# HG changeset patch
# User nishanth
# Date 1284714130 -19800
# Node ID 4032df8f6227101c600621230b1d7fe29277850b
# Parent  234b393cbc85a9e16927b278c80f66976291a98a# Parent  b9ae88095adeeb0ae6cc8f7589f09d3c999e27a2
merged changes by amit

diff -r 234b393cbc85 -r 4032df8f6227 accessing-pieces-arrays.rst
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/accessing-pieces-arrays.rst	Fri Sep 17 14:32:10 2010 +0530
@@ -0,0 +1,339 @@
+========
+ Script
+========
+
+
+{{{ Screen shows welcome slide }}}
+
+Welcome to the tutorial on accessing pieces of arrays
+
+{{{ Show the outline for this tutorial }}} 
+
+In this tutorial we shall learn to access individual elements of
+arrays, get rows and columns and other chunks of arrays using
+slicing and striding. 
+
+{{{ switch back to the terminal }}}
+
+As usual, we start IPython, using 
+::
+
+  ipython -pylab 
+
+Let us have two arrays, A and C, as the sample arrays that we will
+use to work through this tutorial. 
+
+::
+
+  A = array([12, 23, 34, 45, 56])
+
+  C = array([[11, 12, 13, 14, 15],
+             [21, 22, 23, 24, 25],
+             [31, 32, 33, 34, 35],
+             [41, 42, 43, 44, 45],
+             [51, 52, 53, 54, 55]])
+
+Pause the video here and make sure you have the arrays A and C,
+typed in correctly.
+
+Let us begin with the most elementary thing, accessing individual
+elements. Also, let us first do it with the one-dimensional array
+A, and then do the same thing with the two-dimensional array. 
+
+To access, the element 34 in A, we say, 
+
+::
+
+  A[1]
+
+Like lists, indexing starts from 0 in arrays, too. So, 34, the
+third element has the index 2. 
+
+Now, let us access the element 34 from C. To do this, we say
+::
+
+  C[2, 3]
+
+34 is in the third row and the fourth column, and since indexing
+begins from zero, the row index is 2 and column index is 3. 
+
+Now, that we have accessed one element of the array, let us change
+it. We shall change the 34 to -34 in both A and C. To do this, we
+simply assign the new value after accessing the element. 
+::
+
+  A[2] = -34
+  C[2, 3] = -34
+
+Now that we have accessed and changed a single element, let us
+access and change more than one element at a time; first rows and
+then columns.
+
+Let us access one row of C, say the third row. We do it by saying, 
+::
+
+  C[2] 
+
+How do we access the last row of C? We could say,
+::
+
+  C[4] 
+
+for the fifth row, or as with lists, use negative indexing and say
+::
+
+  C[-1]
+
+Now, we could change the last row into all zeros, using either 
+::
+
+  C[-1] = [0, 0, 0, 0, 0]
+
+or 
+
+::
+  
+  C[-1] = 0
+
+Now, how do we access one column of C? As with accessing
+individual elements, the column is the second parameter to be
+specified (after the comma). The first parameter, is now replaced
+with a ``:`` to say, that we want all the elements of that
+dimension, instead of one particular element. We access the third
+column by
+
+::
+  
+  C[:, 2]
+
+%%1%% Pause the video here and change the last column of C to
+zeroes and then resume the video.
+
+::
+  
+  C[:, -1] = 0
+
+Since A is one dimensional, rows and columns of A don't make much
+sense. It has just one row and 
+::
+
+  A[:] 
+
+gives the whole of A. 
+
+%%2%% Pause the video here and change ``A`` to ``[11, 12, 13, 14, 15]``
+and then resume the video. 
+
+To change A, we say
+::
+
+  A[:] = [11, 12, 13, 14, 15]
+
+Now, that we know how to access, rows and columns of an array, we
+shall learn how to access other pieces of an array. For this
+purpose, we will be using image arrays. 
+
+To read an image into an array, we use the ``imread`` command. We
+shall use the image ``squares.png`` present in ``/home/fossee``. We
+shall first navigate to that path in the OS and see what the image
+contains. 
+
+{{{ switch to the browser and show the image }}}
+
+{{{ switch back to the ipython terminal }}}
+
+Let us now read the data in ``squares.png`` into the array ``I``. 
+::
+
+  I = imread('/home/fossee/squares.png')
+
+We can see the contents of the image, using the command
+``imshow``. We say, 
+::
+
+  imshow(I) 
+
+to see what has been read into ``I``.
+
+To see that ``I`` is really, just an array, we say, 
+::
+
+  I 
+
+at the prompt, and see that an array is displayed. 
+
+To check the dimensions of any array, we can use the method
+shape. We say
+::
+
+  I.shape 
+
+to get the dimensions of the image. As we can see, ``squares.png``
+has the dimensions of 300x300. 
+
+Our goal for this part of the tutorial would be to get the
+top-left quadrant of the image. To do this, we need to access, a
+few of the rows and a few of the columns of the array. 
+
+To access, the third column of C, we said, ``C[:, 2]``. Essentially,
+we are accessing all the rows in column three of C. Now, let us
+modify this to access only the first three rows, of column three
+of C. 
+
+We say, 
+::
+
+  C[0:3, 2]
+
+to get the elements of rows indexed from 0 to 3, 3 not included
+and column indexed 2. Note that, the index before the colon is
+included and the index after it is not included, in the slice that
+we have obtained. This is very similar to the ``range`` function,
+where ``range`` returns a list, in which the upper limit or stop
+value is not included.
+
+Now, if we wish to access the elements of row with index 2, and in
+columns indexed 0 to 2 (included), we say, 
+::
+
+  C[2, 0:3]
+
+E%% %% Pause the video here, and first, obtain the elements [22,
+23] from C. Then, obtain the elements [11, 21, 31, 41] from
+C. Finally, obtain the elements [21, 31, 41, 0]. Then, resume the
+video.
+::
+
+  C[1, 1:3] 
+
+gives the elements [22, 23]
+::
+
+  C[0:4, 0]
+
+gives the elements [11, 21, 31, 41]
+::
+
+  C[1:5, 0]
+
+gives the elements [21, 31, 41, 0]
+
+Note that when specifying ranges, if you are starting from or
+going up-to the end, the corresponding element may be dropped. So,
+in the previous example to obtain [11, 21, 31, 41], we could have
+simply said, 
+::
+
+  C[:4, 0]
+
+and 
+::
+
+  C[1:, 0]
+
+gives the elements [21, 31, 41, 0]. If we skip both the indexes,
+we get the slice from end to end, as we already know. 
