This paper establishes a basis for abelian categories, then gives the statement and proof of two equivalent definitions of an abelian category, the development of the basic theory of such categories, and the proof of some theorems involving this basic theory.

This thesis is a study of primary Abelian groups and height.

The basis for this thesis is H. S. Wall's book, Creative Mathematics, with particular emphasis on the chapter in that book entitled "More About Linear Spaces."

The primary purpose of this thesis is to carefully develop and prove some of the fundamental, classical theorems of the differential calculus for functions of two real variables.

The purpose of this paper is to investigate some properties of compact topological spaces and to relate these concepts to the separation properties.

This paper will investigate the geometry that results when Euclid's fifth postulate is replaced by the Lobachevskian assumption. The investigations will be limited to the plane.

This thesis provides a development of integration from two different points of view. In Chapter I, a measure and a measurable function are defined. A theory of integration is then developed in Chapter II based on the measure. In Chapter III, the integral is introduced directly without first going through the process of defining a measure, and a measure is developed from the integral. The concluding chapter shows the equivalence of the two integrals under rather general conditions.

This paper is an introductory, algebraic study of semigroups.

This thesis is presented as an introduction to the Fibonacci sequence of integers. It is hoped that this thesis will create in the reader more interest in this type of sequence and especially the Fibonacci sequence. It seems that this particular area of mathematics is often ignored in the classroom or touched upon far too briefly to stimulate curiosity and develop further interest in this field.

The usual practice in any discussion of an inner-product space is to restrict the field over which the inner-product space is defined to the field of complex numbers. In defining the inner-product function, (x,y), a second function is needed; namely the conjugate function (x,y)* so that (x,y) ± (y,x)*. We will attempt to generalize this concept by investigating the existence of a conjugate function defined on fields other than the field of complex numbers and relate this function to an inner-product function defined on a linear space L over these fields.

The purpose of this paper is the analysis of functions of real numbers which have a special additive property, namely, f(x+y) = f(x)+f(y).

The purpose of this paper is to present a study of partly ordered sets. It includes a rigorous development of relations based on the notion of a relation as a set, lattices, and theorems concerning the lattice of subgroups of a group.

This thesis presents a series of theorems along with proofs to establish a theory of congruences.

This paper investigates the Runge-Kutta method of numerically integrating ordinary differential equations. An existence theorem is given insuring a solution to the differential equation, then the theorem is modified to yield an analytic solution. The derivation of the method itself is followed by an analysis of the inherent error.

This thesis is a study of fundamental properties of Hilbert space, properties of linear manifold, and realizations of Hilbert space.

The main purpose of this paper is to make a detailed study of a certain class T of complex functions. The functions of the class T have a special mapping property and are meromorphic in every region. As an application of this study, certain elementary functions are defined and studied in terms of a special T-function.