arXiv subjects

Aron Gohr

Publications and source records attributed to Aron Gohr.

3 recordsLinked to original sources

arXiv2026

Automated Feedback Generation for Undergraduate Mathematics: Development and Evaluation of an AI Teaching Assistant

Intelligent tutoring systems have long enabled automated immediate feedback on student work when it is presented in a tightly structured format and when problems are very constrained, but reliably assessing free-form mathematical reasoning remains challenging. We present a system that processes free-form natural language input, handles a wide range of edge cases, and comments competently not only on the technical correctness of submitted proofs, but also on style and presentation issues. We discuss the advantages and disadvantages of various approaches to the evaluation of such a system, and show that by the metrics we evaluate, the quality of the feedback generated is comparable to that produced by human experts when assessing early undergraduate homework. We stress-test our system with a small set of more advanced and unusual questions, and report both significant gaps and encouraging successes in that more challenging setting. Our system uses large language models in a modular workflow. The workflow configuration is human-readable and editable without programming knowledge, and allows some intermediate steps to be precomputed or injected by the instructor. A version of our tool is deployed on the Imperial mathematics homework platform Lambdafeedback. We report also on the integration of our tool into this platform.

cs.CY↗

arXiv2009

On unitality conditions for Hom-associative algebras

In hom-associative structures, the associativity condition $(xy)z=x(yz)$ is twisted to $α(x)(yz) = (xy)α(z)$, with $α$ a map in the appropriate category. In the present paper, we consider two different unitality conditions for hom-associative algebras. The first one, existence of a unit in the classical sense, is stronger than the second one, which we call weak unitality. We show associativity conditions connected to the size of the image of the twisting map for unital hom-associative algebras. Also the problem of embedding arbitrary hom-associative algebras into unital or weakly unital ones is investigated. Finally, we show that weakly unital hom-associative algebras with bijective twisting map are twisted versions of associative algebras.

math.RA↗

arXiv2009

On hom-algebras with surjective twisting

A hom-associative structure is a set $A$ together with a binary operation $\star$ and a selfmap $α$ such that an $α$-twisted version of associativity is fulfilled. In this paper, we assume that $α$ is surjective. We show that in this case, under surprisingly weak additional conditions on the multiplication, the binary operation is a twisted version of an associative operation. As an application, an earlier result by Yael Fregier and the author on weakly unital hom-algebras is recovered with a different proof. In the second section, consequences for the deformation theory of hom-algebras with surjective twisting map are discussed.

math.RA↗