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  Partner: UNT Libraries
 Department: Department of Mathematics
 Degree Level: Master's
 Collection: UNT Theses and Dissertations
The Moore-Smith Limit

The Moore-Smith Limit

Date: 1952
Creator: Alexander, Donnie B.
Description: It is the purpose of this thesis to indicate in more detail how various limits defined in analysis, as well as other concepts not ordinarily defined as limits, may be obtained as special cases of the Moore-Smith limit.
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A Development of a Set of Functions Analogous to the Trigonometric and the Hyperbolic Functions

A Development of a Set of Functions Analogous to the Trigonometric and the Hyperbolic Functions

Date: August 1954
Creator: Allen, Alfred I.
Description: The purpose of this paper is to define and develop a set of functions of an area in such a manner as to be analogous to the trigonometric and the hyperbolic functions.
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Absolute Continuity and the Integration of Bounded Set Functions

Absolute Continuity and the Integration of Bounded Set Functions

Date: May 1975
Creator: Allen, John Houston
Description: The first chapter gives basic definitions and theorems concerning set functions and set function integrals. The lemmas and theorems are presented without proof in this chapter. The second chapter deals with absolute continuity and Lipschitz condition. Particular emphasis is placed on the properties of max and min integrals. The third chapter deals with approximating absolutely continuous functions with bounded functions. It also deals with the existence of the integrals composed of various combinations of bounded functions and finitely additive functions. The concluding theorem states if the integral of the product of a bounded function and a non-negative finitely additive function exists, then the integral of the product of the bounded function with an absolutely continuous function exists over any element in a field of subsets of a set U.
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Integration of Vector Valued Functions

Integration of Vector Valued Functions

Date: August 1972
Creator: Anderson, Edmond Cardell, III
Description: This paper develops an integral for Lebesgue measurable functions mapping from the interval [0, 1] into a Banach space.
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R-Modules for the Alexander Cohomology Theory

R-Modules for the Alexander Cohomology Theory

Date: May 1973
Creator: Anderson, Stuart Neal
Description: The Alexander Wallace Spanier cohomology theory associates with an arbitrary topological space an abelian group. In this paper, an arbitrary topological space is associated with an R-module. The construction of the R-module is similar to the Alexander Wallace Spanier construction of the abelian group.
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Complete Ordered Fields

Complete Ordered Fields

Date: August 1977
Creator: Arnold, Thompson Sharon
Description: The purpose of this thesis is to study the concept of completeness in an ordered field. Several conditions which are necessary and sufficient for completeness in an ordered field are examined. In Chapter I the definitions of a field and an ordered field are presented and several properties of fields and ordered fields are noted. Chapter II defines an Archimedean field and presents several conditions equivalent to the Archimedean property. Definitions of a complete ordered field (in terms of a least upper bound) and the set of real numbers are also stated. Chapter III presents eight conditions which are equivalent to completeness in an ordered field. These conditions include the concepts of nested intervals, Dedekind cuts, bounded monotonic sequences, convergent subsequences, open coverings, cluster points, Cauchy sequences, and continuous functions.
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Understanding Ancient Math Through Kepler: A Few Geometric Ideas from The Harmony of the World

Understanding Ancient Math Through Kepler: A Few Geometric Ideas from The Harmony of the World

Date: August 2002
Creator: Arthur, Christopher
Description: Euclid's geometry is well-known for its theorems concerning triangles and circles. Less popular are the contents of the tenth book, in which geometry is a means to study quantity in general. Commensurability and rational quantities are first principles, and from them are derived at least eight species of irrationals. A recently republished work by Johannes Kepler contains examples using polygons to illustrate these species. In addition, figures having these quantities in their construction form solid shapes (polyhedra) having origins though Platonic philosophy and Archimedean works. Kepler gives two additional polyhedra, and a simple means for constructing the “divine” proportion is given.
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The History of the Calculus

The History of the Calculus

Date: 1945
Creator: Ashburn, Andrew
Description: The purpose of this essay is to trace the development of the concepts of the calculus from their first known appearance, through the formal invention of the method of the calculus in the second half of the seventeenth century, to our own day.
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Comparison of Some Mappings in Topology

Comparison of Some Mappings in Topology

Date: January 1964
Creator: Aslan, Farhad
Description: The main purpose of this paper is the study of transformations in topological space and relationships between special types of transformations.
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A Method for Approximating the Distributed Loads of an Airplane by Sets of Point Loads

A Method for Approximating the Distributed Loads of an Airplane by Sets of Point Loads