+
+E%% %% Pause the video here. Obtain the elements [[23, 24], [33,
+-34]] and then resume the video. 
+::
+
+  C[1:3, 2:4] 
+
+gives us the elements, [[23, 24], [33, -34]]. 
+
+Now, we wish to obtain the top left quarter of the image. How do
+we go about doing it? Since, we know the shape of the image to be
+300, we know that we need to get the first 150 rows and first 150
+columns. 
+::
+
+  I[:150, :150]
+
+gives us the top-left corner of the image. 
+
+We use the ``imshow`` command to see the slice we obtained in the
+form of an image and confirm. 
+::
+
+  imshow(I[:150, :150])
+
+E%% %% Pause the video here, and obtain the square in the center
+of the image. 
+::
+
+  imshow(I[75:225, 75:225])
+
+Our next goal is to compress the image, using a very simple
+technique to reduce the space that the image takes on disk while
+not compromising too heavily on the image quality. The idea is to
+drop alternate rows and columns of the image and save it. This way
+we will be reducing the data to a fourth of the original data but
+losing only so much of visual information. 
+
+We shall first learn the idea of striding using the smaller array
+C. Suppose we wish to access only the odd rows and columns (first,
+third, fifth). We do this by, 
+::
+
+  C[0:5:2, 0:5:2]
+
+if we wish to be explicit, or simply, 
+::
+
+  C[::2, ::2]
+
+This is very similar to the step specified to the ``range``
+function. It specifies, the jump or step in which to move, while
+accessing the elements. If no step is specified, a default value
+of 1 is assumed. 
+::
+
+  C[1::2, ::2] 
+
+gives the elements, [[21, 23, 0], [41, 43, 0]]
+
+E%% %% Pause the video here, and obtain the following. 
+[[12, 0], [42, 0]]
+[[12, 13, 14], [0, 0, 0]]
+Then, resume the video. 
+::
+
+  C[::3, 1::3]
+
+gives the elements [[12, 0], [42, 0]]
+::
+
+  C[::4, 1:4]
+
+gives the elements [[12, 13, 14], [0, 0, 0]]
+
+Now, that we know how to stride over an image, we can drop
+alternate rows and columns out of the image in I. 
+::
+
+  I[::2, ::2]
+
+To see this image, we say, 
+::
+
+  imshow(I[::2, ::2])
+
+This does not have much data to notice any real difference, but
+notice that the scale has reduced to show that we have dropped
+alternate rows and columns. If you notice carefully, you will be
+able to observe some blurring near the edges. To notice this
+effect more clearly, increase the step to 4. 
+::
+
+  imshow(I[::4, ::4])
+
+{{{ show summary slide }}}
+
+That brings us to the end of this tutorial. In this tutorial, we
+have learnt to access parts of arrays, specifically individual
+elements, rows and columns and larger pieces of arrays. We have
+also learnt how to modify arrays, element wise or in larger
+pieces.
+
+Thank You!
diff -r 234b393cbc85 -r 4032df8f6227 advanced-features-functions.rst
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/advanced-features-functions.rst	Fri Sep 17 14:32:10 2010 +0530
@@ -0,0 +1,4 @@
+========
+ Script
+========
+
diff -r 234b393cbc85 -r 4032df8f6227 getting-started-files.rst
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/getting-started-files.rst	Fri Sep 17 14:32:10 2010 +0530
@@ -0,0 +1,147 @@
+========
+ Script
+========
+
+Welcome to the tutorial on getting started with files. 
+
+{{{ Screen shows welcome slide }}}
+
+{{{ Show the outline for this tutorial }}} 
+
+In this tutorial we shall learn to read files, and do some basic
+actions on the file, like opening and reading a file, closing a
+file, iterating through the file line-by-line, and appending the
+lines of a file to a list. 
+
+{{{ switch back to the terminal }}}
+
+As usual, we start IPython, using 
+::
+
+  ipython -pylab 
+
+Let us first open the file, ``pendulum.txt`` present in
+``/home/fossee/``. 
+::
+
+  f = open('/home/fossee/pendulum.txt')
+
+``f`` is called a file object. Let us type ``f`` on the terminal to
+see what it is. 
+::
+
+  f
+
+The file object shows, the file which is open and the mode (read
+or write) in which it is open. 
+
+We shall first learn to read the whole file into a single
+variable. Later, we shall look at reading it line-by-line. We use
+the ``read`` method of ``f`` to read, all the contents of the file
+into the variable ``pend``. 
+::
+
+  pend = f.read()
+
+Now, let us see what is in ``pend``, by typing 
+::
+
+  print pend
+
+We can see that ``pend`` has all the data of file. Type just ``pend``
+to see more explicitly, what it contains. 
+::
+
+  pend
+
+%%1%% Pause the video here and split the variable into a list,
+``pend_list``, of the lines in the file and then resume the
+video. Hint, use the tab command to see what methods the string
+variable has. 
+
+#[punch: should this even be put? add dependency to strings LO,
+where we mention that strings have methods for manipulation. hint:
+use splitlines()]
+::
+
+  pend_list = pend.splitlines()
+
+  pend_list
+
+Now, let us learn to read the file line-by-line. But, before that
+we will have to close the file, since the file has already been
+read till the end. 
+#[punch: should we mention file-pointer?]
+
+Let us close the file opened into f.
+::
+
+  f.close()
+
+Let us again type ``f`` on the prompt to see what it shows. 
+::
+
+  f
+
+Notice, that it now says the file has been closed. It is a good
+programming practice to close any file objects that we have
+opened, after their job is done.
+
+Let us, now move on to reading files line-by-line. 
+
+%%1%% Pause the video here and re-open the file ``pendulum.txt``
+with ``f`` as the file object, and then resume the video.
+
+We just use the up arrow until we reach the open command and issue
+it again. 
+::
+
+  f = open('/home/fossee/pendulum.txt')
+
+Now, to read the file line-by-line, we iterate over the file
+object line-by-line, using the ``for`` command. Let us iterate over
+the file line-wise and print each of the lines. 
