Merged Mainline and Madhu branches.

5 files changed, 590 insertions, 106 deletions

diff --git a/day2/handout.tex b/day2/handout.tex
new file mode 100644
index 0000000..7d56088
--- /dev/null
+++ b/day2/handout.tex
@@ -0,0 +1,444 @@
+\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}
+\subsubsection{Basic Numpy}
+\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)
+\end{verbatim}
+
+\subsubsection{Array Creation}
+\begin{verbatim}
+>>> 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]])
+\end{verbatim}
+\subsubsection{Slicing, Striding Arrays}
+\begin{verbatim}
+>>> 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!
+\end{verbatim}
+\subsubsection{Random Numbers}
+\begin{verbatim}
+>>> 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}
+
+\subsubsection{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 $.
+  \item Scale the image to 50\%.
+  \item Introduce some random noise.
+  \item Smooth the image using a mean filter.
+  \\\small{Each element in the array is replaced by mean of all the neighbouring elements}
+  \\\small{How fast does your code run?}
+\end{enumerate}
+
+\subsection{2D Plotting}
+\subsubsection{Basic 2D Plotting}
+\begin{verbatim}
+$ 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')
+\end{verbatim}
+\subsubsection{Tweaking plots}
+\begin{verbatim}
+# 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{verbatim}
+
+\subsubsection{Working with text}
+\begin{verbatim}
+>>> 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))
+\end{verbatim}
+
+\subsubsection{Legends}
+\begin{verbatim}
+>>> 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'])
+\end{verbatim}
+
+\subsubsection{Multiple figures}
+\begin{verbatim}
+>>> figure(1)
+>>> plot(x, sin(x))
+>>> figure(2)
+>>> plot(x, tanh(x))
+>>> figure(1)
+>>> title('Easy as 1,2,3')
+
+\end{verbatim}
+
+\subsubsection{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 #Does this work?
+>>> a+3
+>>> c=np.array([3])
+>>> a+c #Works!
+>>> b+c #But how?
+>>> a.shape, b.shape, c.shape
+
+>>> 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..357f18c 100644
--- a/day2/session1.tex
+++ b/day2/session1.tex
@@ -134,10 +134,8 @@
       \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
+    \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}
@@ -146,16 +144,25 @@
   \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 +185,14 @@ 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 +203,7 @@ 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 +213,85 @@ 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 +341,8 @@ 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 +422,7 @@ 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 +449,7 @@ 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 +458,7 @@ 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 +756,6 @@ title('triangular head; scale '\
     \tiny
     For details see \url{http://matplotlib.sourceforge.net/screenshots/plotmap.py}
   \end{center}
-\inctime{5}
 \end{frame}
 
 
@@ -753,6 +766,7 @@ 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}
@@ -787,4 +801,11 @@ title('triangular head; scale '\
 \end{columns}
 \inctime{20}
 \end{frame}
+\begin{frame}{Summary}
+  \begin{itemize}
+  \item Basics of Numpy.
+  \item Array operations.
+  \item Plotting in 2D.
+  \end{itemize}
+\end{frame}
 \end{document}
diff --git a/day2/session2.tex b/day2/session2.tex
index 07514f7..0f471f5 100644
--- a/day2/session2.tex
+++ b/day2/session2.tex
@@ -116,17 +116,20 @@
 \begin{frame}
   \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+b #Does this work?
     >>> a+3
     >>> c=np.array([3])
-    >>> a+c
-    >>> b+c
+    >>> a+c #Works!
+    >>> b+c #But how?
+    >>> a.shape, b.shape, c.shape
   \end{lstlisting}
   \begin{itemize}
     \item Enter Broadcasting!
@@ -147,7 +150,7 @@
     \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 Allows functions to take inputs that are not of the same shape
     \item 2 rules -
       \begin{enumerate}
       \item 1 is (repeatedly) prepended to shapes of smaller arrays
@@ -174,8 +177,9 @@
 \begin{frame}[fragile]
   \frametitle{Copies \& Views}
   Try it!
+  \vspace{-0.1in}
   \begin{lstlisting}
-    >>> a = np.array([[1,2,3],[4,5,6]])
+    >>> a = np.arange(1,9); a.shape=3,3
     >>> b = a
     >>> b is a
     >>> b[0,0]=0; print a
@@ -192,9 +196,8 @@
 \begin{frame}[fragile]
   \frametitle{Copies \& Views}
   Try it!
+  \vspace{-0.1in}
   \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
@@ -226,6 +229,8 @@
 \inctime{15}
 \end{frame}
 
