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.

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 paper gives the derivation of a method for determining the forces to be applied to these points which will simulate the load distributed over all the airplane.

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

This thesis is a study of some axioms and theorems, and product spaces.

This thesis covers fundamental properties of metric spaces, as well as completeness, compactness, and separability of metric spaces.

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

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 explores some results of two topological spaces.

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

This study of abstract measure covers classes of sets, measures and outer measures, extension of measures, and planer measure.

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 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.

This thesis examines random variables of one dimension.

The purpose of this paper is to describe the mechanization of the basic equations of motion for the performance and maneuver characteristics of an airplane with some simplifications which render solutions more practicable. The results of a study made to program these equations for calculation by the IBM MODEL 650 digital computer are presented as well as the steps to be taken in using this method of calculation.

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.

This thesis is on ordered pairs of cardinal numbers.

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.

This paper will be concerned with some fundamental properties of a line. In particular, fundamental ordering properties of a line segment are covered.

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.

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

In this study the idea of orthogonality of two lines will be generalized to the idea of orthogonality of two functions. In particular, the orthogonality of two lines may be treated from the standpoint of the orthogonality of two vectors in two-dimensional space.

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.