The main purpose of this paper is the study of transformations in topological space and relationships between special types of transformations.

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 describes various forms of metric spaces and establishes some of the properties of functions defined on metric spaces. No attempt is made in this paper to examine a particular type of function in detail. Instead, some of properties of several kinds of functions will be observed as the functions are defined on various forms of metric spaces such as connected spaces, compact spaces, complete spaces, etc.

The main problems of numerical analysis involve performing analytical operations, such as integration, differentiation, finding zeroes, interpolation, and so forth, of a function when all the data available are some samples of the function. Therefore, the purpose of this paper is to investigate the following problem: given a set of data points (x[sub i], y[sub i]) which are samples of some function, determine an approximating function. Further, extend the problem to that of determining an approximating function for a surface given some samples (x[sub i], y[sub j], z[sub ij]) of the surface.

It is intended that this paper present an acceptable proof of the existence of a solution for the wave equation.

Explores topological spaces, filters, and nets with definitions and examples.

The purpose of this paper is to develop some of the more basic Fourier transforms which are the outgrowth of the Fourier theorem. Although often approached from the stand-point of the series, this paper will approach the theorem from the standpoint of the integral.

The purpose of this thesis is to define equivalence classes of Cauchy sequences of rational numbers and the operations of taking a sum and a product and then to show that this system is an uncountable, ordered, complete field. In so doing, a mathematical system is obtained which is isomorphic to the real number system.

The purpose of this thesis is to develop some properties of a special class of functions called valuations. The study begins with and examination of the properties of valuations defined on an arbitrary field, F, and later, consideration is given to valuations defined on the field of rational numbers. The concept of a pseud-valuation is introduced and an investigation is made of the properties of pseudo-valuations.

The purpose of this thesis is to examine general properties, convergence, and limit points of sequences of real numbers.

The purpose of this thesis is to present a definition and some properties of a curved arc in a plane and to present a definition and some properties of the Jordan curve.

This thesis is an investigation of some of the properties of polynomial rings, unique factorization domains, Euclidean domains, and principal ideal domains. The nature of some of the relationships between each of the above systems is also developed in this paper.

The purpose of this paper is devoted to investigating some fundamental properties of valuations and places.

In this paper, elementary properties of relative extreme points are investigated. The properties are defined in linear and topological terms. Proofs of many of these properties require the use of topological concepts.

This thesis analyzes tensor associations with applications to Reimann spaces.

This thesis examines linear programming problems, the theoretical foundations of the simplex method, and how a liner programming problem can be solved with the simplex method.

This paper will be devoted to an examination of several general and specific equations and systems of equations of the diophantine type. Only algebraic equations with integral coefficients, not all zero, will considered. The elementary properties of the integers will be assumed.

This paper is devoted to finding integral solutions of algebraic equations. Only algebraic equations with integral coefficients are considered. The elementary properties of integers are assumed.

This thesis discusses elliptic geometry including the order and incidence properties, projective properties and congruence properties.

This thesis investigates ideals in semigroups.

The purpose of this paper is to study convergence of certain continued fractions.

This thesis presents a series of theorems and proofs describing a twenty-five point geometry in which exists exactly thirty lines.

This thesis examines pseudo-groups and complex groupable lattices.

This paper examines the relationship between Borel sets and Baire functions.