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In this article we propose some Maple procedures, for teaching purposes, to study the basics of General Relativity (GR) and Cosmology. After presenting some features of GRTensorII, a package specially built to deal with GR, we give two…
Computer programming was once thought of as a skill required only by professional software developers. But today, given the ubiquitous nature of computation and data science it is quickly becoming necessary for all scientists and engineers…
For several years, students visit us on different occasions at the university. But how to bridge from the school curriculum to the contents of the university mathematics? And how to find a focal point at which an active contribute, despite…
In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One…
Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of…
In this paper we present our experience in using visualization in mathematics education. The experience with our university courses: "Computer tools in matematics" and "Symbolic algebra" provides the basis for mathematics teacher education…
The aim of this work is to present a series of concrete examples which illustrate how the computer algebra system Cadabra can be used to manipulate expressions appearing in General Relativity and other gravitational theories. We highlight…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…
There have been several modifications of how basic calculus has been taught, but very few of these modifications have considered the computational tools available at our disposal. Here, we present a few tools that are easy to develop and…
In this note for the joint meeting of DMV and GDM we illustrate with examples the role of computer algebra in university mathematics education. We discuss its potential in teaching algebra, but also computer algebra as a subject in its own…
The aim of this paper is to propose a strategy to implement the Minimal Model Program in modern computer algebra systems.
Many professional physicists do not fully understand the implications of the Einstein equivalence principle of general relativity. Consequently, many are unaware of the fact that special relativity is fully capable of handling accelerated…
Aversion to mathematics is a recognised and widespread problem. Following a review of the literature on this subject, this paper presents an education program which has been developed to test the hypothesis that transferring attention from…
Einstein's general relativity is increasingly important in contemporary physics on the frontiers of both the very largest distance scales (astrophysics and cosmology) and the very smallest(elementary particle physics). This paper makes the…
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…
This is a brief introduction to general relativity, designed for both students and teachers of the subject. While there are many excellent expositions of general relativity, few adequately explain the geometrical meaning of the basic…
In this note, we use a natural desingularization of the conormal variety of the variety of n x n symmetric matrices of rank at most r to find a general formula for the algebraic degree in semidefinite programming.
Integer programming is concerned with solving linear systems of equations over the non-negative integers. The basic question is to find a solution which minimizes a given linear objective function for a fixed right hand side. Here we also…
The astrophysics of compact objects, which requires Einstein's theory of general relativity for understanding phenomena such as black holes and neutron stars, is attracting increasing attention. In general relativity, gravity is governed by…