I was wondering if someone could explain this to me. My university is
running a switched ethernet network. I was under the impression that a
switched network meant that I would not see packets which were not sent to
me (assuming they weren't sent to a broadcast address).

However, when I run WinPCap and check for New TCP Sessions, I routinely see
packets that are not addressed to me or to a broadcast address. These seem
to be the initial packets as the ACK=0 and SYN=1.

Can someone explain this to me? Or point me to a site that would do so?