}
->>> a = array([[1,2,3], [4,5,6], 
+>>> a = np.array([[1,2,3], [4,5,6], 
                [7,8,9]])
 >>> a[0,1:3]
 array([2, 3])
@@ -327,8 +343,8 @@ array([[ 0.96276665,  0.77174861],
     \item Scale the image to 50\%
     \item Introduce some random noise
     \item Smooth the image using a mean filter
-      \\\small{Take the mean of all the neighbouring elements}
-      \\\small{How fast can you do it?}
+      \\\small{Each element in the array is replaced by mean of all the neighbouring elements}
+      \\\small{How fast does your code run?}
     \end{enumerate}
 \inctime{15}
 \end{frame}
@@ -408,7 +424,7 @@ array([[ 0.96276665,  0.77174861],
 \begin{frame}[fragile]
   \frametitle{Legends}
 \begin{lstlisting}
->>> x = linspace(0, 2*pi, 1000)
+>>> x = linspace(0, 2*np.pi, 1000)
 >>> plot(x, cos(5*x), 'r--', 
          label='cosine')
 >>> plot(x, sin(5*x), 'g--', 
@@ -435,7 +451,7 @@ array([[ 0.96276665,  0.77174861],
 \end{frame}
 
 \begin{frame}[fragile]
-    \frametitle{Note: \typ{pylab} in Python scripts}
+    \frametitle{\typ{pylab} in Python scripts}
 \begin{lstlisting}
 import pylab
 x = pylab.linspace(0, 20, 1000)
@@ -444,7 +460,7 @@ pylab.plot(x, pylab.sin(x))
 # Can also use:
 from pylab import linspace, sin, plot
 \end{lstlisting}
-\inctime{5}
+\inctime{10}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -742,7 +758,6 @@ title('triangular head; scale '\
     \tiny
     For details see \url{http://matplotlib.sourceforge.net/screenshots/plotmap.py}
   \end{center}
-\inctime{5}
 \end{frame}
 
 
@@ -753,6 +768,7 @@ title('triangular head; scale '\
   \item \url{http://matplotlib.sf.net/tutorial.html}
   \item \url{http://matplotlib.sf.net/screenshots.html}
   \end{itemize}
+\inctime{5}
 \end{frame}
 
 \begin{frame}
diff --git a/day2/session2.tex b/day2/session2.tex
index bc2b157..9a02146 100644
--- a/day2/session2.tex
+++ b/day2/session2.tex
@@ -117,34 +117,52 @@
   \maketitle
 \end{frame}
 
+\section{Advanced Numpy}
 \begin{frame}[fragile]
   \frametitle{Broadcasting}
+  Try it!
+  \begin{lstlisting}
+    >>> a = np.arange(4)
+    >>> b = np.arange(5)
+    >>> a+b
+    >>> a+3
+    >>> c=np.array([3])
+    >>> a+c
+    >>> b+c
+  \end{lstlisting}
   \begin{itemize}
-    \item Used so that functions can take inputs that are not of the same shape.
-    \item 2 rules -
-      \begin{enumerate}
-      \item 1 (repeatedly) pre-pended to shapes of smaller arrays
-      \item Size 1 in a dimension -> Largest size in that dimension
-      \end{enumerate}
+    \item Enter Broadcasting!
   \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Broadcasting}
   \begin{columns}
     \column{0.65\textwidth}
     \hspace*{-1.5in}
     \begin{lstlisting}
-      >>> x = np.arange(4)
-      >>> x+3
+      >>> a = np.arange(4)
+      >>> a+3
       array([3, 4, 5, 6])
     \end{lstlisting}
     \column{0.35\textwidth}
     \includegraphics[height=0.7in, interpolate=true]{data/broadcast_scalar}
   \end{columns}
+  \begin{itemize}
+    \item Allows functions to take inputs not of the same shape
+    \item 2 rules -
+      \begin{enumerate}
+      \item 1 is (repeatedly) prepended to shapes of smaller arrays
+      \item Size 1 in a dimension changed to Largest size in that dimension
+      \end{enumerate}
+  \end{itemize}
 \end{frame}
 
 \begin{frame}[fragile]
   \frametitle{Broadcasting in 3D}
     \begin{lstlisting}
-      >>> x = np.zeros((3, 5))
-      >>> y = np.zeros(8)
+      >>> x = np.ones((3, 5))
+      >>> y = np.ones(8)
       >>> (x[..., None] + y).shape
       (3, 5, 8)
     \end{lstlisting}
@@ -157,14 +175,34 @@
 
