integrate some widgets

source/background/functions/00_basic_notation.mdown

@@ -50,6 +50,33 @@ for _ in range(10):
     print("The output of random_output({}) is {}".format(5, random_output(5)))
 ```
 
+```python
+import random
+import re
+import ipywidgets
+from ipywidgets import Button, Layout
+
+from IPython.display import display
+
+# a programming function that is not a mathematical function
+def random_output(number):
+    # randomly choose between two outputs
+    if random.choice([True, False]):
+        return 2 * number
+    else:
+        return 3 * number
+
+b = ipywidgets.Button(description='Click to run randomization',
+           layout=Layout(width='50%', height='80px'))
+display(b)
+
+def on_button_clicked(b):
+    for _ in range(10):
+        print("The output of random_output({}) is {}".format(5, random_output(5)))
+
+b.on_click(on_button_clicked)
+```
+
 ## Domains and co-domains
 
 Every function has a **domain** and a **co-domain**.

source/background/functions/01_monotonicity.mdown

@@ -39,6 +39,32 @@ for func in [f, g, h, i]:
     plt.show()
 ```
 
+```python
+import numpy as np
+import matplotlib.pyplot as plt
+import ipywidgets
+from ipywidgets import Button, Layout
+
+from IPython.display import display
+
+f = lambda x: 2*x
+g = lambda x: x**2
+h = lambda x: 2*x - 2**(x - 5) + 2**10
+i = lambda x: x/2 - 2**x
+
+b = ipywidgets.Button(description='Show graphs',
+           layout=Layout(width='50%', height='80px'))
+display(b)
+
+def on_button_clicked(b):
+    for func in [f, g, h, i]:
+        values = np.linspace(-10, 10)
+        plt.plot(values, func(values))
+        plt.show()
+
+b.on_click(on_button_clicked)
+```
+
 A function is monotonic iff it does not change direction: once it goes up, it cannot go down, and the other way round.
 Among the functions above, only the first and the last are monotonic.