Thesis (Ph. D.)--University of Missouri-Columbia, 2008. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 4, 2009) Vita. Includes bibliographical references.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 109-114).

M.Sc.

Many general properties of real continuous functions defined on the closed interval [0,1] on the real line have been studied in the past. The present work started with a review of some known analytical results of this class C. An extended class A of positively continuous functions was then defined and its properties compared with that of C. While many of the characteristics of C were inherited from A, some properties of C are not shared by A. The first part of the second section (chapter) is devoted to a study of some elementary algebraic properties of A and C. Results obtained for the two classes showed differences. The rest of the section (chapter) deals with the algebraic structures of some subclasses of F, the set of all real-valued functions of [0,1] on the real line. The concept of an ideal in F was introduced for the class of real functions from [0,1] to the real line. In the last section (chapter), the concept of areas of function, C_f, defined as the closure of the graph of a function, is used to study the properties of elements of I. Integrals of continuous functions in I are completely determined by their C_f’s. Some topological implications of a few analytical subclasses of I were also revealed. This section concluded with an important theorem that fully characterizes the G_f of a real function in I by a closed set in the closed square U = {(x,y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}. / Master of Science

Call number: LD2668 .T4 1962 C44

Thesis (Ph. D.)--University of Idaho, 2006. / Abstract. "April 2006." Includes bibliographical references (leaf 69). Also available online in PDF format.

This study set out to investigate how the use of a Smart Board impacts on the teaching and learning of algebraic functions. The research took place in a school equipped with Smart Boards in each Mathematics classroom. Data collection involved lesson observations in three classes over three lessons each. The teachers and learners were interviewed post observation and the data obtained were analysed according to Sfard‘s three-phase model framework to determine if the learners had a procedural or object view of a function after having been taught on a Smart Board. The findings show that by using a Smart Board learners had both procedural and object view of functions however, much of the teaching occurred in a way which would have been possible without the use of a Smart Board, indicating that teachers did not fully utilise the potential of such a technological tool. However, it emerged that visualisation played an important role in allowing learners to operate on functions as objects. So while the visualization that technology enables encouraged reification or allowed teachers and learners to operate on functions as a whole or even on families of functions, this appeared simply to 'speed up‘ the normal teaching-learning process rather than promote the explorative and investigative aspect of learning. Still, it must be acknowledged that this kind of practice is bound to strengthen these learners‘ function concepts as was evident in the ways they appeared to operate confidently on the objects as shown in the study. It must be acknowledged that teachers were extremely enthusiastic about the possibilities of the technology and were inspired to use technology more in their lessons to allow learners‘ visualisation of concepts. Positive comments made by learners showed that they too, were also motivated by the use of the Smart Board. / Thesis (M.Ed.)-University of KwaZulu-Natal, Pietermaritzburg, 2011.

Thesis (Ph.D.)--McMaster University (Canada), 1991. / Source: Dissertation Abstracts International, Volume: 54-02, Section: B, page: 0867.

No description available.

Thesis (MComm)--Stellenbosch University, 2003. / ENGLISH ABSTRACT: In this dissertation I investigate the class number one problem in function fields. More precisely I give a survey of the current state of research into extensions of a rational function field over a finite field with principal ring of integers. I focus particularly on the quadratic case and throughout draw analogies and motivations from the classical number field situation. It was the "Prince of Mathematicians" C.F. Gauss who first undertook an in depth study of quadratic extensions of the rational numbers and the corresponding rings of integers. More recently however work has been done in the situation of function fields in which the arithmetic is very similar. I begin with an introduction into the arithmetic in function fields over a finite field and prove the analogies of many of the classical results. I then proceed to demonstrate how the algebra and arithmetic in function fields can be interpreted geometrically in terms of curves and introduce the associated geometric language. After presenting some conjectures, I proceed to give a survey of known results in the situation of quadratic function fields. I present also a few results of my own in this section. Lastly I state some recent results regarding arbitrary extensions of a rational function field with principal ring of integers and give some heuristic results regarding class groups in function fields. / AFRIKAANSE OPSOMMING: In hierdie tesis ondersoek ek die klasgetal een probleem in funksieliggame. Meer spesifiek ondersoek ek die huidige staat van navorsing aangaande uitbreidings van 'n rasionale funksieliggaam oor 'n eindige liggaam sodat die ring van heelgetalle 'n hoofidealgebied is. Ek kyk in besonder na die kwadratiese geval, en deurgaans verwys ek na die analoog in die klassieke getalleliggaam situasie. Dit was die beroemde wiskundige C.F. Gauss wat eerste kwadratiese uitbreidings van die rasionale getalle en die ooreenstemende ring van heelgetalle in diepte ondersoek het. Onlangs het wiskundiges hierdie probleme ook ondersoek in die situasie van funksieliggame oor 'n eindige liggaam waar die algebraïese struktuur baie soortgelyk is. Ek begin met 'n inleiding tot die rekenkunde in funksieliggame oor 'n eindige liggaam en bewys die analogie van baie van die klassieke resultate. Dan verduidelik ek hoe die algebra in funksieliggame geometries beskou kan word in terme van kurwes en gee 'n kort inleiding tot die geometriese taal. Nadat ek 'n paar vermoedes bespreek, gee ek 'n oorsig van wat alreeds vir quadratiese funksieliggame bewys is. In hierdie afdeling word 'n paar resultate van my eie ook bewys. Dan vermeld ek 'n paar resultate aangaande algemene uitbreidings van 'n rasionale funksieliggaam oor 'n eindige liggaam waar die van ring heelgetalle 'n hoofidealgebied is. Laastens verwys ek na 'n paar heurisitiese resultate aangaande klasgroepe in funksieliggame.