We define an irrationality measure and show how irrationality measures can be used to bound the size of solutions to Thue equations. We give a review of some of the major results about binary Thue equations.
We study the Hypergeometric Method. We prove an important theorem which shows how irrationality measures can be constructed from sequences of rational numbers. We explicitly construct irrationality measures for some degree 3 algebraic irrationalities.
We look at the application of irrationality measures to binary Thue equations. Throughout this chapter we illustrate each theorem with an example equation using the irrationality measures we constructed.
We look at applications of restricted irrationality measures to continued fractions and exponential Diophantine equations. We prove a theorem about the size of solutions to the generalized Ramanujan-Nagell equation.