A transcendental number is a complex number which is not the root of a polynomial in ℚ[x]. We will give an accessible introduction to the theory of real transcendental numbers. We will touch on basic properties of transcendental numbers (like they actually exist), Liouville's theorem, irrationality measure and Roth's theorem. Time permitting we will include a construction of transcendental numbers relating to the undecidability of the halting problem over Turing machines.
An Introduction to Transcendental Number Theory