This infinite, unanimous dissonance : a study in mathematical existentialism through the work of Jean-Paul Sartre and Alain Badiou

This thesis seeks to elucidate a motif common to the work both of Jean-Paul Sartre and Alain Badiou (with special attention being given to Being and Nothingness and Being and Event respectively): the thesis that the subject 's existence precedes and determines its essence. To this end, the author aims to explicate the structural invariances, common to both philosophies, that allow this thesis to take shape. Their explication requires the construction of an overarching conceptual framework within which it may be possible to embed both the phenomenological ontology elaborated in Being and Event and the mathematical ontology outlined in Being and Event. Within this framework, whose axial concept is that of multiplicity, the precedence of essence by existence becomes intelligible in terms of a priority of extensional over intensional determination. A series of familiar existentialist concepts are reconstructed on this basis, such as lack and value, and these are set to work in the task of fleshing out the more or less skeletal theory of the subject presented in Being and Event.

Buried Treasure: The Economics of Leak Detection and Water Loss Prevention in Ontario

On average approximately 13% of the water that is withdrawn by Canadian municipal water suppliers is lost before it reaches final users. This is an important topic for several reasons: water losses cost money, losses force water agencies to draw more water from lakes and streams thereby putting more stress on aquatic ecosystems, leaks reduce system reliability, leaks may contribute to future pipe failures, and leaks may allow contaminants to enter water systems thereby reducing water quality and threatening the health of water users. Some benefits of leak detection fall outside water agencies’ accounting purview (e.g. reduced health risks to households connected to public water supply systems) and, as a result, may not be considered adequately in water agency decision-making. Because of the regulatory environment in which Canadian water agencies operate, some of these benefits-especially those external to the agency or those that may accrue to the agency in future time periods- may not be fully counted when agencies decide on leak detection efforts. Our analysis suggests potential reforms to promote increased efforts for leak detection: adoption of a Canada-wide goal of universal water metering; development of full-cost accounting and, pricing for water supplies; and co-operation amongst the provinces to promulgate standards for leak detection efforts and provide incentives to promote improved efficiency and rational investment decision-making.

Undergraduate Students' Experiences of Their Mathematical Identity

This research study explored how undergraduate mathematics students perceive themselves as capable mathematics learners and whether gender differences exist in the undergraduates students' perceptions. The research was framed by three approaches of understanding identity: self-efficacy, environment, and four faces of learner's identity. A mixed methods approach to the study was used where data were collected from interviews and an online questionnaire. Data analysis revealed that undergraduate mathematics students' perceptions of their mathematical identity as capable mathematics learners are influenced by their perceptions of their experiences such as: (a) perceptions of having previous knowledge of the course, (b) being able teach others and others understand it, (c) being recognized by their professors, (d) contributing and fitting in, (e) having opportunities to interact with their peers, and (f) being able to fit in with their image of a capable mathematics learner.