Related papers: Domain-Specific Languages of Mathematics: Presenti…
Recent releases of pre-trained Large Language Models (LLMs) have gained considerable traction, yet research on fine-tuning and employing domain-specific LLMs remains scarce. This study investigates approaches for fine-tuning and leveraging…
Making meaning with math in physics requires blending physical conceptual knowledge with mathematical symbology. Students in introductory physics classes often struggle with this, but it is an essential component of learning how to think…
The focus of these lecture notes is on abstract models and basic ideas and results that relate to the operational semantics of programming languages largely conceived. The approach is to start with an abstract description of the computation…
Rigid body dynamics algorithms play a crucial role in several components of a robot controller and simulations. Real time constraints in high frequency control loops and time requirements of specific applications demand these functions to…
Mathematical learning environments give domain-specific and immediate feedback to students solving a mathematical exercise. Based on a language for specifying strategies, we have developed a feedback framework that automatically calculates…
Disco is a pure, strict, statically typed functional programming language designed to be used in the setting of a discrete mathematics course. The goals of the language are to introduce students to functional programming concepts early, and…
The functional programming paradigm has a long and storied history, with its beginnings in the Lambda Calculus. In recent decades, pure functional languages such as Haskell have been shown to be highly effective in producing robust software…
Large language models (LLMs) are changing the way researchers interact with code and data in scientific computing. While their ability to generate general-purpose code is well established, their effectiveness in producing scientifically…
The increasing complexity of software systems has driven significant advancements in program analysis, as traditional methods unable to meet the demands of modern software development. To address these limitations, deep learning techniques,…
We give an overview of our philosophy of pictures in mathematics. We emphasize a bi-directional process between picture language and mathematical concepts: abstraction and simulation. This motivates a program to understand different…
The theory of fractional calculus in the complex plane was not built with a specific application in mind. The main obstacle to application was the difficulty with obtaining analytic continuations of fractional derivatives and integrals. It…
Domain experts are increasingly employing machine learning to solve their domain-specific problems. This article presents six key challenges that a domain expert faces in transforming their problem into a computational workflow, and then…
The philosophy of mathematical practice (PMP) looks to evidence from working mathematics to help settle philosophical questions. One prominent program under the PMP banner is the study of explanation in mathematics, which aims to understand…
The amount of data generated in the modern society is increasing rapidly. New problems and novel approaches of data capture, storage, analysis and visualization are responsible for the emergence of the Big Data research field. Machine…
Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to…
Natural language processing for programming aims to use NLP techniques to assist programming. It is increasingly prevalent for its effectiveness in improving productivity. Distinct from natural language, a programming language is highly…
This report (written in French) is devoted to studying special functions the most used in physics. Special functions are a very broad branch of mathematics, theoretical physics, and mathematical physics. They appeared in the nineteenth…
The languages of mathematical physics and modelling are endowed with a rich ``grammar of dimensions'' that common abstractions of programming languages fail to represent. We propose a dependently typed domain-specific language (embedded in…
Mathematical programming -- the task of expressing operations and decision-making problems in precise mathematical language -- is fundamental across domains, yet remains a skill-intensive process requiring operations research expertise.…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…