LGRT 1681
In this talk, we'll generalize the familiar notion of "prime number" from the integers to more general settings (rings of integers) which allow for a certain amount of irrationality. The subtleties of rings (sets with addition and multiplicaiton) and fields (commutative rings with inverses) are demonstrated very effectively in this setting. Along the way, we will also see how the search for a proof of Fermat's Last Theorem greatly informed the development of these theories. In essence, this will be a brief and non-rigorous introduction to some important ideas from algebraic number theory.