+::
+
+  for line in f:
+      print line
+
+As we already know, ``line`` is just a dummy variable, and not a
+keyword. We could have used any other variable name, but ``line``
+seems meaningful enough.
+
+Instead of just printing the lines, let us append them to a list,
+``line_list``. We first initialize an empty list, ``line_list``. 
+::
+
+  line_list = [ ]
+
+Let us then read the file line-by-line and then append each of the
+lines, to the list. We could, as usual close the file using
+``f.close`` and re-open it. But, this time, let's leave alone the
+file object ``f`` and directly open the file within the for
+statement. This will save us the trouble of closing the file, each
+time we open it. 
+
+for line in open('/home/fossee/pendulum.txt'):
+line_list.append(line)
+
+Let us see what ``line_list`` contains. 
+::
+
+  line_list
+
+Notice that ``line_list`` is a list of the lines in the file, along
+with the newline characters. If you noticed, ``pend_list`` did not
+contain the newline characters, because the string ``pend`` was
+split on the newline characters. 
+
+{{{ show the summary slide }}}
+
+That brings us to the end of this tutorial. In this tutorial we
+have learnt to open and close files, read the data in the files as
+a whole, using the read command or reading it line by line by
+iterating over the file object. 
+
+Thank you!   
+
diff -r 234b393cbc85 -r 4032df8f6227 getting-started-ipython.rst
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/getting-started-ipython.rst	Fri Sep 17 14:32:10 2010 +0530
@@ -0,0 +1,174 @@
+========
+ Script
+========
+
+Welcome to so and so..
+
+
+This tutorial will cover the basic usage of the ``ipython``
+interpreter. The following topics would be covered.
+
+{{{ Show slide with outline of the session. }}}
+
+IPython is an enhanced Python interpreter that provides features like
+tabcompletion, easier access to help and many other functionalities
+which are not available in the vannila Python interpreter.
+
+First let us see how to invoke the ``ipython`` interpreter.
+
+We type
+::
+
+  ipython
+
+at the terminal prompt to invoke the ipython interpreter.
+
+We get a prompt with ``In [1]:`` after getting some information about
+the version of Python installed and some help commands.   
+
+If you get an error saying something like ``ipython is not
+installed``, refer to the tutorial on how to install the packages
+required for this course.
+
+Now, to quit the ipython interpreter, type Ctrl-D.  You are prompted
+asking if you really want to exit, type y to say yes and quit ipython.
+
+Start ipython again, as you did before.
+
+The prompt that you have says ``In [1]``. ``In`` stands for input and the
+ipython interpreter is ready to accept input from you.
+
+Now let us see, how we can type some commands into the interpreter.
+
+Start with the simplest thing, addition.
+
+Let's type 
+::
+  1+2 
+
+at the prompt. IPython promptly gives back the output as 3.  Notice
+that the output is displayed with an ``Out[1]`` indication.
+
+Let's try out few other mathematical operations.
+::
+
+  5 - 3
+  7 - 4
+  6 * 5
+
+Now let's ``print 1+2``. Instead of typing the whole thing, we make
+use of the fact that IPython remembers the history of the commands
+that you have already used. We use the up arrow key to go back the
+command ``1+2``. We then use the left-arrow key to navigate to the
+beginning of the line and add the word ``print`` and a space. Then hit
+enter and observe that the interpreter prints out the value as 3,
+without the Out[] indication.
+
+Now, let's change the previous command ``print 1+2`` to ``print
+10*2``.  We use the up arrow again to navigate to the previous command
+and use the left arrow key to move the cursor on to the + symbol and
+then use the delete key to remove it and type 0 and * to change the
+expression to the required one.  We hit enter to see the output of
+``print``. 
+
+Now, let's say we want to use the function ``round``. We type ``ro``
+at the prompt and hit the tab key. As you can see, the IPython
+completes the command. This feature is called the tab-completion.
+
+Now, we remove all the characters and just type ``r`` and then hit
+tab. IPython does not complete the command since there are many
+possibilities. It just lists out all the possible completions.
+
+%% %% Pause the video here and type ``ab`` and hit tab to see what
+happens. Next, jut type ``a`` and hit tab to see what happens. 
+
+``ab`` tab completes to ``abs`` and ``a<tab>`` gives us a list of all
+the commands starting with a. 
+
+Now, let's see what these functions are used for.  We will use the
+help features of ipython to find this out.
+
+To get the help of any function, we first type the function, ``abs``
+in our case and then add a ? at the end and hit enter.
+
+As the documentation says, ``abs`` accepts a number as an input and
+returns it's absolute value.
+
+We say, 
+::
+
+  abs(-19)
+
+  abs(19)
+
+We get 19, as expected, in both the cases.  
+
+Does it work for decimals (or floats)?  Let's try typing abs(-10.5)
+and we do get back 10.5.
+
+%% %% Pause the video here, and look-up the documentation of ``round``
+and see how to use it. 
+
+::
+
+ round?
+
+If you notice, there are extra square brackets around the ``ndigits``.
+This means that ``ndigits`` is optional and 0 is the default value.
+Optional parameters are shown in square brackets anywhere in Python
+documentation.
+
+The function ``round``, rounds a number to a given precision.
+
+%% %% Pause the video here and check the output of
+round(2.48)
+round(2.48, 1)
+round(2.48, 2)
+and then resume the video. 
+
+::
+  round(2.484)
+  round(2.484, 1)
+  round(2.484, 2)
+
+We get 2.0, 2.5 and 2.48, which are what we expect. 
+
+Let's now see how to correct typing errors that we make when typing at
+the terminal. As already shown, if we haven't hit the enter key
+already, we could navigate using the arrow keys and make deletions
+using delete or backspace key and correct the errors. 
+
+Let's now type round(2.484 and hit enter, without closing the
+parenthesis. We get a prompt with dots.  This prompt is the
+continuation prompt of ``ipython``.  It appears, the previous line is
+incomplete in some way.  We now complete the command by typing, the
+closing parenthesis and hitting enter.  We get the expected output of
+2.5. 
+
+In other instances, if we commit a typing error with a longer and more
+complex expression and end up with the continuation prompt, we can
+type Ctrl-C to interrupt the command and get back the ``ipython`` input
+prompt.
+
+%% %% Pause the video here. 
+Try typing round(2.484, and hit enter. and then cancel the command
+using Ctrl-C. Then, type the command, round(2.484, 2) and resume the
+video. 