 \begin{frame}[fragile]
   \frametitle{Copies \& Views}
+  Try it!
   \begin{lstlisting}
-    >>> a = array([[1,2,3], [4,5,6],     
-                   [7,8,9]])
-    >>> a[0,1:3]
-    array([2, 3])
-    >>> a[0::2,0::2]
-    array([[1, 3],
-          [7, 9]])
+    >>> a = np.array([[1,2,3],[4,5,6]])
+    >>> b = a
+    >>> b is a
+    >>> b[0,0]=0; print a
+    >>> c = a.view()
+    >>> c is a
+    >>> c.base is a
+    >>> c.flags.owndata
+    >>> d = a.copy()
+    >>> d.base is a
+    >>> d.flags.owndata
+  \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Copies \& Views}
+  Try it!
+  \begin{lstlisting}
+    >>> a = np.arange(1,9)
+    >>> a.shape=3,3
+    >>> b = a[0,1:3]
+    >>> c = a[0::2,0::2]
+    >>> a.flags.owndata
+    >>> b.flags.owndata
+    >>> b.base
+    >>> c.base is a
   \end{lstlisting}
   \begin{itemize}
   \item Slicing and Striding just reference the same memory
@@ -175,37 +213,23 @@
 \begin{frame}[fragile]
   \frametitle{Copies contd \ldots}
   \begin{lstlisting}
-    >>> a[np.array([0,1,2])]
+    >>> b = a[np.array([0,1,2])]
     array([[1, 2, 3],
            [4, 5, 6],
            [7, 8, 9]])
+    >>> b.flags.owndata
+    >>> abool=np.greater(a,2)
+    >>> c = a[abool]
+    >>> c.flags.owndata
   \end{lstlisting}
   \begin{itemize}
-  \item Index arrays or Boolean arrays produce copies
+  \item Indexing arrays or Boolean arrays produce copies
   \end{itemize}
 \inctime{15}
 \end{frame}
 
-\begin{frame}
-  \frametitle{More Numpy Functions \& Methods}
-  More functions
-  \begin{itemize}
-    \item \typ{take}
-    \item \typ{choose}
-    \item \typ{where}
-    \item \typ{compress}
-    \item \typ{concatenate}
-  \end{itemize}
-  Ufunc methods 
-  \begin{itemize}
-    \item \typ{reduce}
-    \item \typ{accumulate}
-    \item \typ{outer}
-    \item \typ{reduceat}
-  \end{itemize}
-\inctime{5}
-\end{frame}
-
+\section{SciPy}
+\subsection{Introduction}
 \begin{frame}
     {Intro to SciPy}
   \begin{itemize}
@@ -235,37 +259,72 @@
 \end{frame}
 
 \begin{frame}[fragile]
-  \frametitle{Linear Algebra}
-  \typ{>>> from scipy import linalg}
+  \frametitle{SciPy - Functions \& Submodules}
   \begin{itemize}
-    \item \typ{linalg.det, linalg.norm}
-    \item \typ{linalg.eig, linalg.lu}
-    \item \typ{linalg.expm, linalg.logm}
-    \item \typ{linalg.sinm, linalg.sinhm}
+    \item All \typ{numpy} functions are in \typ{scipy} namespace
+    \item Domain specific functions organized into subpackages
+    \item Subpackages need to be imported separately
   \end{itemize}
+  \begin{lstlisting}
+    >>> from scipy import linalg
+  \end{lstlisting}
+\end{frame}
+
+\subsection{Linear Algebra}
+\begin{frame}[fragile]
+  \frametitle{Linear Algebra}
+  Try it!
+  \begin{lstlisting}
+    >>> import scipy as sp
+    >>> from scipy import linalg
+    >>> A=sp.mat(np.arange(1,10))
+    >>> A.shape=3,3
+    >>> linalg.inv(A)
+    >>> linalg.det(A)
+    >>> linalg.norm(A)
+    >>> linalg.expm(A) #logm
+    >>> linalg.sinm(A) #cosm, tanm, ...
+  \end{lstlisting}
 \end{frame}
 
