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

Some of the properties of the specific summation methods will be investigated, such as what type of divergent series a method can or cannot sum, if the insertion of zeros into a series does change the sum, and when different methods give the same sum for a series.

This paper is concerned with equations in which all derivatives are ordinary rather than partial derivatives. The customary meanings of differential order and difference order of an equation are observed.

This paper will be devoted to an exposition of some of the relationships existing between a field and certain of its extension fields. In particular, it will be shown that many fields may be characterized rather simply in terms of their subfields which, in turn, may be directly correlated with the subgroups of a finite group of automorphisms of the given field.

One of the classic theorems concerning the real numbers states that every open cover of a closed and bounded subset of the real line contains a finite subcover. Compactness is an abstraction of that notion, and there are several ideas concerning it which are equivalent and many which are similar. The purpose of this paper is to synthesize the more important of these ideas. This synthesis is accomplished by demonstrating either situations in which two ordinarily different conditions are equivalent or combinations of two or more properties which will guarantee a third.

This thesis discusses groups, modules, the module of homomorphisms, and extension of modules.

The purpose of this paper is to investigate some of the more basic properties of peripherally continuous functions, graph maps and connectivity maps.

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.

This thesis describes semigroups and the properties of both regular and inverse semigroups.