Relations between logic and mathematics in the work of Benjamin and Charles S. Peirce.

Charles Peirce (1839-1914) was one of the most important logicians of the nineteenth century. This thesis traces the development of his algebraic logic from his early papers, with especial attention paid to the mathematical aspects. There are three main sources to consider. 1) Benjamin Peirce (1809-1880), Charles's father and also a leading American mathematician of his day, was an inspiration. His memoir Linear Associative Algebra (1870) is summarised and for the first time the algebraic structures behind its 169 algebras are analysed in depth. 2) Peirce's early papers on algebraic logic from the late 1860s were largely an attempt to expand and adapt George Boole's calculus, using a part/whole theory of classes and algebraic analogies concerning symbols, operations and equations to produce a method of deducing consequences from premises. 3) One of Peirce's main achievements was his work on the theory of relations, following in the pioneering footsteps of Augustus De Morgan. By linking the theory of relations to his post-Boolean algebraic logic, he solved many of the limitations that beset Boole's calculus. Peirce's seminal paper `Description of a Notation for the Logic of Relatives' (1870) is analysed in detail, with a new interpretation suggested for his mysterious process of logical differentiation. Charles Peirce's later work up to the mid 1880s is then surveyed, both for its extended algebraic character and for its novel theory of quantification. The contributions of two of his students at the Johns Hopkins University, Oscar Mitchell and Christine Ladd-Franklin are traced, specifically with an analysis of their problem solving methods. The work of Peirce's successor Ernst Schröder is also reviewed, contrasting the differences and similarities between their logics. During the 1890s and later, Charles Peirce turned to a diagrammatic representation and extension of his algebraic logic. The basic concepts of this topological twist are introduced. Although Peirce's work in logic has been studied by previous scholars, this thesis stresses to a new extent the mathematical aspects of his logic - in particular the algebraic background and methods, not only of Peirce but also of several of his contemporaries

Augustus De Morgan and the development of university mathematics in London in the nineteenth century.

This thesis investigates the teaching of mathematics at university level in London, and in particular by Augustus De Morgan (1806-1871) during his period as founder professor of mathematics at London University (later University College London) from 1828 to 1867. An examination of De Morgan's life and professorial career is followed by a review of changes in instruction at the college under his successors, together with a survey of higher mathematical tuition at other university-level institutions in the capital up to the turn of the twentieth century. Particular attention is paid to original teaching material and the set of students who later achieved distinction in mathematics and other disciplines. A key feature of the research undertaken for this project has been its intensive use of previously unpublished archival documents, hitherto mostly unstudied. Consequently, much of the information which has been gleaned from these sources (such as De Morgan's lecture material, student notes and contemporary correspondence) has never appeared in print before. The data thus derived has been used in conjunction with publications from the period, as well as more recent works, to produce a contribution to the history of mathematical education which gives a more complete picture of how well nineteenth-century London was served for mathematical instruction than was previously available. Previous studies of De Morgan have mainly concentrated on his work in algebra and logic, with little or no reference to his mathematical teaching, while published histories of relevant institutions (e. g. University College, University of London) are similarly localised, with few comparisons being drawn with other bodies, and almost no reference to mathematical tuition. By concentrating on the work of De Morgan as a teacher in the context of London mathematics, this thesis will attempt to fill these two important gaps in the literature

Queensland Institute of Technology: Handbook 1973

The Queensland Institute of Technology handbook gives an outline of the faculties and subject offerings available that were offered by QIT

The Question: Could a multi-sensory approach to design facilitate a re-enchantment of the food industry in Britain?

This thesis explores the potential of design industries ability to re-enchant the food industry in Britain in 2007. My research is informed by the increasing evidence of the negative impact on human and biosphere wellbeing and industrialization practice in food production and marketing. I highlight the connection between design's promotion of the hegemony of visuality and the marginalization of opportunities to construct connections between food source and its quality through multi-sensory engagement. I have adapted Webber's (2000) idea of disenchantment to describe a condition .in which the deterioration of quality of food experience. I argue that industrialization has created a loss of intangible qualities and traditions that have a clear potential to provide deep sources of pleasure and meaning to participants. I have focused on the relationship between design and food in order to evidence how design has become a tool of instrumental rationality by primarily servicing the short-term economic agendas of corporate business. I argue that design's focus on the role of seduction has led to the marginalization of a latent ability to connect consumers and producers to value through their non-visual senses. I propose that a multi-sensory form of design is capable of informing the restoration/creation of a deeper and more reflective relationship with the food chain. I argue that the route to this outcome is through the re-evaluation and re-education of the role that multi-sensory aesthetics play in the construction of promoting more benign rituals of production and consumption. I use evidence of multi-sensory practice in the non-industrialized and ethical food sector as an analogy and source that could sensory awareness to the designer's portfolio. I draw on a wide range of evidence to inform and support my explanation of the origins and character of the syndrome of industrialized production, marketing and consumption. My goal is informed by a concern to demonstrate that multi-sensory design could support the viability of alternative production and consumption strategie

Queensland Institute of Technology: Handbook 1972

The Queensland Institute of Technology handbook gives an outline of the faculties and subject offerings available that were offered by QIT

Educating and training mathematics teachers for secondary schools in Ireland: a new perspective on teacher education

This thesis is a record of experiments in the education of mathematics teachers for Irish Secondary schools conducted at Thomond College of Education, Limerick during the years 1975–77 inclusive. But it is more than a mere record of successes and failures. In its analyses and syntheses, based on experiments and programmes conducted under actual conditions, it endeavours in a true spirit of research in mathematical education to provide new insights. The research culminates in the redefinition of an old problem in mathematical education, and a first step towards a viable solution to the redefined problem is presented