 \begin{frame}[fragile]
-  \frametitle{Linear Algebra \ldots}
+  \frametitle{Linear Algebra ...}
+  Try it!
+  \begin{lstlisting}
+    >>> A = sp.mat(np.arange(1,10))
+    >>> A.shape=3,3
+    >>> linalg.lu(A)
+    >>> linalg.eig(A)
+    >>> linalg.eigvals(A)
+  \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Solving Linear Equations}
   \begin{align*}
     3x + 2y - z  & = 1 \\
     2x - 2y + 4z  & = -2 \\
     -x + \frac{1}{2}y -z & = 0
   \end{align*}
+  To Solve this, 
   \begin{lstlisting}
+    >>> A = sp.mat([[3,2,-1],[2,-2,4]
+                  ,[-1,1/2,-1]])
+    >>> B = sp.mat([[1],[-2],[0]])
     >>> linalg.solve(A,B)
   \end{lstlisting}
 \inctime{15}
 \end{frame}
 
+\subsection{Integration}
 \begin{frame}[fragile]
+  \frametitle{Integrate}
   \begin{itemize}
     \item Integrating Functions given function object
     \item Integrating Functions given fixed samples
     \item Numerical integrators of ODE systems
   \end{itemize}
-  \frametitle{Integrate}
-  Calculate $\int^1_0sin(x) + x^2$
+  Calculate the area under $(sin(x) + x^2)$ in the range $(0,1)$
   \begin{lstlisting}
     >>> def f(x):
             return np.sin(x)+x**2
@@ -277,39 +336,53 @@
   \frametitle{Integrate \ldots}
   Numerically solve ODEs\\
   \begin{align*}
-  \frac{dx}{dt}&=-e^{(-t)}x^2(t)\\ 
+  \frac{dx}{dt}&=-e^{-t}x^2\\ 
            x(0)&=2    
   \end{align*}
   \begin{lstlisting}
-    def dx_dt(x,t):
+>>> def dx_dt(x,t):
         return -np.exp(-t)*x**2
 
-    x=integrate.odeint(dx_dt, 2, t)
-    plt.plot(x,t)
+>>> x=integrate.odeint(dx_dt, 2, t)
+>>> plt.plot(x,t)
   \end{lstlisting}
 \inctime{10}
 \end{frame}
 
+\subsection{Interpolation}
 \begin{frame}[fragile]
   \frametitle{Interpolation}
-  \begin{itemize}
-    \item \typ{interpolate.interp1d, ...}
-    \item \typ{interpolate.splrep, splev}
-  \end{itemize}
-  Cubic Spline of $sin(x)$
+  Try it!
   \begin{lstlisting}
-    x = np.arange(0,2*np.pi,np.pi/8)
-    y = np.sin(x)
-    t = interpolate.splrep(x,y,s=0)
-    X = np.arange(0,2*np.pi,np.pi/50)
-    Y = interpolate.splev(X,t,der=0)
-
-    plt.plot(x,y,'o',x,y,X,Y)
-    plt.show()
+>>> from scipy import interpolate
+>>> interpolate.interp1d?
+>>> x = np.arange(0,2*np.pi,np.pi/4)
+>>> y = np.sin(x)
+>>> fl = interpolate.interp1d(
+            x,y,kind='linear')
+>>> fc = interpolate.interp1d(
+             x,y,kind='cubic')
+>>> fl(np.pi/3)
+>>> fc(np.pi/3)
+  \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+  \frametitle{Interpolation - Splines}
+  Plot the Cubic Spline of $sin(x)$
+  \begin{lstlisting}
+>>> x = np.arange(0,2*np.pi,np.pi/4)
+>>> y = np.sin(x)
+>>> tck = interpolate.splrep(x,y)
+>>> X = np.arange(0,2*np.pi,np.pi/50)
+>>> Y = interpolate.splev(X,tck,der=0)
+>>> plt.plot(x,y,'o',x,y,X,Y)
+>>> plt.show()
   \end{lstlisting}
 \inctime{10}
 \end{frame}
 
