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.

Exploring Gifted Adults' Perception of Giftedness in their Pursuit of Graduate Education

This qualitative study explores 8 gifted adults' perceptions of their own giftedness and how those perceptions influenced their pursuit of graduate education as revealed by retrospective interviews. This study serves to inform the existing literature surrounding giftedness especially as it relates to gifted individuals across the lifespan and their experiences and perceptions of education at all levels. This study also provides insight into the emotional impact being labeled gifted has on an individual's self-concept and academic identity. The major themes that emerged using the interpretive phenomenological analysis method (Smith & Osborn, 2003) were discussed under five main headings: Evolution of Giftedness, Success and Failure, Expectations, Effort, and Doubt and Proof. An adaptation of the listening guide method (Gilligan, Spencer, Weinberg, & Bertsch, 2003) was used to provide a unique and personal perspective of the phenomenon of giftedness and revealed the feelings behind the themes that emerged in the interpretive phenomenological analysis method. Specifically; this study illuminates the lack of evolution that an individual's understanding and perception of giftedness undergoes across the lifespan, and the impact such a static and school-bound understanding has on gifted adults' self-concept. It also reveals the influence that gifted individuals' innate need to achieve has on their academic aspirations and their perceptions of themselves as gifted. Furthermore, it reveals how important the understanding and internalization of failure can be on the self-concept of gifted individuals, and that this issue needs immediate attention at all levels of education.

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.