Transcendental Numbers

A number is called transcendental if it is not algebraic, that is it does not satisfy a polynomial equation with rational coefficients. It is easy to see that the algebraic numbers are countable, hence the transcendental numbers are uncountable. Despite this fact, it turns out to be very difficult to determine whether a given number is transcendental. In this talk I will discuss some famous examples and the theorems which allow one to construct many different transcendental numbers. I will also give an outline of some of the many open problems in the field.