+\subsection{Signal Processing}
 \begin{frame}[fragile]
   \frametitle{Signal \& Image Processing}
     \begin{itemize}
@@ -330,19 +403,18 @@
   \frametitle{Signal \& Image Processing}
   Applying a simple median filter
   \begin{lstlisting}
-    from scipy import signal, ndimage
-    from scipy import lena
-    A=lena().astype('float32')
-    B=signal.medfilt2d(A)
-    imshow(B)
+>>> from scipy import signal, ndimage
+>>> from scipy import lena
+>>> A=lena().astype('float32')
+>>> B=signal.medfilt2d(A)
+>>> imshow(B)
   \end{lstlisting}
   Zooming an array - uses spline interpolation
   \begin{lstlisting}
-    b=ndimage.zoom(A,0.5)
-    imshow(b)
-    \inctime{5}
+>>> b=ndimage.zoom(A,0.5)
+>>> imshow(b)
   \end{lstlisting}
-
+    \inctime{5}
 \end{frame}
 
 \begin{frame}[fragile]
@@ -351,7 +423,8 @@
   \begin{equation*}
   \frac{d^2x}{dt^2}+\mu(x^2-1)\frac{dx}{dt}+x= 0
   \end{equation*}
-\inctime{25}
+  Make a plot of $\frac{dx}{dt}$ vs. $x$.
+\inctime{30}
 \end{frame}
 
 
@@ -362,5 +435,3 @@
     - random number generation.
     - Image manipulation: jigsaw puzzle.
     - Monte-carlo integration.
-
-
diff --git a/day2/session3.tex b/day2/session3.tex
index d2daa20..8154c74 100644
--- a/day2/session3.tex
+++ b/day2/session3.tex
@@ -22,7 +22,7 @@
 
 \mode<presentation>
 {
-  \usetheme{CambridgeUS}
+  \usetheme{Warsaw}
   %\usetheme{Boadilla}
   %\usetheme{default}
   \useoutertheme{split}
@@ -95,7 +95,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Title page
-\title[]{3D data Vizualization\\ \& \\Test Driven Approach}
+\title[]{3D data Visualization}
 
 \author[FOSSEE Team] {Asokan Pichai\\Prabhu Ramachandran}
 
@@ -192,7 +192,67 @@
 \inctime{10}
 \end{frame}
 
-\section{Tools at your disposal:}
+\section{Tools at your disposal}
+
+\subsection{Mayavi2.0}
+
+\begin{frame}
+  \frametitle{Introduction to Mayavi}
+  \begin{itemize}
+  \item Most scientists not interested in details of visualization
+  \item Visualization of data files with a nice UI
+  \item Interactive visualization of data (think Matlab)
+  \item Embedding visualizations in applications
+  \item Customization
+  \end{itemize}
+  \pause
+  \begin{block}{The Goal}
+      Provide a \alert{flexible} library/app for every one of these needs!
+  \end{block}
+\end{frame}
+
+\begin{frame}
+    {Overview of features}
+      \vspace*{-0.3in}
+  \begin{center}    
+    \hspace*{-0.2in}\pgfimage[width=5in]{MEDIA/m2/m2_app3_3}
+  \end{center}    
+\end{frame}
+
+
+\begin{frame}
+    \frametitle{Mayavi in applications}
+      \vspace*{-0.3in}
+  \begin{center}    
+    \hspace*{-0.2in}\pgfimage[width=4.5in]{MEDIA/m2/m2_envisage}
+  \end{center}
+\end{frame}
+
+\begin{frame}
+    {Exploring the documentation}
+    \begin{center}
+    \pgfimage[width=4in]{MEDIA/m2/m2_ug_doc}
+    \end{center}
+\end{frame}
+
+
+\begin{frame}
+  \frametitle{Summary}
+      \begin{itemize}
+          \item \url{http://code.enthought.com/projects/mayavi}
+          \item Uses VTK (\url{www.vtk.org})
+          \item BSD license
+          \item Linux, win32 and Mac OS X
+          \item Highly scriptable
+          \item Embed in Traits UIs (wxPython and PyQt4)
+          \item Envisage Plugins
+          \item Debian/Ubuntu/Fedora
+          \item \alert{Pythonic}
+      \end{itemize}
+    
+      \inctime{10}
+
+\end{frame}
 
 \subsection{mlab}
 
@@ -220,7 +280,7 @@
 \end{frame}
 
 \begin{frame}[fragile]
-    \frametitle{Using mlab:}
+    \frametitle{Using mlab}
 
     \begin{lstlisting}
 >>> from enthought.mayavi import mlab
@@ -228,7 +288,7 @@
 
     \vspace*{0.5in}
 
-    \myemph{\Large Try these:}
+    \myemph{\Large Try these}
 
     \vspace*{0.25in}
 
@@ -249,7 +309,7 @@
             \item Mouse
             \item Keyboard
             \item Toolbar
-            \item Mayavi icon(wait for it...) \pgfimage[width=0.2in]{MEDIA/m2/m2_icon}
+            \item Mayavi icon\pgfimage[width=0.2in]{MEDIA/m2/m2_icon}
         \end{itemize}
     \end{columns}
 \end{frame}
@@ -319,7 +379,8 @@
 >>> y = sin(phi)*sin(theta)
 >>> z = cos(phi)
 >>> mlab.mesh(x, y, z, 
-...           representation='wireframe')
+...           representation=
+...           'wireframe')
 \end{lstlisting}
 