+\section{SciPy}
+\subsection{Introduction}
 \begin{frame}
     {Intro to SciPy}
   \begin{itemize}
@@ -266,6 +271,7 @@
   \end{lstlisting}
 \end{frame}
 
+\subsection{Linear Algebra}
 \begin{frame}[fragile]
   \frametitle{Linear Algebra}
   Try it!
@@ -311,6 +317,7 @@
 \inctime{15}
 \end{frame}
 
+\subsection{Integration}
 \begin{frame}[fragile]
   \frametitle{Integrate}
   \begin{itemize}
@@ -318,7 +325,7 @@
     \item Integrating Functions given fixed samples
     \item Numerical integrators of ODE systems
   \end{itemize}
-  Calculate $\int^1_0(sin(x) + x^2)dx$
+  Calculate the area under $(sin(x) + x^2)$ in the range $(0,1)$
   \begin{lstlisting}
     >>> def f(x):
             return np.sin(x)+x**2
@@ -331,48 +338,50 @@
   Numerically solve ODEs\\
   \begin{align*}
   \frac{dx}{dt}&=-e^{-t}x^2\\ 
-           x(0)&=2    
+           x&=2 \quad at \ t=0
   \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)
+>>> t=np.linspace(0,2,100)
+>>> x=integrate.odeint(dx_dt, 2, t)
+>>> plt.plot(x,t)
   \end{lstlisting}
 \inctime{10}
 \end{frame}
 
+\subsection{Interpolation}
 \begin{frame}[fragile]
   \frametitle{Interpolation}
   Try it!
   \begin{lstlisting}
-    >>> 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)
+>>> 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}
-  Cubic Spline of $sin(x)$
+  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()
+>>> 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}
@@ -393,16 +402,16 @@
   \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)
+>>> b=ndimage.zoom(A,0.5)
+>>> imshow(b)
   \end{lstlisting}
     \inctime{5}
 \end{frame}
@@ -413,10 +422,21 @@
   \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}
+\begin{frame}{Summary}
+  \begin{itemize}
+    \item Advanced NumPy
+    \item SciPy
+      \begin{itemize}
+        \item Linear Algebra
+        \item Integration
+        \item Interpolation
+        \item Signal and Image processing
+      \end{itemize}
+  \end{itemize}
 \end{frame}
-
-
 \end{document}
 
 - Numpy arrays (30 mins)
@@ -424,5 +444,3 @@
     - random number generation.
     - Image manipulation: jigsaw puzzle.
     - Monte-carlo integration.
-
-
diff --git a/day2/session3.tex b/day2/session3.tex
index 02caa0b..b1221e5 100644
--- a/day2/session3.tex
+++ b/day2/session3.tex
@@ -192,9 +192,9 @@
 \inctime{10}
 \end{frame}
 
-\section{Tools at your disposal:}
+\section{Tools at your disposal}
 
-\subsection{Mayavi2.0}
+\subsection{Mayavi2}
 
 \begin{frame}
   \frametitle{Introduction to Mayavi}
@@ -280,7 +280,7 @@
 \end{frame}
 
 \begin{frame}[fragile]
-    \frametitle{Using mlab:}
+    \frametitle{Using mlab}
 
     \begin{lstlisting}
 >>> from enthought.mayavi import mlab
@@ -288,7 +288,7 @@
 
     \vspace*{0.5in}
 
-    \myemph{\Large Try these:}
+    \myemph{\Large Try these}
 
     \vspace*{0.25in}
 
diff --git a/day2/tda.tex b/day2/tda.tex
index ae39f4a..664eed3 100644
--- a/day2/tda.tex
+++ b/day2/tda.tex
@@ -261,7 +261,7 @@ def test_function_ignore_cases_words():
 
 \begin{frame}[fragile]
     \frametitle{Exercise}
-    Based on Euclid's theorem:
+    Based on Euclid's algorithm:
         $gcd(a,b)=gcd(b,b\%a)$\\
     gcd function can be written as:
     \begin{lstlisting}
@@ -269,14 +269,15 @@ def test_function_ignore_cases_words():
       if a%b == 0: return b
       return gcd(b, a%b)
     \end{lstlisting}
+    \vspace*{-0.15in}
     \begin{block}{Task}
-      For given gcd implementation write
-      at least two tests.
-    \end{block}
-    \begin{block}{Task}
-      Write a non recursive implementation
+      \begin{itemize}
+      \item Write at least 
+        two tests for above mentioned function.
+      \item Write a non recursive implementation
       of gcd(), and test it using already 
       written tests.
+      \end{itemize}
     \end{block}
     
 \inctime{15}