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 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 purpose of this study is to show the use of random sampling in solving certain mathematical problems. The origin of random numbers to be used in sampling is discussed and methods of sampling from known distributions are then given together with an indication that the sampling procedures are unbiased.

This thesis examines random variables of one dimension.

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 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.

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.

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.

This thesis is on ordered pairs of cardinal numbers.

Since infinite products are seldom encountered in elementary mathematics, it is the purpose of this paper to familiarize the reader with their concept and properties. In the main, it is the compilation of material found in various references and revised to conform to standard notation.

The primary purpose of this paper is to state a set of postulates for Boolean algebra and show the characteristic theorems derivable from them, and to unify in one paper the more important methods of representing Boolean algebra and show their equivalence.

This paper will be concerned with the convergence of complex power series.

This thesis investigates atmospheric gusts and their effect on aircraft.

The principal purpose of this paper is to develop the properties of Riemann-Stieljes Integrals. Consequently, a knowledge of the terminology and theory of point sets and functions of real variables shall be assumed.

This thesis is concerned with an investigation of the generalizations of continuous real functions of a real variable. In particular, the relationship between uniform continuity and ordinary continuity is concerned. The concept of uniform continuity was first introduced by Heine about 1900.

This study involves the ultraspherical polynomials, the Legendre polynomials, the Tchebichef polynomials of the first kind, and the Tchebichef polynomials of the second kind.

This paper is a study of the properties of commutators, and deals exclusively with finite groups.

This paper will be mostly concerned with matrices of infinite order with elements which lie in Hilbert Space. All the properties of real and complex numbers and all the properties of infinite series and infinite sequences that are not listed will be assumed.

This paper is an extension of various projects that the writer has been associated with at Chance Vought Aircraft, Incorporated.

This paper shall be mostly concerned with the development and the properties of three quadratic polynomials. The primary interest will by with n-ary quadratic polynomials, called forms.

The purpose of this thesis is to provide a beginning graduate student in mathematics with the general theory underlying competition between rational, intelligent opponents. This competition can be described as a game of opposing strategies; hence, the name game theory.