 \end{frame}
@@ -356,66 +417,6 @@
 \inctime{20}
 \end{frame}
 
-\subsection{Mayavi2.0}
-
-\begin{frame}
-  \frametitle{Introduction to Mayavi}
-  \begin{itemize}
-  \item Most scientists not interested in details of visualization
-  \item Visualization of data files with a nice UI
-  \item Interactive visualization of data (think Matlab)
-  \item Embedding visualizations in applications
-  \item Customization
-  \end{itemize}
-  \pause
-  \begin{block}{The Goal}
-      Provide a \alert{flexible} library/app for every one of these needs!
-  \end{block}
-\end{frame}
-
-\begin{frame}
-    {Overview of features}
-      \vspace*{-0.3in}
-  \begin{center}    
-    \hspace*{-0.2in}\pgfimage[width=5in]{MEDIA/m2/m2_app3_3}
-  \end{center}    
-\end{frame}
-
-
-\begin{frame}
-    \frametitle{Mayavi in applications}
-      \vspace*{-0.3in}
-  \begin{center}    
-    \hspace*{0.2in}\pgfimage[width=4.5in]{MEDIA/m2/m2_envisage}
-  \end{center}
-\end{frame}
-
-\begin{frame}
-    {Exploring the documentation}
-    \begin{center}
-    \pgfimage[width=4.5in]{MEDIA/m2/m2_ug_doc}
-    \end{center}
-\end{frame}
-
-
-\begin{frame}
-  \frametitle{Summary}
-      \begin{itemize}
-          \item \url{http://code.enthought.com/projects/mayavi}
-          \item Uses VTK (\url{www.vtk.org})
-          \item BSD license
-          \item Linux, win32 and Mac OS X
-          \item Highly scriptable
-          \item Embed in Traits UIs (wxPython and PyQt4)
-          \item Envisage Plugins
-          \item Debian/Ubuntu/Fedora
-          \item \alert{Pythonic}
-      \end{itemize}
-    
-      \inctime{10}
-
-\end{frame}
-
 \begin{frame}
     {Getting hands dirty!}
 
@@ -468,118 +469,6 @@ x, y, z = mgrid[-50:50:20j,-50:50:20j,
   \end{lstlisting}
 \inctime{20}
 \end{frame}
-
-\section{Test Driven Approach}
-
-\begin{frame}
-    \frametitle{Testing code with \typ{nosetests}}
-   
-    \begin{itemize}
-        \item Writing tests is really simple!
-
-        \item Using nose
-
-        \item Example!
-    \end{itemize}
-\end{frame}
-
-\begin{frame}
-    \frametitle{Need of Testing!}
-   
-    \begin{itemize}
-        \item Quality
-
-        \item Regression
-
-        \item Documentation
-    \end{itemize}
-\end{frame}
-
-\begin{frame}[fragile]
-    \frametitle{Nosetest}
-  \begin{lstlisting}
-def gcd(a, b):
-    """Returns gcd of a and b, 
-     handles only positive numbers."""
-    if a%b == 0: return b
-    return gcd(b, a%b)
-def lcm(a, b):
-    return a*b/gcd(a, b)
-
-if __name__ == '__main__':
-    import nose
-    nose.main()
-  \end{lstlisting}
-\inctime{15}
-\end{frame}
-
-\begin{frame}[fragile]
-    \frametitle{Example}
-    \begin{block}{Problem Statement:}
-      Write a function to check whether a given input
-      string is a palindrome.
-    \end{block}
-\end{frame}
-
-\begin{frame}[fragile]
-    \frametitle{Function: code.py}
-\begin{lstlisting}    
-def is_palindrome(input_str):
-  return input_str == input_str[::-1]
-\end{lstlisting}    
-\end{frame}
-
-\begin{frame}[fragile]
-    \frametitle{Test for the palindrome: code.py}
-\begin{lstlisting}    
-from code import is_palindrome
-def test_function_normal_words():
-  input = "noon"
-  assert is_palindrome(input) == True
-\end{lstlisting}    
-\end{frame}
-
-\begin{frame}[fragile]
-    \frametitle{Running the tests.}
-\begin{lstlisting}    
-$ nosetests test.py 
-.
-----------------------------------------------
-Ran 1 test in 0.001s
-
-OK
-\end{lstlisting}    
-\end{frame}
-
-\begin{frame}[fragile]
-    \frametitle{Exercise: Including new tests.}
-\begin{lstlisting}    
-def test_function_ignore_cases_words():
-  input = "Noon"
-  assert is_palindrome(input) == True
-\end{lstlisting}
-Check
-
-\PythonCode{$ nosetests test.py} 
-
-Tweak the code to pass this test.
-\end{frame}
-
-\begin{frame}[fragile]
-    \frametitle{Exercise: Some more tests.}
-\begin{lstlisting}    
-def test_function_ignore_spaces_in_text():
-    input = "ab raca carba"
-    assert is_palindrome(input) == True
-\end{lstlisting}
-Check
-
-\PythonCode{$ nosetests test.py} 
-
-Tweak the code to pass this test.
-
-\inctime{15} 
-\end{frame}
-
+  
 \end{document}
 
