Do you have any idea that £ódź Widzew is far from al. Politechniki? I stay in there.
£ódź Widzew is never the set-off station. In most cases trains from £ódź Fabryczna stop at £ódź Widzew while trains from £ódź Kaliska stop at £ódź Żabieniec railstation. However I thought that trains to Cracow set off at £ódź Kaliska mostly.
I've checked it for you: IR train is at 6.14 a.m. from £ódź Fabryczna, arrives to Cracow about 11 o'clock. The next direct train is at 4.46 p.m. And those are the only direct trains to Cracow. On the other hand there many trains from £ódź Kaliska (TLK).
Prices:
IR 43,50 PLN (if you have students' discount you have to take 33%)
TLK 50-56 PLN for second class ticket (depends on hour, not sure about the students' discount)
Attention: you have to check if those trains still course at that day you're leaving
Another option would be pks bus (pks station is at Fabryczny dworzec).
not sure about the students' discount
ok, I believe that if you take second class then the students' discount are in force, so there is no big difference in price of tickets