The main Birmingham University web site contains a useful page at http://www.location.bham.ac.uk/ with maps of the university and directions to get to the university from various locations. The School of Mathematics and Statistics is in the Watson building, which is marked on the map as number 33, about ten minutes' walk from the university train station.
Getting a taxi to the university is possible (just) but will turn out to be very expensive. You are much better off taking a train to Birmingham New Street station and changing trains there for University (two stops south on the Redditch/Longbridge line). It is best to buy a ticket for the whole journey when you are at the airport train station. (Ask for a ticket to "university".)
As far as I know Birmingham University is the only UK university with its own train station. So you should ask for a ticket to "University"! (You may have to help the person at the ticket booth out if they haven't heard of this station, but if they start typing "University of Birmingham" in their machine the right station seems to come up quickly.) You will almost certainly travel to Birmingham New Street station and change trains there for University, and provided you buy your ticket to University at the beginning of your journey, it is no more expensive than a ticket to anywhere else in Birmingham! Also, the British train pricing system heavily favours buying return tickets, and these are usually only a few pence more than the equivalent single ticket, so you should almost never buy single tickets.
Train timetables are available on-line at various places including at railtrack's site.
You have two choices, either to use the train and possibly the tube and travel via london (total journey time around three hours) or to travel by bus directly to Birmingham. The railtrack link above will provide timetable information for you by train and tube, the bus alternative is provided by "FlightLink" described in the next paragraph.
"FlightLink" buses (run by National Express) run buses bewteen Heathrow, Birmingham and Manchester Airports, and stop at some city centres, including Birmingham. These provide an easy way to do most of your journey in a single step, but advance booking is, I believe, essential. If you get a FlightLink bus, you should get off at Birmingham city centre and take a local bus (slightly cheaper) or train (much easier) to the university.
Birmingham University has its own train stop, called "University" which is two stops south of Birmingham New Street on the Redditch/Longbridge line.
If you are travelling by car you should probably print off the maps from the university web site (see link above). If travelling to the university from the south, the standard university dirctions describe (or, at least, used to describe) this route as being "too complicated". I beg to differ! From junction 2 of the M42, follow brown tourist signs to "Cadbury World" (or follow signs to Bourneville or Selly Oak). You will pas through Bournville, a very pretty looking suburb near the Cadbury factory and the visitors' centre. Keep going straight on until you meet the Bristol Road (A38) and can see the University Clock Tower. Turn half right here at the traffic lights, and follow the Bristol Road north for a mile until you see the university entrance on the left. If you need to park a car on the campus please inform me in advance.
Richard Kaye
Email: R.W.Kaye@bham.ac.uk
Home page: http://web.mat.bham.ac.uk/R.W.Kaye/
LMS regional meeting and Models 2002:
http://web.mat.bham.ac.uk/R.W.Kaye/models2002/