+
+::
+  
+  round(2.484 
+  ^C
+
+  round(2.484, 2)
+  
+This brings us to the end of the tutorial on getting started with
+``ipython``.
+
+In this tutorial we have seen 
+{{{ show the outline/summary slide. }}}
+
+Thank you!
+
+
+
diff -r 234b393cbc85 -r 4032df8f6227 loading-data-from-files.rst
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/loading-data-from-files.rst	Fri Sep 17 14:32:10 2010 +0530
@@ -0,0 +1,137 @@
+========
+ Script
+========
+
+Welcome to this tutorial on loading data from files. 
+
+{{{ Screen shows welcome slide }}}
+
+Until now, all the plots we have made use analytic functions. We have
+been using analytic functions to generate a sequence of points and
+plotting them, against another sequence of points. But, this is not
+what we do most often. We often require to plot points obtained from
+experimental observations.
+
+#[punch: the initial part of the paragraph may be removed, to make
+this a more generic LO?]
+
+In this tutorial we shall learn to read data from files and save it
+into sequences that can later be used to plot.
+
+{{{ Show the outline for this tutorial }}} 
+
+We shall use the ``loadtxt`` command to load data from files. We will
+be looking at how to get multiple columns of data into multiple
+sequences.
+
+{{{ switch back to the terminal }}}
+
+As usual, let us start IPython, using 
+::
+
+  ipython -pylab 
+
+Now, Let us begin with reading the file primes.txt, which contains
+just a list of primes listed in a column, using the loadtxt command.
+The file, in our case, is present in ``/home/fossee/primes.txt``.
+
+#[punch: do we need a slide for showing the path?]
+
+We use the ``cat`` command to see the contents of this file. 
+
+#[punch: should we show the cat command here? seems like a good place
+to do it] ::
+
+  cat /home/fossee/primes.txt
+
+Now let us read this list into the variable ``primes``.
+::
+
+  primes = loadtxt('/home/fossee/primes.txt')
+
+``primes`` is now a sequence of primes, that was listed in the file,
+``primes.txt``.
+
+We now type, ``print primes`` to see the sequence printed.
+
+We observe that all of the numbers end with a period. This is so,
+because these numbers are actually read as ``floats``. We shall learn
+about them, later.
+
+Now, let us use the ``loadtxt`` command to read a file that contains
+two columns of data, ``pendulum.txt``. This file contains the length
+of the pendulum in the first column and the corresponding time period
+in the second.
+
+%%1%% Pause the video here, and use the ``cat`` command to view the
+contents of this file and then resume the video.
+
+This is how we look at the contents of the file, ``pendulum.txt``
+::
+
+  cat /home/fossee/pendulum.txt
+
+Let us, now, read the data into the variable ``pend``. Again, it is
+assumed that the file is in ``/home/fossee/``
+::
+
+  pend = loadtxt('/home/fossee/pendulum.txt')
+
+Let us now print the variable ``pend`` and see what's in it. 
+::
+
+  print pend
+
+Notice that ``pend`` is not a simple sequence like ``primes``. It has
+two sequences, containing both the columns of the data file. Let us
+use an additional argument of the ``loadtxt`` command, to read it into
+two separate, simple sequences.
+::
+
+  L, T = loadtxt('/home/fossee/pendulum.txt', unpack=True)
+
+Let us now, print the variables L and T, to see what they contain.
+::
+
+  print L
+  print T
+
+Notice, that L and T now contain the first and second columns of data
+from the data file, ``pendulum.txt``, and they are both simple
+sequences.
+
+{{{ show the slide with loadtxt --- other features }}}
+
+In this tutorial, we have learnt the basic use of the ``loadtxt``
+command, which is capable of doing a lot more than we have used it for
+until now, for example
+
+%%2%% Pause the video here, and read the file
+``pendulum_semicolon.txt`` which contains the same data as
+``pendulum.txt``, but the columns are separated by semi-colons instead
+of spaces. Use the IPython help to see how to do this. Once you have
+finished, resume the video to look at the solution.
+
+{{{ switch back to the terminal }}}
+::
+
+  L, T = loadtxt('/home/fossee/pendulum.txt', unpack``True, delimiter``';')
+
+  print L
+
+  print T
+
+This brings us to the end of this tutorial. 
+
+{{{ show the summary slide }}}
+
+You should now be able to do the following, comfortably. 
+
+  + Read data from files, containing a single column of data using the
+    ``loadtxt`` command.
+  + Read multiple columns of data, separated by spaces or other
+    delimiters.
+
+Thank you!   
+
+
diff -r 234b393cbc85 -r 4032df8f6227 loops.rst
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/loops.rst	Fri Sep 17 14:32:10 2010 +0530
@@ -0,0 +1,4 @@
+========
+ Script
+========
+
diff -r 234b393cbc85 -r 4032df8f6227 manipulating-strings.rst
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/manipulating-strings.rst	Fri Sep 17 14:32:10 2010 +0530
@@ -0,0 +1,179 @@
+========
+ Script
+========
+
+{{{ show the welcome slide }}}
+
+Welcome to this tutorial on manipulating strings. 
+
+{{{ show the slide with outline }}} 
+
+In this tutorial we shall learn to manipulate strings, specifically
+slicing and reversing them, or replacing characters, converting from
+upper to lower case and vice-versa 
+
+#[punch: reversed returns an iterator. should we still teach it?]
+
+We have an ``ipython`` shell open, in which we are going to work,
+through out this session. 
+
+Let us consider a simple problem, and learn how to slice strings and
+get sub-strings. 
+
+Let's say the variable ``week`` has the list of the names of the days
+of the week. 
+
+::
+
+    week = ["sun", "mon", "tue", "wed", "thu", "fri", "sat"]
+
+
+Now given a string ``s``, we should be able to check if the string is a
+valid name of a day of the week or not. 
+
+::
+
+    s = saturday
+
+
+``s`` could be in any of the forms --- sat, saturday, Sat, Saturday,
+SAT, SATURDAY. We shall now be solving the problem only for the forms,
+sat and saturday. We shall solve it for the other forms, at the end of
+the tutorial. 
+
+{{{ show these forms in a slide }}}
+
+So, we need to check if the first three characters of the given string
+exists in the variable ``week``. 
