pandas groupby where you get the max of one column and the min of another column

Use groupby + agg by dict, so then is necessary order columns by subset or reindex_axis. Last add reset_index for convert index to column if necessary.

df = a.groupby('user').agg({'num1':'min', 'num2':'max'})[['num1','num2']].reset_index()
print (df)
  user  num1  num2
0    a     1     3
1    b     4     5

What is same as:

df = a.groupby('user').agg({'num1':'min', 'num2':'max'})
                      .reindex_axis(['num1','num2'], axis=1)
                      .reset_index()
print (df)
  user  num1  num2
0    a     1     3
1    b     4     5