The field of infinite series is so large that any investigation into that field must necessarily be limited to a particular phase. An attempt has been made to develop a number of tests having a wide range of applications. Particular emphasis has been placed on tests for series of positive terms.

The purpose of this paper is to develop certain fundamental properties of exhaustible sets and their complements and to examine various set properties which are generalizations, with respect to exhaustible neglect, or well-known set properties.

The purpose of this paper is to present proofs for six cases of L'Hospital's Rule for the evaluation of indeterminate forms. It is also a purpose to reduce to one of these six cases some other indeterminate forms to which L'Hospital's Rule is applicable. In the course of presenting these proofs several theorems and definitions will be used without proof.

This thesis attempts to prove the Lebesgue measure is a concrete realization of measure.

The object of this paper is to define, to establish necessary and sufficient conditions for the existence of, and to consider the elementary properties of the Riemann definite integral of a bounded function.

The elementary notion of a function originated in the work of mathematicians of the seventeenth century, and was somewhat closely connected with investigations in the field of algebra. This paper will be concerned with an investigation of a generalized type of continuity known as semi-continuity.

It will be our purpose to study a generalized definition of sum of a series and the restrictions which must be placed upon it in order that it shall satisfy the generally accepted requirements of any generalized definition of sum of a series. We shall then proceed to investigate the possibilities of further generalizing this process.

This thesis is a study of the analytical development of the trigonometric functions.

This thesis covers the development of the natural numbers by means of the peano postulates.

This study covers means, mean value theorems of the differential calculus, and mean value theorems of integral calculus.

In this paper, we will be concerned primarily with series of functions and a particular type of convergence which will be described. The purpose of this paper is to familiarize the reader with the concept of uniform convergence. In the main it is a compilation of material found in various references and revised to conform to standard notation.

It is the purpose of this paper to define a Lebesgue integral over a measurable set, the integration being performed with respect to a monotone non-decreasing function as in the Stieltjes integral, and to develop a few of the fundamental properties of such an integral.

This paper is concerned with certain properties of derivatives and some characterizations of linear point sets with derivatives. In 1946, Zygmunt Zahorski published a letter on this topic listing a number of theorems without proof, and no proof of these assertions has been published. Some of the theorems presented here are paraphrases of Zahorski's statements, developed in a slightly different order.

In this thesis, we shall attempt to present a study of certain properties of real functions related to the set property exhaustible.

It is the purpose of this thesis to indicate in more detail how various limits defined in analysis, as well as other concepts not ordinarily defined as limits, may be obtained as special cases of the Moore-Smith limit.

This thesis discusses a development of the exponential and logarithmic functions.

This thesis discusses a theorem on the convergence of a continued fraction.

The purpose of this paper is to derive certain of the fundamental properties of the Dini derivatives of an arbitrary real function. To this end it will be necessary to investigate the properties of the limits superior and inferior of real functions and to prove the Vitali Covering Theorem as well as a fundamental theorem on the metric density of arbitrary point sets.

The purpose of this paper is to define and develop a set of functions of an area in such a manner as to be analogous to the trigonometric and the hyperbolic functions.

This thesis is intended as an introduction to the study of one type of trigonometric series, the Fourier series.

The purpose of this thesis is to present a study of the Lebesgue definite integral, defined in four different ways.

The purpose of this thesis is to restate the definition of the integral as given by O. Perron, to establish some of the fundamental properties of the Perron integral, and to prove the equivalence between the Perron and Lebesgue integrals in the bounded case.

This thesis explores some results of two topological spaces.

The object of this thesis is (1) to demonstrate the value of an electronic analog computer for the solution of non-linear ordinary differential equations particularly when a large family of solutions is required; and (2) to obtain as a by-product results of practical applicability to servomechanism selection and analysis.