In the numerous problems of matrix algebra, one finds the problem of determining the eigenvalues of eigenvectors of a matrix quite frequently. The theory and methods leading to the solution of the eigenvalue and eigenvector problem are of considerable interest. The relation between vector spaces, matrices, eigenvalues, and eigenvectors is to be considered in this chapter, with particular concentration directed toward the eigenvalues and eigenvectors shall be developed in the following chapters with detailed examples of the methods.

The purpose of this paper is to explore some of the properties of the Cantor set and to extend the idea of this set to metric spaces, in general, and to other sets of real numbers and sets in N-dimensional Euclidean space, in particular.

The purpose of this paper is to study two differential equations. A method of approximation by iteration is used to define sequences of functions which converge to solutions of these equations. Some properties of the solutions are proved for general boundary conditions and certain special solutions are studied in detail.

This paper deals with the development of the convolution ring and the construction of a field from this ring.

This thesis examines pseudo-groups and complex groupable lattices.

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 purpose of this chapter is to develop a form of a "free" Boolean algebra with Σ as a base, by imposing the usual Boolean operations on the set Σ and thus generating new elements freely within explicitly prescribed restrictions.

This paper will be concerned mainly with automorphisms of groups. The concept of a group endomorphism will be used at various points in this paper.

A set of definitions, theorems and proofs to describe the Laplace transformation.

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 examine general properties, convergence, and limit points of sequences of real numbers.

This thesis investigates ideals in semigroups.

This thesis examines measure functions. A measure function has as its domain of definition a class of sets. It also must satisfy a certain additive condition. To state a concise definition of a measure function, it is convenient to define set function and completely additive set function.