SUMS: Lee -- Diophantine Analysis and Transcendental Numbers

This week’s SUMS talk is by Honours student David Lee.  

Abstract: 
Transcendental numbers are real or complex numbers that are not algebraic,
that is not a root of a non zero polynomial with rational coefficients.  The existence
of Transcendental numbers is not immediately obvious.  In fact the first proof that a
particular number has this property was discovered in the mid-19th century.  

For this talk we are going to establish the connection between transcendental numbers
and approximation by rational numbers.  Whilst this connection may seem unusual at
first, it is a key approach in proving certain numbers are transcendental.