This thesis brings together under one cover a survey
of the history of the real number e along with a study
of the present state of its theory and calculation.
The notion of a normal number and the Normal Number Theorem date back over 100 years. Émile Borel first stated his Normal Number Theorem in 1909. Despite their seemingly basic nature, normal numbers are still engaging many mathematicians to this day. In this paper, we provide a reinterpretation of the...
This white paper gives an overview of the software applications used by university presses to publish digital monographs. In addition, we will look at routes taken by university presses to move from all print to some e-publishing and list the supplemental online content that is typically offered for a fee.
We introduce a numerical criterion which allows us to bound the degree of any algebraic integer having all of Galois conjugates in an interval of length less than 4. Using this criterion, we study two arithmetic dynamical questions with local rationality conditions. First, we classify all unicritical polynomials defined over...
The height of an algebraic number A is a measure of how arithmetically complicated A is. We say A is totally p-adic if the minimal polynomial of A splits completely over the field of p-adic numbers. In this paper, we investigate what can be said about the smallest nonzero height...
By using continued fractions the set of positive
irrationals can be put in one to one correspondence
with the set of sequences of positive integers. The
entries of an arbitrary sequence of integers can be any
subset of Z and each integer appearing can occur once,
infinitly often, or anything...
Let A and B be two subsets of the set of all non-negative
integers with 0 ε A and O ε B. The sum of the sets A and B is
the set C = A + B = {a + b: a ε A, b ε B). For n...