Binary forms and cubic fields

A binary form is a homogeneous polynomial of degree n in two variables. One can define an equivalence relation on these forms by a certain linear transformation of the variables.  In this talk, we present the classical results on the theory of binary forms of degree two and three.  We also highlight the connection between this theory and cubic fields.  Finally, we explain how this fits in with my thesis research.

 Frequent use of the phrases: ``The rest are similar," ``this clearly holds" and ``I don't know" should be expected. This talk will be accesible to anyone who doesn't take what I have to say too seriously and inaccesible to anyone who demands a rigorous definition of the objects in question.