diff --git a/MDP/MDP_David_class_first_example.py b/MDP/MDP_David_class_first_example.py
new file mode 100644
index 000000000..35e5fded8
--- /dev/null
+++ b/MDP/MDP_David_class_first_example.py
@@ -0,0 +1,76 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Jul 10 10:51:18 2018
+
+@author: olmer.garciab
+"""
+
+# implementing class example
+
+P=[[0,0.5,0,0,0.,0.5,0],
+   [0,0,0.8,0,0.0,0,0.2],
+   [0,0.,0,0.6,0.4,0,0],
+   [0,0.,0,0,0.,0,1],
+   [0.2,0.4,0.4,0,0,0,0],
+   [0.1,0.,0,0,0.,0.9,0],
+   [0,0.,0,0,0.,0,1]]
+R=[-2,-2,-2,10,1,-1,0]
+
+
+# total dicount reward
+def G_t(S,R,gamma):
+    g=0
+    for s,i in zip(S,range(len(S))): 
+        g=g+R[s]*gamma**i  
+    return g
+
+#g = lambda y: sum(  f(y) for f in (lambda x: x**i for i in range(n))  )
+# for example for the chain of state S_1
+gamma=0.5
+S_1=[0,1,2,3,6]
+print(G_t(S_1,R,gamma))
+
+
+
+
+#dynamic programming
+#based in #https://harderchoices.com/2018/02/26/dynamic-programming-in-python-reinforcement-learning/
+def iterative_value_function(N, theta=0.0001, gamma=0.9):
+    V_s =R.copy() # 1.
+    probablitiy_map = P # 2.
+    delta = 100 # 3.
+    while not delta < theta: # 4.
+        delta = 0 # 5.
+        for state in range(0,N): # 6.
+            v = V_s[state] # 7.
+            
+            total =R[state] # 8.
+            for state_prime in range(0,N):
+                total += probablitiy_map[state][state_prime] * (gamma * V_s[state_prime])
+                #print(total)
+                
+            V_s[state] =total # 9.
+            delta = max(delta, abs(v - V_s[state])) # 10.
+            #print(delta)
+    V_s=[round(v,2) for v in V_s]
+    return V_s # 11.
+
+
+N=len(R)
+
+
+
+
+print('gamma',0.9,iterative_value_function(N,gamma=0.9))
+print('gamma',1,iterative_value_function(N,gamma=1))
+print('gamma',0,iterative_value_function(N,gamma=0))
+
+
+#vectorial way
+import numpy as np
+from numpy.linalg import inv
+gamma=0.9
+P=np.array(P)
+R=np.array(R).reshape((-1,1))
+v=np.matmul(inv(np.eye(N)-gamma*P),R)
+print(v)