This thesis documents a method of proving that Turing machines
work for every case, if the construction of the Turing machine is
known. Mathematical Induction is used to construct the proof that the
Turing machine for binary addition will work in every well-formed case
of the input that it receives....
An operator scheme for composition of Turing machines is
developed and applied to the computation of the recursive functions
over an arbitrary alphabet.
Computational scheme, equivalence, and Turing machine are
defined. Some computational schemes are examined and shown to
be equivalent to the computational scheme of a Turing machine.
