you don't serialize classes. classes are already serialized in the form of class bytes. you serialize instances of classes. call me a nit-pick if you want, but it's an important difference, and also leads on to answer your question: no, methods in java are bound to a class, not an instance of a class
the fact that you asked the question leads me to believe you don't quite understand what serialization is, and what we use it for, though. what did you intend to do with a serialized method?