Richard G. Swan

Expository Papers - R. G. Swan

Tarski's Principle and the Elimination of Quantifiers(pdf)

This is an expository article on Tarski's principle and the elimination
of quantifiers for real closed and algebraically closed fields.
van der Waerden's Theorem on Arithmetic Progressions(pdf)

We give a simplified version of a proof of van der Waerden's
theorem that if a sufficiently long interval of integers is
partitioned into a specified number of parts, one will contain
an arithmetic progression of given length.
The Morse Sequence(pdf)

We give a proof that the Morse sequence has no 3 times repeated block
and derive from it a sequence on 3 letters that has no repeated block.
Goldie's Theorem(pdf)

This is an exposition of Goldie's theorem with a section on Ore localization
and with an application to defining ranks for finitely generated modules
over non--commutative noetherian rings.
The Flabby Class Group of a Finite Cyclic Group(pdf)

This is an expository paper on work of Endo and Miyata which leads
to a computation of the flabby class group of a finite cyclic group.
Ptolemy's Theorem and its Converse(pdf)

This is an expository paper on Ptolemy's Theorem giving a simple
algebraic proof of the theorem and its converse.