pandas - return column of exponential values

Well math.exp doesn't understand Series datatype, use numpy np.exp which does and is vectorised so operates on the entire column:

In [24]:
df['exp'] = np.exp(df['b'])
df

Out[24]:
   a     b       exp
0  0  0.71  2.033991
1  1  0.75  2.117000
2  2  0.80  2.225541
3  3  0.90  2.459603