+
+As, with any of the string data-types, strings can be sliced into
+sub-strings. To get the first three characters of s, we say, 
+
+::
+
+    s[0:3]
+
+Note that, we are slicing the string from the index 0 to index 3, 3
+not included. 
+
+As we already know, the last element of the string can be accessed
+using ``s[-1]``.  
+
+%%1%% Pause the video here and obtain the sub-string excluding the
+first and last characters from the string. 
+
+::
+
+    s[1:-1]
+
+gives the a substring of s, without the first and the last
+characters. 
+
+::
+
+    s = saturday
+    s[:3]
+
+Now, we just check if that substring is present in the variable
+``week``. 
+
+::
+
+    s[:3] in week          
+
+Let us now consider the problem of finding out if a given string is
+palindromic or not. First of all, a palindromic string is a string
+that remains same even when it has been reversed.
+
+Let the string given be ``malayalam``.
+
+::
+
+    s = "malayalam"
+
+Now, we need to compare this string with it's reverse. 
+
+Again, we will use a technique common to all sequence data-types,
+[::-1]
+
+So, we obtain the reverse of s, by simply saying, 
+
+::
+
+    s[::-1]
+
+Now, to check if the string is ``s`` is palindromic, we say
+::
+
+    s == s[::-1]
+
+As, expected, we get ``True``. 
+
+Now, if the string we are given is ``Malayalam`` instead of
+``malayalam``, the above comparison would return a False. So, we will
+have to convert the string to all lower case or all upper case, before
+comparing. Python provides methods, ``s.lower`` and ``s.upper`` to
+achieve this. 
+
+Let's try it out. 
+::
+
+   s = "Malayalam"
+
+   s.upper()
+
+   s
+
+   s.lower()
+
+   s.lower() == s.lower()[::-1]
+   
+Note that these methods, do not change the original string, but return
+a new string.
+
+a%% %% Pause the video here, and finish the problem of checking if
+``s`` is a valid name of a day of the week and then resume the
+video. Change the solution to this problem, to include forms like,
+SAT, SATURDAY, Saturday and Sat. 
+
+::
+
+    s.lower()[:3] in week
+
+We just convert any input string to lower case and then check if it is
+present in the list ``week``. 
+
+Now, let us consider another problem. We often encounter e-mail id's
+which have @ and periods replaced with text, something like
+info[at]fossee[dot]in. We now wish to get back proper e-mail
+addresses.  
+
+Let's say the variable email has the email address. 
+::
+
+   email = "info[at]fossee[dot]in"
+
+Now, we first replace the ``[at]`` with the ``@``, using the replace
+method of strings. 
+::
+
+   email = email.replace("[at]", "@")
+   print email
+
+%%1%% Pause the video here and replace the ``[dot]`` with ``.`` and then
+resume the video. 
+
+::
+
+   email = email.replace("[dot]", ".")        
+   print email
+
+
+That brings us to the end of the tutorial. 
+
+{{{ show summary slide }}}
+
+In this tutorial, we have learnt how to get substrings, reverse
+strings and a few useful methods, namely upper, lower and replace. 
+
+Thank You!
diff -r 234b393cbc85 -r 4032df8f6227 module-assessment-arrays-matrices.rst
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/module-assessment-arrays-matrices.rst	Fri Sep 17 14:32:10 2010 +0530
@@ -0,0 +1,88 @@
+========
+ Script
+========
+
+Welcome. 
+
+This spoken tutorial is a self-assessment tutorial and you will be
+able to assess yourself on the concepts learnt in the Module on Arrays
+and Matrices. 
+
+
+As with all other assessments we will first start with a few short
+questions that will not take you more that 15 to 20 seconds to
+answer. Then we shall move on to a bigger problem, that you are
+expected to solve in less than 10 mins. 
+
+
+  * Given a list of marks::
+   
+      marks = [10, 20, 30, 50, 55, 75, 83]
+
+    How will you convert it to an array?
+
+  * What is the shape of the following array?::
+
+      x = array([[1,2,3,4],
+                 [3,4,2,5]])
+
+  * What is the resulting array::
+
+      a = array([[1, 2],
+                 [3, 4]])
+      
+      a[1,0] = 0
+ 
+  * What is the resulting array?::
+
+      x = array(([1,2,3,4],
+                 [2,3,4,5]))
+
+      x[-2][-3] = 4
+
+
+  * How do we change the array ``x = array([[1,2,3,4]])`` to
+    ``array([[1,2,0,4]])``?
+
+  * How do we get the slice::
+
+      array([[2,3],
+             [4,2]])
+
+    out of the array::
+
+      x = array([[1,2,3,4],
+                 [3,4,2,5]])
+
+
+  * What is the output of x[::3,::3], when x is::
+
+      x = array([[9,18,27],
+                 [30,60,90],
+                 [14,7,1]])
+
+  * How do you get the transpose of this array?::
+
+      a = array([[1, 2],
+                 [3, 4]])
+
+  * What is the output of the following?::
+
+      a = array([[1, 2],
+                 [3, 4]])
+
+      b = array([[1, 1],
+                 [2, 2]])
+
+      a*b
+
+
+{{{ show slides with solutions to these problems }}}
+
+Now, let us move on to a larger problem. From the image
+`tagore-einstein.png``
+
+  + extract the face of Einstein alone.
+  + extract the face of Tagore alone.
+  + get a smaller copy of the image, that is a fourth it's size. 
+                 
diff -r 234b393cbc85 -r 4032df8f6227 plotting-data.rst
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/plotting-data.rst	Fri Sep 17 14:32:10 2010 +0530
@@ -0,0 +1,137 @@
+Plotting   Experimental  Data  
+=============================   
+Hello  and welcome , this tutorial on  Plotting Experimental data is 
+presented by the fossee  team.  
+
+{{{ Show the slide containing title }}}
+
+
+{{{ Show the Outline Slide }}}
+
+Here  we will discuss plotting  Experimental data. 
+
+1.We will see how we can represent a sequence of numbers in Python. 
+
+2.We will also become fimiliar with  elementwise squaring of such a
+sequence. 
+
+3. We will also see how we can use our graph to indicate Error.
+
+One needs   to  be  fimiliar  with  the   concepts  of  plotting
+mathematical functions in Python.
+
+We will use  data from a Simple Pendulum  Experiment to illustrate our
+points. 
