The closest airport is Stuttgart, but it might not have direct flights to get there. The next best alternative is Frankfurt.
If you arrive in Stuttgart, you can take a direct bus from the airport to Tübingen Hauptbahnhof.
Otherwise you can rely on the train network (bahn.de) to get to Tübingen Hauptbahnhof.
To get to the math department you can take busses (Neckarbrücke is the central bus stop in town) and use lines 5, 13, 18 or 19 (anything that goes to "Kliniken"). The bus stop on campus is BG Unfallklinik.