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We present OGRe, a modern Mathematica package for tensor calculus, designed to be both powerful and user-friendly. The package can be used in a variety of contexts where tensor calculations are needed, in both mathematics and physics, but…
We describe the development of a junior-senior level course for Physics majors designed to teach Mathematica skills in support of their undergraduate coursework, but also to introduce students to modern research level results. Standard…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…
This is the first part of a series of papers aiming to show how trigonometry and analytic tools can help into tackling demanding Olympiad geometry problems. We present several novel techniques for tackling hard problems from various…
This paper develops an autonomous agentic framework called V-Math that aims to assist Vietnamese high school students in preparing for the National High School Graduation Mathematics Exams (NHSGMEs). The salient framework integrates three…
Vector calculus in three-dimensional space is ubiquitous in applications of mathematics in physics and engineering. Its two-dimensional version is, however, quite rare. Here we try to provide a pedagogical account of the subject. It is…
Generative AI has shown potential in solving physics problems and providing feedback on assessments. However, results are sometimes still inaccurate, at the wrong level, or using notations and definitions not appropriate for a particular…
Graph algorithms play an important role in many computer science areas. In order to solve problems that can be modeled using graphs, it is necessary to use a data structure that can represent those graphs in an efficient manner. On top of…
To synthesize Maxwell optics systems, the mathematical apparatus of tensor and vector analysis is generally employed. This mathematical apparatus implies executing a great number of simple stereotyped operations, which are adequately…
Sketching is an important means of communication in software engineering practice. Yet, there is little research investigating the use of sketches. We want to contribute a better understanding of sketching, in particular its use during…
Competitive programming contests play a crucial role in cultivating computational thinking and algorithmic skills among learners. However, generating comprehensive test cases to effectively assess programming solutions remains…
We review some basic results of convex analysis and geometry in $\mathbb{R}^n$ in the context of formulating a differential equation to track the distance between an observer flying outside a convex set $K$ and $K$ itself.
We present the first version of CYJAX, a package for machine learning Calabi-Yau metrics using JAX. It is meant to be accessible both as a top-level tool and as a library of modular functions. CYJAX is currently centered around the…
For the last four years, the School of Physics at Georgia Tech have been preparing new Graduate Teaching Assistants (GTAs) through a program that integrates pedagogy, physics content, and professional development strategies. Here we discuss…
Physlets are scriptable Java applets that can be used for physics instruction. In this article we discuss the pedagogical foundations of Physlet use and provide a sample of Physlet-based exercises that could be used to teach optics.
The mathematical software system polymake provides a wide range of functions for convex polytopes, simplicial complexes, and other objects. A large part of this paper is dedicated to a tutorial which exemplifies the usage. Later sections…
LaTeX is a widely-used document preparation system. Its powerful ability in mathematical equation editing is perhaps the main reason for its popularity in academia. Sometimes, however, even an expert user may spend much time fixing an…
The generalized extreme value (GEV) distribution is commonly employed to help estimate the likelihood of extreme events in many geophysical and other application areas. The recently proposed blended generalized extreme value (bGEV)…
Collaborative competitions have gained popularity in the scientific and technological fields. These competitions involve defining tasks, selecting evaluation scores, and devising result verification methods. In the standard scenario,…
TensorKit.jl is a Julia-based software package for tensor computations, especially focusing on tensors with internal symmetries. This paper introduces the design philosophy, core functionalities, and distinctive features, including how to…