Manin's conjecture on a nonsingular quartic del Pezzo surface

Given a nonsingular quartic del Pezzo surface, a conjecture of Manin predicts the density of rational points on the open subset of the surface formed by deleting the lines. We prove that this prediction is of the correct order of magnitude for a particular surface.Comment: 29 page

Navigating the landscape of pedagogical training: The journeys of three mathematics graduate students

This article describes the landscape of teaching assistantships (TAships) in the Mathematics Department of a large, public, research institution. First, we present visualized data describing the terrain for all mathematics graduate students. Second, we focus on three specific journeys in that terrain. We employ an autoethnographical research methodology to analyze the pedagogical paths of three recent graduates through written reflection. We highlight some surprising themes that emerge, identify key moments in each reflection, and make three proposals, applicable in broader contexts, to capture and confer their benefits.   Dans notre article, nous traçons le portrait de l’assistanat d’enseignement dans le département de Mathématique d’un grand établissement public de recherche. Tout d’abord, nous présentons des données sous forme visuelle de manière à décrire la réalité sur le terrain des étudiants en mathématique des cycles supérieurs. Ensuite, nous portons notre attention sur trois parcours particuliers. Au moyen de réflexions menées par écrit, nous utilisons une méthodologie de recherche autoethnographique afin d’analyser le parcours pédagogique de trois nouveaux diplômés. Nous soulignons certains thèmes surprenants, nous dégageons les moments clés de chaque réflexion, puis nous énonçons trois propositions – lesquelles peuvent être utilisées dans un contexte plus large – et nous en présentons les avantages

The Development and Delivery of a Multidisciplinary Research Course for First-Year International Science Students

Students who engage in undergraduate research experiences acquire many benefits, including an understanding of how scientific knowledge is constructed, recognition that knowledge can be complex and uncertain, and the habit of viewing knowledge critically. This paper describes a first-year two-course sequence that provides multidisciplinary opportunities for international science students to engage in the research process and present at a student-led research conference. We describe course goals and structure, and discuss whether the goals were attained using instructor reflections, student performance, and student survey data. We also evaluate the impact of changes to the curriculum between Year 1 and Year 2. In both years, we found that students engaged meaningfully with the research process and began to understand how scientific knowledge is created. We also found that a modular model with front-end support worked better for instructors as compared to a continuous individualized project mentorship model. This modular approach involved structured pre- and post-class assignments within discipline-specific themes containing examples of the research process embedded into the discipline. These discipline-specific modules were followed by modules covering broader research process themes. We encourage instructors who are thinking of delivering a similar research-based course for first-year students to provide support via example research questions and other example templates for student submissions