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An Approximate Solution to the Dirichlet Problem

Description: In the category of mathematics called partial differential equations there is a particular type of problem called the Dirichlet problem. Proof is given in many partial differential equation books that every Dirichlet problem has one and only one solution. The explicit solution is very often not easily determined, so that a method for approximating the solution at certain points becomes desirable. The purpose of this paper is to present and investigate one such method.
Date: August 1964
Creator: Redwine, Edward William
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Equivalence Classes of Cauchy Sequences of Rational Numbers

Description: 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.
Date: January 1965
Creator: Darnell, Linda Jane
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Topological Properties of Chains

Description: The purpose of this paper is to define and investigate some of the properties of chains. Particular attention is given to a natural topology for chains, called the interval topology, and how the chain properties and topological properties of chains affect each other.
Date: January 1966
Creator: Womack, Robert A.
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Which Came First : The Measure or the Integral?

Description: 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.
Date: June 1966
Creator: Chapman, John Barnes
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The Role of the Quasigroup in the Development of Binary Systems

Description: The objective here is to give a logical development of some mathematical systems beginning with those having relatively little algebraic structure, and progressing to systems rich in structure. The discussion will commence with a mathematical system called the groupoid, a nonempty set with a binary operation.
Date: August 1966
Creator: Stingel, Charles Willard
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A Fundamental Study of Cardinal and Ordinal Numbers

Description: The purpose of this paper is to present a discussion on the basic fundamentals of the theory of sets. Primarily, the discussion will be confined to the study of cardinal and ordinal numbers. The concepts of sets, classes of sets, and families of sets will be undefined quantities, and the concept of the class of all sets will be avoided.
Date: August 1966
Creator: Thornton, Robert Leslie
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Lattices

Description: Because lattice theory is so vast, the primary purpose of this paper will be to present some of the general properties of lattices, exhibit examples of lattices, and discuss the properties of distributive and modular lattices.
Date: August 1966
Creator: Rintala, Richard Arne
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