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+########## Break Here ##########
+
+Now, let us look at Graph Theory in Sage. 
+
+We shall look at some ways to create graphs and some of the graph
+families available in Sage. 
+
+The simplest way to define an arbitrary graph is to use a dictionary
+of lists. We create a simple graph by using the ``Graph()`` function.
+
+.. L17
+::
+
+    G = Graph({0:[1,2,3], 2:[4]})
+
+.. R18
+
+to view the visualization of the graph, we say 
+
+.. L18
+::
+
+    G.show()
+
+.. R19
+
+Similarly, we can obtain a directed graph using the ``DiGraph``
+function. 
+
+.. L19
+::
+
+    G = DiGraph({0:[1,2,3], 2:[4]})
+
+.. R20
+
+Sage also provides a lot of graph families which can be viewed by
+typing ``graph.<tab>``. Let us obtain a complete graph with 5 vertices
+and then show the graph. 
+
+.. L20
+::
+
+    G = graphs.CompleteGraph(5)
+
+    G.show()
+
+.. R21
+
+Sage provides other functions for Number theory and
+Combinatorics. Let's have a glimpse of a few of them.  
+``prime_range`` gives primes in the range 100 to 200. 
+
+.. L21
+::
+
+    prime_range(100, 200)
+
+.. R22
+
+``is_prime`` checks if 1999 is a prime number or not. 
+
+.. L22
+::
+
+    is_prime(1999) 
+
+.. R23
+
+``factor(2001)`` gives the factorized form of 2001. 
+
+.. L23
+::
+
+    factor(2001)
+
+.. R24
+
+The ``Permutations()`` gives the permutations of ``[1, 2, 3, 4]``
+
+.. L24
+::
+
+    C = Permutations([1, 2, 3, 4])
+    C.list()
+
+.. R25
+
+And the ``Combinations()`` gives all the combinations of ``[1, 2, 3, 4]``
+
+.. L25
+::
+
+    C = Combinations([1, 2, 3, 4])
+    C.list()
+
+.. L26
+
+{{{ Show summary slide }}} 
+
+.. R26
+
+This brings us to the end of the tutorial.In this tutorial, 
+we have learnt to,
+
+ 1. Use functions for calculus like --
+    - lim()-- to find out the limit of a function
+    - diff()-- to find out the differentiation of an expression
+    - integrate()-- to integrate over an expression  
+    - integral()-- to find out the definite integral of an 
+      expression by specifying the limits
+    - solve()-- to solve a function, relative to it's position. 
+ #. Create Both a simple graph and a directed graph, using the 
+    functions ``graph`` and ``digraph`` respectively.
+ #. Use functions for Number theory.For eg: 
+    - primes_range()-- to find out the prime numbers within the 
+      specified range
+    - factor()-- to find out the factorized form of the number specified
+    - Permutations(), Combinations()-- to obtain the required permutation 
+      and combinations for the given set of values.  
+
+.. L27
+
+{{{Show self assessment questions slide}}}
+
+.. R27
+
+Here are some self assessment questions for you to solve
+
+1. How do you find the limit of the function ``x/sin(x)`` as ``x`` tends 
+   to ``0`` from the negative side.
+
+
+2. List all the primes between 2009 and 2900
+
+
+3. Solve the system of linear equations
+     
+    x-2y+3z = 7
+    2x+3y-z = 5
+    x+2y+4z = 9
+
+.. L28
+
+{{{solution of self assessment questions on slide}}}
+
+.. R28
+
+And the answers,  
+
+1. To find out the limit of an expression from the negative side,we add 
+   an argument dir="left" as
+::
+
+    lim(x/sin(x), x=0, dir="left")
+
+2. The prime numbers from 2009 and 2900 can be obtained as,
+::
+
+    prime_range(2009, 2901)
+
+3. We shall first write the equations in matrix form and then use the 
+   solve() function
+::
+
+    A = Matrix([[1, -2, 3], 
+                [2, 3, -1], 
+                [1, 2, 4]])
+
+    b = vector([7, 5, 9])
+
+    x = A.solve_right(b)
+
+To view the output type x
+::
+    
+    x 
+