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

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

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

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.

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.

This thesis investigates atmospheric gusts and their effect on aircraft.

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 thesis examines random variables of one dimension.

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

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

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

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.

In this paper a definitions shall be given for different types of improper integrals and several theorems concerning them shall be proved.

This paper considers the concept of inner and outer content, which was introduced by Camille Jordan and Giuseppe Peano near the end of the nineteenth century.

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

This thesis is on ordered pairs of cardinal numbers.

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.

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

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.