Thesis (Ph. D.)--Carleton University, 1992. / Also available in electronic format on the Internet.

Diss.--Stuttgart. / Vita. Bibliography: p. 86-88.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M.Sc.)(Mathematics)--University of Pretoria, 2004. / Title from opening screen (viewed March 27, 2006). Includes summary. Includes bibliographical references.

In 1854 Cayley proposed an interesting sequence 1,1,3,13,75,541,... in connection with analytical forms called trees. Since then there has been various combinatorial interpretations of the sequence. The sequence has been interpreted as the number of preferential arrangements of members of a set with n elements. Alternatively the sequence has been interpreted as the number of ordered partitions; the outcomes in races in which ties are allowed or geometrically the number of vertices, edges and faces of simplicial objects. An interesting application of the sequence is found in combination locks. The idea of a preferential arrangement has been extended to a wider combinatorial object called barred preferential arrangement with multiple bars. In this thesis we study barred preferential arrangements combinatorially with application to resistance of certain electrical circuits. In the process we derive some results on cyclic properties of the last digit of the number of barred preferential arrangements. An algorithm in python has been developed to find the number of barred preferential arrangements.

For a given abelian category o/, a category E is formed by considering exact sequences of o/. If one imposes the condition that a split sequence be regarded as the zero object, then the resulting sequence category E/S is shown to be abelian. The intrinsic algebraic structure of E/S is examined and related to the theory of coherent functors and functor rings. E/S is shown to be the natural setting for the study of pure and copure sequences and the theory is further developed by introducing repure sequences. The concept of pure semi-simple categories is examined in terms of E/S. Localization with respect to pure sequences is developed, leading to results concerning the existence of algebraically compact objects. The final topic is a study of the simple sequences and their relationship to almost split exact sequences. / Science, Faculty of / Mathematics, Department of / Graduate

Piaget and Freudenthal advocated thinking levels. In the 1950's the van Hieles developed a five level model of geometric thought. Judith Land adapted the model in 1990, utilising four levels to teach the concept of functions. These four levels have been considered here in the formation of concepts of sequences and series. The origin and relevance of sequences and series have been studied and the importance of visualisation, patterning and generalisation in the instructional process investigated. A series of lessons on these topics was taught to a group of six higher grade matriculation students of mixed ability and gender. Questionnaires related to student progress through the various levels were answered, categorised, graphed and analysed. Despite the small number of students, results seem to indicate that emphasising visualisation, exploring patterns and generalisation and teaching the topics as a reinvention had made a positive contribution towards progress through the various thought levels. / Mathematics Education / M.A. (Mathematics Education)

No description available.

Counting problems lead naturally to integer sequences. For example if one asks for the number of subsets of an $n$-set, the answer is $2^n$, or the integer sequence $1,~2,~4,~8,~ldots$. Conversely, given an integer sequence, or part of it, one may ask if there is an associated counting problem. There might be several different counting problems that produce the same integer sequence. To illustrate the nature of mathematical research involving integer sequences, we will consider Escher's counting problem and a generalization, as well as counting problems associated with the Catalan numbers, and the Collatz conjecture. We will also discuss the purpose of the On-Line-Encyclopedia of Integer Sequences.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Bibliography: leaves 48-49. / by David Jay Anick. / Ph.D.