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Studying physics of very large scale like the solar system is difficult in real life, using telescope on clear skies over years. We are probably a world first to create four well designed gravity computer models to serve as powerful…
Although metaheuristics have been widely recognized as efficient techniques to solve real-world optimization problems, implementing them from scratch remains difficult for domain-specific experts without programming skills. In this…
This paper is on customization of computer models using the Easy Java Simulation authoring toolkit for the Singapore syllabus, based on real astronomical data, supported with literature reviewed researched pedagogical features. These 4 new…
In our contribution we will reflect, through a collection of selected examples, on the potential impact of the GeoGebra Discovery application on different social and educational contexts.
What is the best representation for doing euclidean geometry on computers? These notes from a SIGGRAPH 2019 short course entitled "Geometric algebra for computer graphics" introduce projective geometric algebra (PGA) as a modern framework…
This paper presents an open tool for standardizing the evaluation process of the layout analysis task of document images at pixel level. We introduce a new evaluation tool that is both available as a standalone Java application and as a…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
In this primer, we will describe a number of projects that can be completed with a 3D printer, particularly by mathematics professors and their students. For many of the projects, we will utilize Mathematica to design objects that…
Graph convexity has been used as an important tool to better understand the structure of classes of graphs. Many studies are devoted to determine if a graph equipped with a convexity is a {\em convex geometry}. In this work we survey…
This application for learning APPROXIMATION ALGORITHM has been designed in Java which will make user comfortable in learning the very complex subject "NP-Completeness" and the solution to NP-Complete problem using approximation algorithm.
Author developed a uniform model for different spaces where distance and angle measure kinds are parameters. This model is calculus centric, but can also be used in theoretical research. It is useful in the following domains: deduction of…
Large language models have shown impressive results for multi-hop mathematical reasoning when the input question is only textual. Many mathematical reasoning problems, however, contain both text and image. With the ever-increasing adoption…
LogEx is a learning environment that supports students in rewriting propositional logical formulae, using standard equivalences. We organized a pilot study to prepare a large scale evaluation of the learning environment. In this paper we…
We study sequential programs that are instruction sequences with jump-shift instructions in the setting of PGA (ProGram Algebra). Jump-shift instructions preceding a jump instruction increase the position to jump to. The jump-shift…
The mathematical modeling of generics in Java and other similar nominally-typed object-oriented programming languages is a challenge. In this short paper we present the outline of a novel order-theoretic approach to modeling generics, in…
This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…
In Bayesian machine learning, conjugate priors are popular, mostly due to mathematical convenience. In this paper, we show that there are deeper reasons for choosing a conjugate prior. Specifically, we formulate the conjugate prior in the…
The emergence of ChatGPT has been rapid, and although it has demonstrated positive impacts in certain domains, its influence is not universally advantageous. Our analysis focuses on ChatGPT's capabilities in Mathematics Education,…
Geometry is essentially a global language, which is fully understood in different times, countries and cultures. The proof of a geometric theorem (e.g. the Pythagorean Theorem) or a geometric construction (e.g. the construction of an…
JaTeCS is an open source Java library that supports research on automatic text categorization and other related problems, such as ordinal regression and quantification, which are of special interest in opinion mining applications. It covers…