Some applications of computing to number theory

This thesis describes the application of a computer to certain problems in number theory. Chapter 1 is a general description of the use of computers in this field. Chapter 2 contains the results of computations relating to certain non - congruence subgroups of the full modular group, while chapter 3 describes the use of variable precision arithmetic, mainly in connection with continued fraction expansions. The last chapter describes a small library of subroutines, the majority of which are written in Fortran. A computer - printed listing of these subroutines is given at the end of the thesis.