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Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…
The quality of mathematics education depends largely on the quality of education in general. The main idea may be summarized as follows: in order to educate the younger generation of people to be able to meet adequately the demands of the…
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.
Background: Software modelling is a creative yet challenging task. Modellers often find themselves lost in the process, from understanding the modelling problem to solving it with proper modelling strategies and modelling tools. Students…
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…
With the aim of finding ways that can lead to solving the problem of learning the exact sciences and involving the university student in a participatory and active way during the semester period with the help of new technologies, the…
Software is now a vital scientific instrument, providing the tools for data collection and analysis across disciplines from bioinformatics and computational physics, to the humanities. The software used in research is often home-grown and…
The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer…
This paper lays out the current landscape of tools used in statistics education. In particular, it considers graphing calculators, spreadsheets, applets and microworlds, standalone educational software, statistical programming tools, tools…
In this paper, we are concerned with geometric constraint solvers, i.e., with programs that find one or more solutions of a geometric constraint problem. If no solution exists, the solver is expected to announce that no solution has been…
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…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
The activities of requirements engineering and software testing are intrinsically related to each other, as these two areas are linked when seeking to specify and also ensure the expectations of a software product, with quality and on time.…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and…
So far, the scope of computer algebra has been needlessly restricted to exact algebraic methods. Its possible extension to approximate analytical methods is discussed. The entangled roles of functional analysis and symbolic programming,…
When is good, good enough? This question lingers in approximation theory and numerical methods as a competition between accuracy and practicality. Numerical Analysis is traditionally where the rubber meets the road: students begin to use…
Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…