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.

Autonomic prediction of error-related ERP components in perceptual and conceptual tasks in older and younger adults

In studies of cognitive processing, the allocation of attention has been consistently linked to subtle, phasic adjustments in autonomic control. Both autonomic control of heart rate and control of the allocation of attention are known to decline with age. It is not known, however, whether characteristic individual differences in autonomic control and the ability to control attention are closely linked. To test this, a measure of parasympathetic function, vagal tone (VT) was computed from cardiac recordings from older and younger adults taken before and during performance of two attentiondemanding tasks - the Eriksen visual flanker task and the source memory task. Both tasks elicited event-related potentials (ERPs) that accompany errors, i.e., error-related negativities (ERNs) and error positivities (Pe's). The ERN is a negative deflection in the ERP signal, time-locked to responses made on incorrect trials, likely generated in the anterior cingulate. It is followed immediately by the Pe, a broad, positive deflection which may reflect conscious awareness of having committed an error. Age-attenuation ofERN amplitude has previously been found in paradigms with simple stimulus-response mappings, such as the flanker task, but has rarely been examined in more complex, conceptual tasks. Until now, there have been no reports of its being investigated in a source monitoring task. Age-attenuation of the ERN component was observed in both tasks. Results also indicated that the ERNs generated in these two tasks were generally comparable for young adults. For older adults, however, the ERN from the source monitoring task was not only shallower, but incorporated more frontal processing, apparently reflecting task demands. The error positivities elicited by 3 the two tasks were not comparable, however, and age-attenuation of the Pe was seen only in the more perceptual flanker task. For younger adults, it was Pe scalp topography that seemed to reflect task demands, being maximal over central parietal areas in the flanker task, but over very frontal areas in the source monitoring task. With respect to vagal tone, in the flanker task, neither the number of errors nor ERP amplitudes were predicted by baseline or on-task vagal tone measures. However, in the more difficult source memory task, lower VT was marginally associated with greater numbers of source memory errors in the older group. Thus, for older adults, relatively low levels of parasympathetic control over cardiac response coincided with poorer source memory discrimination. In both groups, lower levels of baseline VT were associated with larger amplitude ERNs, and smaller amplitude Pe's. Thus, low VT was associated in a conceptual task with a greater "emergency response" to errors, and at the same time, reduced awareness of having made them. The efficiency of an individual's complex cognitive processing was therefore associated with the flexibility of parasympathetic control of heart rate, in response to a cognitively challenging task.

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.

Disambiguating the Effects of Social Instability Stress in Adolescence on Learning and Memory Tasks that Involve the Medial Prefrontal Cortex and Hippocampus

Exposure to chronic stress can alter the structure and function of brain regions involved in learning and memory, and these effects are typically long-lasting if the stress occurs during sensitive periods of development. Until recently, adolescence has received relatively little attention as a sensitive period of development, despite marked changes in behaviour, heightened reactivity to stressors, and cognitive and neural maturation. Therefore, the purpose of the present study was to investigate the long-term effects of chronic stress in adolescence on two spatial learning and memory tasks (Morris water maze and Spatial Object Location test) and on a working memory task (Delayed Alternation task). Male rats were randomly assigned to chronic social instability stress (SS; daily 1 hour isolation and subsequent change of cage partner between postnatal days 30 and 45) or to a no-stress control group (CTL). During acquisition learning in the Morris water maze task, SS rats demonstrated impaired long-term memory for the location of the hidden escape platform compared to CTL rats, although the impairment was only seen after the first day of training. Similarly, SS rats had impaired long-term memory in the Spatial Object Location test after a long delay (240 minutes), but not after shorter delays (15 or 60 minutes) compared to CTL rats. On the Delayed Alternation task, which assessed working memory across delays ranging from 5 to 90 seconds, no group differences were observed. These results are partially in line with previous research that revealed adult impairment on spatial learning and memory tasks after exposure to chronic social instability stress in adolescence. The observed deficits, however, appear to be limited to long-term memory as no group differences were observed during brief periods of retention.

Electrophysiology of Oculomotor Delayed Response Tasks: A Model for the Maturation of Visual-Spatial Working Memory Networks

In the literature, persistent neural activity over frontal and parietal areas during the delay period of oculomotor delayed response (ODR) tasks has been interpreted as an active representation of task relevant information and response preparation. Following a recent ERP study (Tekok-Kilic, Tays, & Tkach, 2011 ) that reported task related slow wave differences over frontal and parietal sites during the delay periods of three ODR tasks, the present investigation explored developmental differences in young adults and adolescents during the same ODR tasks using 128-channel dense electrode array methodology and source localization. This exploratory study showed that neural functioning underlying visual-spatial WM differed between age groups in the Match condition. More specifically, this difference is localized anteriorly during the late delay period. Given the protracted maturation of the frontal lobes, the observed variation at the frontal site may indicate that adolescents and young adults may recruit frontal-parietal resources differently.