Date: 1957
Creator: Austin, Charles Wayne
Description: This paper gives the derivation of a method for determining the forces to be applied to these points which will simulate the load distributed over all the airplane.
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Valuations and Valuation Rings

Valuations and Valuation Rings

Date: August 1975
Creator: Badt, Sig H.
Description: This paper is an investigation of several basic properties of ordered Abelian groups, valuations, the relationship between valuation rings, valuations, and their value groups and valuation rings. The proofs to all theorems stated without proof can be found in Zariski and Samuel, Commutative Algebra, Vol. I, 1858. In Chapter I several basic theorems which are used in later proofs are stated without proof, and we prove several theorems on the structure of ordered Abelian groups, and the basic relationships between these groups, valuations, and their valuation rings in a field. In Chapter II we deal with valuation rings, and relate the structure of valuation rings to the structure of their value groups.
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Near-Rings

Near-Rings

Date: May 1972
Creator: Baker, Edmond L.
Description: The primary objective of this work is to discuss some of the elementary properties of near-rings as they are related to rings. This study is divided into three subdivisions: (1) Basic Properties and Concepts of Near-Rings; (2) The Ideal Structure of Near-Rings; and (3) Homomorphism and Isomorphism of Near-Rings.
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Completely Simple Semigroups

Completely Simple Semigroups

Date: August 1968
Creator: Barker, Bruce W.
Description: The purpose of this thesis is to explore some of the characteristics of 0-simple semigroups and completely 0-simple semigroups.
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T-Functions

T-Functions

Date: June 1960
Creator: Barlow, John Rice
Description: 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.
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Product and Function Spaces

Product and Function Spaces

Date: August 1971
Creator: Barrett, Lewis Elder
Description: In this paper the Cartesian product topology for an arbitrary family of topological spaces and some of its basic properties are defined. The space is investigated to determine which of the separation properties of the component spaces are invariant.
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Properties of Order Relations and Certain Partly Ordered Systems

Properties of Order Relations and Certain Partly Ordered Systems

Date: June 1961
Creator: Barros, David Nicholas
Description: 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.
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A Set of Axioms for a Topological Space

A Set of Axioms for a Topological Space

Date: August 1960
Creator: Batcha, Joseph Patrick
Description: Axioms for a topological space are generally based on neighborhoods where "neighborhood" is an undefined term. Then, limit points are defined in terms of neighborhoods. However, limit points seem to be the basic concept of a topological space, rather than neighborhoods. For this reason, it will be attempted to state a set of axioms for a topological space, using limit point as the undefined concept, and to delete the idea of neighborhoods from the theory.
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The Development of the Natural Numbers by Means of the Peano Postulates

The Development of the Natural Numbers by Means of the Peano Postulates

Date: 1951
Creator: Baugh, Orvil Lee
Description: This thesis covers the development of the natural numbers by means of the peano postulates.
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On Sets and Functions in a Metric Space

On Sets and Functions in a Metric Space

Date: December 1971
Creator: Beeman, Anne L.
Description: The purpose of this thesis is to study some of the properties of metric spaces. An effort is made to show that many of the properties of a metric space are generalized properties of R, the set of real numbers, or Euclidean n--space, and are specific cases of the properties of a general topological space.
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Lebesgue Linear Measure

Lebesgue Linear Measure

Date: 1940
Creator: Beeman, William Edwin
Description: This paper discusses the concept of a general definition of measure, and shows that the Lebesgue measure satisfies the requirements set forth for the ideal definition.
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Compactness and Equivalent Notions

Compactness and Equivalent Notions

Date: August 1967
Creator: Bell, Wayne Charles
Description: 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.
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Some Theorems and Product Spaces

Some Theorems and Product Spaces

Date: 1957
Creator: Bethel, Edward Lee
Description: This thesis is a study of some axioms and theorems, and product spaces.
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Metric Spaces

Metric Spaces

Date: 1957
Creator: Bilyeu, Russell Gene
Description: This thesis covers fundamental properties of metric spaces, as well as completeness, compactness, and separability of metric spaces.
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Algebraic Integers

Algebraic Integers

Date: August 1969
Creator: Black, Alvin M.
Description: The primary purpose of this thesis is to give a substantial generalization of the set of integers Z, where particular emphasis is given to number theoretic questions such as that of unique factorization. The origin of the thesis came from a study of a special case of generalized integers called the Gaussian Integers, namely the set of all complex numbers in the form n + mi, for m,n in Z. The main generalization involves what are called algebraic integers.
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