Publication Date
12-2015
Date of Final Oral Examination (Defense)
10-9-2015
Type of Culminating Activity
Thesis
Degree Title
Master of Science in Mathematics
Department
Mathematics
Major Advisor
Andrés Caicedo, Ph.D.
Major Advisor
Zachariah Teitler, Ph.D.
Advisor
Samuel Coskey, Ph.D.
Advisor
Marion Scheepers, Ph.D.
Abstract
One type of conditionally convergent series that has long been considered by mathematicians is the Alternating Harmonic Series and its sum under various types of rearrangements. The purpose of this thesis is to introduce results from the classical theory of rearrangements dating back to the 19th and early 20th century. We will look at results by mathematicians such as Ohm, Riemann, Schlömilch, Pringsheim, and Sierpiński. In addition, we show examples of each classical result by applying the Alternating Harmonic Series under the different types of rearrangements, and also introducing theorems by Lévy and Steinitz, and Wilczyński which are modern extensions of results of Sierpiński.
Recommended Citation
Agana, Monica Josue, "The Classical Theory of Rearrangements" (2015). Boise State University Theses and Dissertations. 1039.
https://scholarworks.boisestate.edu/td/1039