Search results for "VDP::Mathematics: 410"
showing 4 items of 4 documents
Geometric rough paths on infinite dimensional spaces
2022
Similar to ordinary differential equations, rough paths and rough differential equations can be formulated in a Banach space setting. For $\alpha\in (1/3,1/2)$, we give criteria for when we can approximate Banach space-valued weakly geometric $\alpha$-rough paths by signatures of curves of bounded variation, given some tuning of the H\"older parameter. We show that these criteria are satisfied for weakly geometric rough paths on Hilbert spaces. As an application, we obtain Wong-Zakai type result for function space valued martingales using the notion of (unbounded) rough drivers.
The sine anecdote in Kovalevskaya’s memoirs; British Journal for the History of Mathematics
2022
In Sofya Vasilyevna Kovalevskaya’s memoirs there is a rather ambiguous story about how she came to understand trigonometric functions on her own as a teenager by reading the chapter on optics in Tyrtov’s elementary physics textbook. Furthermore, she claims that in so doing, she happened to follow ‘the same road that had been taken historically: that is, instead of a sine I used a chord’. We examine Tyrtov’s textbook in search of sources for such inspiration and quote hitherto unknown critical reactions to her autobiographical reflections by Kovalevskaya’s teacher I I Malevich. We conclude that Kovalevskaya’s memoirs may well be marred by personal interests and/or faltering memory. By adding…
Imaginary Dialogues – In-service Teachers’ Steps Towards Mathematical Argumentation in Classroom Discourse
2018
The purpose of this qualitative study was to explore in-service teachers’ first experiences with imaginary dialogues – a form of mathematical writing where students are introduced to a written and unfinished dialogue between two imaginary persons discussing a mathematical problem. Students are supposed to continue working with the problem and to complete the initial dialogue between these persons. In-service teachers were enrolled in a continuing university education mathematics course. They were given the task to try out imaginary dialogues in their classes from grades 4 to 10. Based on in-service teachers’ responses in open-ended self-evaluation forms, the study examined how the in-servic…
Engaging Mathematical Reasoning-and-Proving: A Task, a Method, and a Taxonomy
2019
This article is the second paper in a series of papers on studies focusing on teaching mathematical reasoning-and-proving in elementary mathematics classroom. Participants are in-service teachers enrolled in a continuing university education program in mathematics. Results from the first paper suggested the method of imaginary dialogues to have the potential to support in-service teachers in engaging their students in mathematical reasoning-and-proving, and Balacheff’s taxonomy of proofs to support in-service teachers in identifying students’ argumentation. This study is on the following years’ in-service teachers in the program. It examines their perceptions of the usefulness of two consti…