A taxi from the airport to the city center should cost 40-60 Polish Złoty (9-13 Euro).
There is just one bus 406 at the Airport (Lotnisko - PORT LOTNICZY stop), which goes to the Main Train Station (Dworzec Główny - DWORCOWA stop). You need to go a bit straight and then right to get from the DWORCOWA bus stop to the Main Train Station tram stop.
From the Main Train Station to the Mathematical Institute and the Ołówek dormitory
Take tram 2 (direction Biskupin) and
get off at the PL. GRUNWALDZKI stop (a big square, 6 stops from the train station). You can see Kredka (crayon) and
Ołówek (pencil, in the picture on the left) and walk there as explained here.
If you go in the direction opposite to Ołówek, you will reach the
Grunwaldzki Bridge
and the Mathematical Institute.