+
+{{{ Simple Pendulum data Slide }}} 
+
+  
+  
+  
+As we know for a simple pendulum length,L is directly  proportional to 
+the square of time,T. We shall be plotting L and T^2 values.
+
+
+First  we will have  to initiate L and  T values. We initiate them as sequence 
+of values.  To tell ipython a sequence of values we  write the sequence in 
+comma  seperated values inside two square brackets.  This is also  called List 
+so to create two sequences
+
+L,t type in ipython shell. ::
+
+    In []: L = [0.1, 0.2, 0.3, 0.4, 0.5,0.6, 0.7, 0.8, 0.9]
+    
+    In []: t= [0.69, 0.90, 1.19,1.30, 1.47, 1.58, 1.77, 1.83, 1.94]
+
+
+  
+To obtain the  square of sequence t we will  use the function square
+with argument t.This is saved into the variable tsquare.::
+
+   In []: tsquare=square(t)
+  
+   array([  0.4761, 0.81 , 1.4161,  1.69 , 2.1609,  2.4964, 3.1329, 
+   3.3489, 3.7636])
+
+  
+Now to plot L vs T^2 we will simply type ::
+
+  In []: plot(L,t,.)
+
+'.' here represents to plot use small dots for the point. ::
+
+  In []: clf()
+
+You can also specify 'o' for big dots.::
+ 
+  In []: plot(L,t,o)
+
+  In []: clf()
+
+
+{{{ Slide with Error data included }}}
+
+
+Now we  shall try  and take into  account error  into our plots . The
+Error values for L and T  are on your screen.We shall again intialize
+the sequence values in the same manner as we did for L and t ::
+
+  In []: delta_L= [0.08,0.09,0.07,0.05,0.06,0.00,0.06,0.06,0.01]
+  
+  In []: delta_T= [0.04,0.08,0.11,0.05,0.03,0.03,0.01,0.07,0.01]
+
+
+  
+Now to plot L vs T^2 with an error bar we use the function errorbar()
+
+The syntax of the command is as given on the screen. ::
+
+    
+    In []: errorbar(L,tsquare,xerr=delta_L, yerr=delta_T, fmt='b.')
+
+This gives a  plot with error bar for  x and y axis. The  dots are of
+blue color.
+
+
+similarly we can draw the same error bar with big red dots just change 
+the parameters to fmt to 'ro'. ::
+
+    In []: clf()
+    In []: errorbar(L,tsquare,xerr=delta_L, yerr=delta_T, fmt='ro')
+
+
+
+thats it. you can explore other options to errorbar using the documentation 
+of errorbar.::
+
+   In []: errorbar?
+
+
+{{{ Summary Slides }}}
+
+In this tutorial we have learnt : 
+
+1. How to declare a sequence of number , specifically the kind of sequence we learned was a list.
+
+2. Plotting experimental data extending our knowledge from mathematical functions. 
+
+3. The various options available for plotting dots instead of lines.
+
+4. Plotting experimental data such that we can also represent error. We did this using the errorbar() function.
+
+
+ {{{ Show the "sponsored by FOSSEE" slide }}}
+
+
+
+This tutorial was created as a part of FOSSEE project.
+
+Hope you have enjoyed and found it useful.
+
+ Thankyou
+
+ 
+
+Author              : Amit Sethi
+Internal Reviewer   :
+Internal Reviewer 2 : 
diff -r 234b393cbc85 -r 4032df8f6227 plotui.rst
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/plotui.rst	Fri Sep 17 14:32:10 2010 +0530
@@ -0,0 +1,177 @@
+Hello and welcome to the tutorial on creating simple plots using
+Python.This tutorial is presented by the Fossee group.  
+{{{ Show the Title Slide }}} 
+
+I hope you have IPython running on your computer.
+
+In this tutorial we will look at plot command and also how to study
+the plot using the UI.
+
+{{{ Show Outline Slide }}}
+
+Lets start ipython on your shell, type :: 
+
+      $ipython -pylab
+
+
+Pylab is a python library which provides plotting functionality.It
+also provides many other important mathematical and scientific
+functions. After running IPython -pylab in your shell if at the top of
+the result of this command, you see something like ::
+ 
+
+   `ERROR: matplotlib could NOT be imported!  Starting normal
+      IPython.`
+
+
+{{{ Slide with Error written on it }}}
+
+Then you have to install matplotlib and run this command again.
+
+Now type in your ipython shell ::
+
+             In[]: linpace?
+
+
+
+as the documentation says, it returns `num` evenly spaced samples,
+calculated over the interval start and stop.  To illustrate this, lets
+do it form 1 to 100 and try 100 points.  ::
+
+           In[]: linspace(1,100,100)
+
+As you can see a sequence of numbers from 1 to 100 appears.
+
+Now lets try 200 points between 0 and 1 you do this by typing ::
+
+
+            In[]: linspace(0,1,200)
+
+0 for start , 1 for stop and 200 for no of points.  In linspace 
+the start and stop points can be integers, decimals , or
+constants. Let's try and get 100 points between -pi to pi. Type ::
+           
+            In[]: p = linspace(-pi,pi,100)
+
+
+'pi' here is constant defined by pylab. Save this to the variable, p
+.
+
+If you now ::
+     
+	   In[]: len(p)
+
+You will get the no. of points. len function gives the no of elements
+of a sequence.
+
+
+Let's try and plot a cosine curve between -pi and pi using these
+points.  Simply type :: 
+
+
+       	  In[]: plot(p,cos(points))
+
+Here cos(points) gets the cosine value at every corresponding point to
+p.
+
+
+We can also save cos(points) to variable cosine and plot it using
+plot.::
+
+           In[]: cosine=cos(points) 
+
+	   In[]: plot(p,cosine)
+
+ 
+
+Now do ::
+       	 
+	   In[]: clf()
+
+this will clear the plot.
+
+This is done because any other plot we try to make shall come on the
+same drawing area. As we do not wish to clutter the area with
+overlaid plots , we just clear it with clf().  Now lets try a sine
+plot. ::
+
+
+    	 In []: plot(p,sin(p))
+
+
+
+ 
+The Window on which the plot appears can be used to study it better.
+
+First of all moving the mouse around gives us the point where mouse
+points at.  
+
+Also we have some buttons the right most among them is
+for saving the file. 
+
+Just click on it specifying the name of the file.  We will save the plot 
+by the name sin_curve in pdf format.