diff --git a/day2/tda.tex b/day2/tda.tex
new file mode 100644
index 0000000..ae39f4a
--- /dev/null
+++ b/day2/tda.tex
@@ -0,0 +1,299 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Tutorial slides on Python.
+%
+% Author: Prabhu Ramachandran <prabhu at aero.iitb.ac.in>
+% Copyright (c) 2005-2009, Prabhu Ramachandran
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\documentclass[compress,14pt]{beamer}
+% \documentclass[handout]{beamer}
+% \usepackage{pgfpages}
+% \pgfpagesuselayout{4 on 1}[a4paper,border, shrink=5mm,landscape]
+\usepackage{tikz}
+\newcommand{\hyperlinkmovie}{}
+%\usepackage{movie15}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Note that in presentation mode 
+% \paperwidth  364.19536pt
+% \paperheight 273.14662pt
+% h/w = 0.888
+
+
+\mode<presentation>
+{
+  \usetheme{Warsaw}
+  %\usetheme{Boadilla}
+  %\usetheme{default}
+  \useoutertheme{split}
+  \setbeamercovered{transparent}
+}
+
+% To remove navigation symbols
+\setbeamertemplate{navigation symbols}{}
+
+\usepackage{amsmath}
+\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}
+\usepackage{pgf}
+
+\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}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% My Macros
+\setbeamercolor{postit}{bg=yellow,fg=black}
+\setbeamercolor{emphbar}{bg=blue!20, fg=black}
+\newcommand{\emphbar}[1]
+{\begin{beamercolorbox}[rounded=true]{emphbar} 
+      {#1}
+ \end{beamercolorbox}
+}
+%{\centerline{\fcolorbox{gray!50} {blue!10}{
+%\begin{minipage}{0.9\linewidth}
+%    {#1} 
+%\end{minipage}
+%    }}}
+
+\newcommand{\myemph}[1]{\structure{\emph{#1}}}
+\newcommand{\PythonCode}[1]{\lstinline{#1}}
+
+\newcommand{\tvtk}{\texttt{tvtk}}
+\newcommand{\mlab}{\texttt{mlab}}
+
+\newcounter{time}
+\setcounter{time}{0}
+\newcommand{\inctime}[1]{\addtocounter{time}{#1}{\vspace*{0.1in}\tiny \thetime\ m}}
+
+\newcommand\BackgroundPicture[1]{%
+  \setbeamertemplate{background}{%
+      \parbox[c][\paperheight]{\paperwidth}{%
+      \vfill \hfill
+ \hfill \vfill
+}}}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Configuring the theme
+%\setbeamercolor{normal text}{fg=white}
+%\setbeamercolor{background canvas}{bg=black}
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Title page
+\title[]{Test Driven Approach}
+
+\author[FOSSEE Team] {Asokan Pichai\\Prabhu Ramachandran}
+
+\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
+\date[] {11, October 2009}
+\date[] % (optional)
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%\pgfdeclareimage[height=0.75cm]{iitblogo}{iitblogo}
+%\logo{\pgfuseimage{iitblogo}}
+
+\AtBeginSection[]
+{
+  \begin{frame}<beamer>
+    \frametitle{Outline}
+      \Large
+    \tableofcontents[currentsection,currentsubsection]
+  \end{frame}
+}
+
+%% 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}
+}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% DOCUMENT STARTS
+\begin{document}
+
+\begin{frame}
+  \maketitle
+\end{frame}
+
+\section{Test Driven Approach}
+
+\begin{frame}
+    \frametitle{Testing code with \typ{nosetests}}
+   
+    \begin{itemize}
+        \item Writing tests is really simple!
+
+        \item Using nose.
+
+        \item Example!
+    \end{itemize}
