Origines algébrique et géométrique des nombres complexes et leur extension aux quaternions : fondements de la géométrie

La première partie de ce mémoire relève les principaux problèmes de nature algébrique et géométrique qu'ont dû résoudre les mathématiciens avant d'accepter l'existence des nombres complexes; l'une des conséquences de cet exercice est de proposer l'esquisse d'une approche plus adéquate à l'enseignement des nombres complexes au collégial. La deuxième partie présente l'approche géométrique des quaternions, tel que formulée par leur inventeur (Hamilton), puis démontre leurs principales propriétés géométriques dans le contexte de l'algèbre linéaire. Dans la troisième partie, l'axiomatisation de l'intuition géométrique est abordée dans le contexte des fondements proposés par Hilbert en regard des géométries non euclidiennes.\ud ______________________________________________________________________________ \ud MOTS-CLÉS DE L’AUTEUR : Histoire des nombres complexes, quaternions, fondements de la géométrie

How to engage patients in research and quality improvement in community-based primary care settings: protocol for a participatory action research pilot study

Plain English summary Making primary care clinics more patient-centered is key to improving patients’ experience of care. If patients themselves were engaged in helping define priorities and suggesting quality improvements in the clinic, care would respond better to their needs. However, patient engagement is a new phenomenon, particularly in community based primary care clinics. How to engage patients in quality improvement in these clinics, or what effect this might have, is not well known. The involvement of patients needs to be adapted to the way these clinics function. The aim of this study is to create and evaluate a new model of patient engagement for quality improvement in community based primary care clinics. Patients, primary care professionals and researchers will create advisory councils in two primary care clinics in Quebec City (Canada). In each clinic, the advisory council will include 12 patients or caregivers registered at the clinic, a clinician and a clinic manager. The advisory council will meet every 6 weeks for a total of six meetings. Two patient-experts will facilitate meetings. During meetings, members of the council will list their needs in order of importance. Then they will suggest improvements in line with these needs. We will study if our advisory council model is well adapted to community based primary care settings and meets participants’ expectations. At the end of the study we will be able to offer guidance about engaging patients with health professionals in quality improvement in primary care clinics. Abstract Background Involvement of end-users, including patients, managers and clinicians, in identifying quality improvement and research priorities might improve the relevance of projects and increase their impact. Few patient engagement initiatives have taken place in community based primary care practices (CBPCPs) and best practices for engaging patients in such settings are not well defined. The aim of this pilot study is to develop and assess the feasibility of a new collaborative model of advisory council involving clinicians, managers, patients and caregivers in CBPCP to strengthen their capacity to conduct quality improvement and patient-oriented research projects. Methods We will conduct a participatory action research project in two non-academic CBPCPs in Quebec City (Canada). In each CBPCP, the advisory council will include 12 patients or caregivers, a clinician and a clinic manager. Patients or their caregivers will be identified by clinicians and contacted by patient-experts. They will be eligible if they are registered at the practice, motivated, and available to attend meetings. The council will meet every 6 weeks for a total of six meetings. Two patient-experts will guide council members to identify quality improvement priorities and patient-oriented research questions based on their experience in the clinic. They will then be supported to plan actions to target these priorities. Analysis of meetings will be based on feasibility criteria, notes by non-participant observers in log books, audio-recording of the meetings and questionnaires to evaluate council members’ perceptions and the likelihood they would engage in such councils. Discussion The results of this study will  be a model of patient engagement and a discussion of factors to improve the model to fit the needs of primary care patients and professionals. This will lay the foundation for a sustainable structure for long-term patient engagement and contribute to the development of a patient-centered and quality-improvement culture in CBPCPs