+
+{{{ Action corelating with the words }}}
+
+As you can see I can specify format of file.  
+Left to the save button is the slider button to specify the margins.  
+
+{{{ Action corelating with the words  }}}
+
+Left to this is zoom button to zoom into the plot. Just specify the 
+region to zoom into.  
+The button left to it can be used to move the axes of the plot.  
+
+{{{ Action corelating with the words }}}
+ 
+The next two buttons with a left and right arrow icons change the state of the 
+plot and take it to the previous state it was in. It more or less acts like a
+back and forward button in the browser.  
+
+{{{ Action corelating with the words }}}
+
+The last one is 'home' referring to the initial plot.
+
+{{{ Action corelating with the words}}}
+
+
+
+{{{ Summary Slide }}}
+
+
+In this tutorial we have looked at 
+
+1. Starting Ipython with pylab 
+
+2. Using linspace function to create `num` equaly spaced points in a region.
+
+3. Finding length of sequnces using  len.
+ 
+4. Plotting mathematical functions using plot.
+
+4. Clearing drawing area using clf 
+ 
+5. Using the UI of plot for studying it better . Using functionalities like save , zoom , moving the plots on x and y axis 
+
+etc ..
+ 
+
+
+{{{ Show the "sponsored by FOSSEE" slide }}}
+
+ 
+
+This tutorial was created as a part of FOSSEE project, NME ICT, MHRD India
+
+ 
+
+ Hope you have enjoyed and found it useful.
+
+ Thankyou
+
+ 
+
+Author              : Amit Sethi
+Internal Reviewer   :
+Internal Reviewer 2 : 
diff -r 234b393cbc85 -r 4032df8f6227 symbolics.rst
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/symbolics.rst	Fri Sep 17 14:32:10 2010 +0530
@@ -0,0 +1,248 @@
+Symbolics with Sage
+-------------------
+
+This tutorial on using Sage for symbolic calculation is brought to you
+by Fossee group.
+
+{{{ Part of Notebook with title }}}
+
+We would be using simple mathematical functions on the sage notebook
+for this tutorial .
+
+During the course of the tutorial we will learn
+
+
+{{{ Part of Notebook with outline }}}
+
+To define symbolic expressions in sage .  Use built-in costants and
+function.  Integration , differentiation using sage .  Defining
+matrices.  Defining Symbolic functions .  Simplifying and solving
+symbolic expressions and functions
+    
+
+
+Using sage we can perform mathematical operations on symbols .
+
+On the sage notebook type::
+   
+    sin(y)
+
+It raises a name error saying that y is not defined . But in sage we
+can declare y as a symbol using var function. ::
+   
+    var('y')
+   
+Now if you type::
+
+    sin(y)
+
+     sage simply returns the expression .
+
+thus now sage treats sin(y) as a symbolic expression . You can use
+this to do a lot of symbolic maths using sage's built-in constants and
+expressions .
+
+Try out ::
+   
+   var('x,alpha,y,beta') x^2/alpha^2+y^2/beta^2
+ 
+Similarly , we can define many algebraic and trigonometric expressions
+using sage .
+
+
+
+Sage also provides a few built-in constants which are commonly used in
+mathematics .
+
+example : pi,e,oo , Function n gives the numerical values of all these
+    constants.
+
+For instance::
+
+   n(e)
+   
+   2.71828182845905
+
+gives numerical value of e.
+
+If you look into the documentation of n by doing ::
+
+   n(<Tab>
+
+You will see what all arguments it can take etc .. It will be very
+helpful if you look at the documentation of all functions introduced
+      
+
+Also we can define the no of digits we wish to use in the numerical
+value . For this we have to pass an argument digits.  Type::
+  
+   n(pi, digits = 10)
+
+Apart from the constants sage also has a lot of builtin functions like
+sin,cos,sinh,cosh,log,factorial,gamma,exp,arcsin,arccos,arctan etc ...
+lets try some out on the sage notebook. ::
+     
+   sin(pi/2)
+   
+   arctan(oo)
+     
+   log(e,e)
+
+
+Given that we have defined variables like x,y etc .. , We can define
+an arbitrary function with desired name in the following way.::
+
+       var('x') function(<tab> {{{ Just to show the documentation
+       extend this line }}} function('f',x)
+
+Here f is the name of the function and x is the independent variable .
+Now we can define f(x) to be ::
+
+     f(x) = x/2 + sin(x)
+
+Evaluating this function f for the value x=pi returns pi/2.::
+	   
+	   f(pi)
+
+We can also define function that are not continuous but defined
+piecewise.  We will be using a function which is a parabola between 0
+to 1 and a constant from 1 to 2 .  type the following as given on the
+screen::
+      
+
+      var('x') h(x)=x^2 g(x)=1 f=Piecewise(<Tab> {{{ Just to show the
+      documentation extend this line }}}
+      f=Piecewise([[(0,1),h(x)],[(1,2),g(x)]],x) f
+
+Checking f at 0.4, 1.4 and 3 :: f(0.4) f(1.4) f(3)
+
+for f(3) it raises a value not defined in domain error .
+
+
+Apart from operations on expressions and functions one can also use
+them for series .
+
+We first define a function f(n) in the way discussed above.::
+
+   var('n') function('f', n)
+
+
+To sum the function for a range of discrete values of n, we use the
+sage function sum.
+
+ For a convergent series , f(n)=1/n^2 we can say ::
+   
+   var('n') function('f', n)
+
+   f(n) = 1/n^2
+
+   sum(f(n), n, 1, oo)
+
+For the famous Madhava series :: var('n') function('f', n)
+
+    f(n) = (-1)^(n-1)*1/(2*n - 1)
+
+This series converges to pi/4. It was used by ancient Indians to
+interpret pi.
+
+For a divergent series, sum would raise a an error 'Sum is
+divergent' :: 
+	
+	var('n') 
+	function('f', n) 
+	f(n) = 1/n sum(f(n), n,1, oo)
+
+
+
+
+We can perform simple calculus operation using sage
+
+For example lets try an expression first ::
+
+    diff(x**2+sin(x),x) 2x+cos(x)
+
+The diff function differentiates an expression or a function . Its
+first argument is expression or function and second argument is the
+independent variable .