+\end{frame}
+
+\begin{frame}
+    \frametitle{Need of Testing!}
+   
+    \begin{itemize}
+        \item Quality
+
+        \item Regression
+
+        \item Documentation
+    \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+    \frametitle{Nosetest}
+  \begin{lstlisting}
+def gcd(a, b):
+    """Returns gcd of a and b, 
+     handles only positive numbers."""
+    if a%b == 0: return b
+    return gcd(b, a%b)
+def lcm(a, b):
+    return a*b/gcd(a, b)
+
+if __name__ == '__main__':
+    import nose
+    nose.main()
+  \end{lstlisting}
+\inctime{10}
+\end{frame}
+
+\begin{frame}[fragile]
+    \frametitle{Example}
+    \begin{block}{Problem Statement:}
+      Write a function to check whether a given input
+      string is a palindrome.
+    \end{block}
+\end{frame}
+
+\begin{frame}[fragile]
+    \frametitle{Function: palindrome.py}
+\begin{lstlisting}    
+def is_palindrome(input_str):
+  return input_str == input_str[::-1]
+\end{lstlisting}    
+\end{frame}
+
+\begin{frame}[fragile]
+    \frametitle{Test for the palindrome: palindrome.py}
+\begin{lstlisting}    
+from plaindrome import is_palindrome
+def test_function_normal_words():
+  input = "noon"
+  assert is_palindrome(input) == True
+\end{lstlisting}    
+\end{frame}
+
+\begin{frame}[fragile]
+    \frametitle{Running the tests.}
+\begin{lstlisting}    
+$ nosetests test.py 
+.
+----------------------------------------------
+Ran 1 test in 0.001s
+
+OK
+\end{lstlisting}    
+\end{frame}
+
+\begin{frame}[fragile]
+    \frametitle{Exercise: Including new tests.}
+\begin{lstlisting}    
+def test_function_ignore_cases_words():
+  input = "Noon"
+  assert is_palindrome(input) == True
+\end{lstlisting}
+     \vspace*{0.25in}
+     Check\\
+     \PythonCode{$ nosetests test.py} \\
+     \begin{block}{Task}
+     Tweak the code to pass this test.
+     \end{block}
+\end{frame}
+
+%\begin{frame}[fragile]
+%    \frametitle{Lets write some test!}
+%\begin{lstlisting}    
+%#for form of equation y=mx+c
+%#given m and c for two equation,
+%#finding the intersection point.
+%def intersect(m1,c1,m2,c2):
+%    x = (c2-c1)/(m1-m2)
+%    y = m1*x+c1
+%    return (x,y)
+%\end{lstlisting}
+%
+%Create a simple test for this
+%
+%function which will make it fail.
+%
+%\inctime{15} 
+%\end{frame}
+%
+
+\begin{frame}[fragile]
+    \frametitle{Exercise}
+    Based on Euclid's theorem:
+        $gcd(a,b)=gcd(b,b\%a)$\\
+    gcd function can be written as:
+    \begin{lstlisting}
+    def gcd(a, b):
+      if a%b == 0: return b
+      return gcd(b, a%b)
+    \end{lstlisting}
+    \begin{block}{Task}
+      For given gcd implementation write
+      at least two tests.
+    \end{block}
+    \begin{block}{Task}
+      Write a non recursive implementation
+      of gcd(), and test it using already 
+      written tests.
+    \end{block}
+    
+\inctime{15} 
+\end{frame}
+
+\begin{frame}{In this session we have covered:}
+  \begin{itemize}
+    \item Need for visualization.
+    \item Tools available.
+    \item How to follow Test Driven Approach.
+  \end{itemize}
+\end{frame}
+\begin{frame}
+    \begin{center}
+        \Huge    
+        Thank you!
+    \end{center}
+\end{frame}
+
+\end{document}