diff --git a/dynamic_programming/coin_change.py b/dynamic_programming/coin_change.py
index a85d8e08dbb1..12ced411780f 100644
--- a/dynamic_programming/coin_change.py
+++ b/dynamic_programming/coin_change.py
@@ -8,6 +8,18 @@
 
 
 def dp_count(S, m, n):
+    """
+    >>> dp_count([1, 2, 3], 3, 4)
+    4
+    >>> dp_count([1, 2, 3], 3, 7)
+    8
+    >>> dp_count([2, 5, 3, 6], 4, 10)
+    5
+    >>> dp_count([10], 1, 99)
+    0
+    >>> dp_count([4, 5, 6], 3, 0)
+    1
+    """
 
     # table[i] represents the number of ways to get to amount i
     table = [0] * (n + 1)
@@ -24,7 +36,7 @@ def dp_count(S, m, n):
 
     return table[n]
 
-
 if __name__ == "__main__":
-    print(dp_count([1, 2, 3], 3, 4))  # answer 4
-    print(dp_count([2, 5, 3, 6], 4, 10))  # answer 5
+    import doctest
+
+    doctest.testmod()
diff --git a/linear_algebra/src/lib.py b/linear_algebra/src/lib.py
index 5ce0f696ad71..bf9e0d302a89 100644
--- a/linear_algebra/src/lib.py
+++ b/linear_algebra/src/lib.py
@@ -27,7 +27,7 @@
 
 class Vector(object):
     """
-        This class represents a vector of arbitray size.
+        This class represents a vector of arbitrary size.
         You need to give the vector components. 
         
         Overview about the methods:
@@ -37,7 +37,7 @@ class Vector(object):
         __str__() : toString method
         component(i : int): gets the i-th component (start by 0)
         __len__() : gets the size of the vector (number of components)
-        euclidLength() : returns the eulidean length of the vector.
+        euclidLength() : returns the euclidean length of the vector.
         operator + : vector addition
         operator - : vector subtraction
         operator * : scalar multiplication and dot product
@@ -46,11 +46,13 @@ class Vector(object):
         TODO: compare-operator
     """
 
-    def __init__(self, components=[]):
+    def __init__(self, components=None):
         """
             input: components or nothing
             simple constructor for init the vector
         """
+        if components is None:
+            components = []
         self.__components = list(components)
 
     def set(self, components):
@@ -86,9 +88,9 @@ def __len__(self):
         """
         return len(self.__components)
 
-    def eulidLength(self):
+    def euclidLength(self):
         """
-            returns the eulidean length of the vector
+            returns the euclidean length of the vector
         """
         summe = 0
         for c in self.__components:
@@ -112,7 +114,7 @@ def __sub__(self, other):
         """
             input: other vector
             assumes: other vector has the same size
-            returns a new vector that represents the differenz.
+            returns a new vector that represents the difference.
         """
         size = len(self)
         if size == len(other):
@@ -136,7 +138,7 @@ def __mul__(self, other):
                 summe += self.__components[i] * other.component(i)
             return summe
         else:  # error case
-            raise Exception("invalide operand!")
+            raise Exception("invalid operand!")
 
     def copy(self):
         """
@@ -223,7 +225,7 @@ class Matrix(object):
 
     def __init__(self, matrix, w, h):
         """
-            simple constructor for initialzes 
+            simple constructor for initializing
             the matrix with components.
         """
         self.__matrix = matrix
@@ -249,7 +251,7 @@ def changeComponent(self, x, y, value):
         """
             changes the x-y component of this matrix
         """
-        if x >= 0 and x < self.__height and y >= 0 and y < self.__width:
+        if 0 <= x < self.__height and 0 <= y < self.__width:
             self.__matrix[x][y] = value
         else:
             raise Exception("changeComponent: indices out of bounds")
@@ -258,7 +260,7 @@ def component(self, x, y):
         """
             returns the specified (x,y) component
         """
-        if x >= 0 and x < self.__height and y >= 0 and y < self.__width:
+        if 0 <= x < self.__height and 0 <= y < self.__width:
             return self.__matrix[x][y]
         else:
             raise Exception("changeComponent: indices out of bounds")