+
+We have already tried an expression now lets try a function ::
+
+   f=exp(x^2)+arcsin(x) diff(f(x),x)
+
+To get a higher order differentiation we need to add an extra argument
+for order ::
+ 
+   diff(<tab> diff(f(x),x,3)
+
+
+in this case it is 3.
+
+
+Just like differentiation of expression you can also integrate them ::
+
+     x = var('x') s = integral(1/(1 + (tan(x))**2),x) s
+
+
+
+To find factors of an expression use the function factor
+
+    factor(<tab> y = (x^100 - x^70)*(cos(x)^2 + cos(x)^2*tan(x)^2) f =
+    factor(y)
+
+One can also simplify complicated expression using sage ::
+    f.simplify_full()
+
+This simplifies the expression fully . You can also do simplification
+of just the algebraic part and the trigonometric part ::
+
+    f.simplify_exp() f.simplify_trig()
+    
+
+One can also find roots of an equation by using find_root function::
+
+    phi = var('phi') find_root(cos(phi)==sin(phi),0,pi/2)
+
+Lets substitute this solution into the equation and see we were
+correct ::
+
+     var('phi') f(phi)=cos(phi)-sin(phi)
+     root=find_root(f(phi)==0,0,pi/2) f.substitute(phi=root)
+
+
+as we can see the solution is almost equal to zero .
+
+
+We can also define symbolic matrices ::
+
+
+
+   var('a,b,c,d') A=matrix([[a,1,0],[0,b,0],[0,c,d]]) A
+
+
+Now lets do some of the matrix operations on this matrix ::
+
+
+    A.det() A.inverse()
+
+You can do ::
+    
+    A.<Tab>
+
+To see what all operations are available
+
+
+{{{ Part of the notebook with summary }}}
+
+So in this tutorial we learnt how to
+
+
+We learnt about defining symbolic expression and functions .  
+And some built-in constants and functions .  
+Getting value of built-in constants using n function.  
+Using Tab to see the documentation.  
+Also we learnt how to sum a series using sum function.  
+diff() and integrate() for calculus operations .  
+Finding roots , factors and simplifying expression using find_root(), 
+factor() , simplify_full, simplify_exp , simplify_trig .
+Substituting values in expression using substitute function.
+And finally creating symbolic matrices and performing operation on them .
diff -r 234b393cbc85 -r 4032df8f6227 using-sage.rst
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/using-sage.rst	Fri Sep 17 14:32:10 2010 +0530
@@ -0,0 +1,119 @@
+========
+ Script
+========
+
+{{{ show the welcome slide }}}
+
+Welcome to this tutorial on using Sage.
+
+{{{ show the slide with outline }}} 
+
+In this tutorial we shall quickly look at a few examples of the areas
+(name the areas, here) in which Sage can be used and how it can be
+used.
+
+{{{ show the slide with Calculus outline }}} 
+
+Let us begin with Calculus. We shall be looking at limits,
+differentiation, integration, and Taylor polynomial.
+
+{{{ show sage notebook }}}
+
+We have our Sage notebook running. In case, you don't have it running,
+start is using the command, ``sage --notebook``.
+
+To find the limit of the function x*sin(1/x), at x=0, we say::
+
+   lim(x*sin(1/x), x=0)
+
+We get the limit to be 0, as expected. 
+
+It is also possible to the limit at a point from one direction. For
+example, let us find the limit of 1/x at x=0, when approaching from
+the positive side.::
+
+    lim(1/x, x=0, dir='above')
+
+To find the limit from the negative side, we say,::
+
+    lim(1/x, x=0, dir='above')   
+
+Let us now see how to differentiate, using Sage. We shall find the
+differential of the expression ``exp(sin(x^2))/x`` w.r.t ``x``. We
+shall first define the expression, and then use the ``diff`` function
+to obtain the differential of the expression.::
+
+    var('x')
+    f = exp(sin(x^2))/x
+
+    diff(f, x)
+
+We can also obtain the partial differentiation of an expression w.r.t
+one of the variables. Let us differentiate the expression
+``exp(sin(y - x^2))/x`` w.r.t x and y.::
+
+    var('x y')
+    f = exp(sin(y - x^2))/x
+
+    diff(f, x)
+
+    diff(f, y)
+
+Now, let us look at integration. We shall use the expression obtained
+from the differentiation that we did before, ``diff(f, y)`` ---
+``e^(sin(-x^2 + y))*cos(-x^2 + y)/x``. The ``integrate`` command is
+used to obtain the integral of an expression or function.::
+
+    integrate(e^(sin(-x^2 + y))*cos(-x^2 + y)/x, y)
+
+We get back the correct expression. The minus sign being inside or
+outside the ``sin`` function doesn't change much. 
+
+Now, let us find the value of the integral between the limits 0 and
+pi/2. ::
+
+    integral(e^(sin(-x^2 + y))*cos(-x^2 + y)/x, y, 0, pi/2)
+
+Let us now see how to obtain the Taylor expansion of an expression
+using sage. Let us obtain the Taylor expansion of ``(x + 1)^n`` up to
+degree 4 about 0.::
+
+    var('x n')
+    taylor((x+1)^n, x, 0, 4)
+
+This brings us to the end of the features of Sage for Calculus, that
+we will be looking at. For more, look at the Calculus quick-ref from
+the Sage Wiki. 
+
+Next let us move on to Matrix Algebra. 
+
+{{{ show the equation on the slides }}}
+
+Let us begin with solving the equation ``Ax = v``, where A is the
+matrix ``matrix([[1,2],[3,4]])`` and v is the vector
+``vector([1,2])``. 
+
+To solve the equation, ``Ax = v`` we simply say::
+
+    x = solve_right(A, v)
+
+To solve the equation, ``xA = v`` we simply say::
+
+    x = solve_left(A, v)
+
+The left and right here, denote the position of ``A``, relative to x. 
+
+
+
+Now, let us look at Graph Theory in Sage. 
+
+Graph: G = Graph({0:[1,2,3], 2:[4]})
+Directed Graph: DiGraph(dictionary)
+Graph families: graphs. tab
+Invariants: G.chromatic polynomial(), G.is planar()
+Paths: G.shortest path()
+Visualize: G.plot(), G.plot3d()
+Automorphisms: G.automorphism group(), G1.is isomorphic(G2), G1.is subgraph(G2)
+
+Now let us look at bits and pieces of Number theory, combinatorics, 
+