La enseñanza y aprendizaje del análisis matemático haciendo uso de CAS (computer algebra system).

Se presentan dos investigaciones sobre la enseñanza y el aprendizaje de la integral definida y la integral impropia. Se destacan los aspectos relacionados con el uso de los CAS (Computer Algebra System) Derive y Maple. Se hace incapié en el papel que ha jugado cada uno de ellos en la investigación.

Teaching and learning algebra.

El álgebra esta reconocida como una parte difícil del currículo de matemáticas; sin embargo, la comprensión del álgebra es clave en las matemáticas en general. El propósito de este recurso es explorar los problemas y las posibilidades de enseñanza y aprendizaje del álgebra, y mirar algunas de las dificultades que los estudiantes suelen tener. Sugiere distintos enfoques en la enseñanza y el aprendizaje de las ideas clave.

Algebra, gráficas : Matemáticas, primer curso : actividades para los alumnos y alumnas.

Existe un ejemplar en lengua valenciana con el título: Algebra.Gràfiques : activitats per als-els alumnes de matemàtiques. ISBN: 84-482-0410-7

Algebra, gráficas : Matemáticas, segundo curso : actividades para los alumnos y alumnas.

Existe un ejemplar en lengua valenciana con el título: Algebra.Gràfiques : activitats per a l'alumnat de matemàtiques. ISBN: 84-482-0441-7

Spontaneous Meta-Arithmetic as the First Step Toward School Algebra. 'La meta-aritmética espontánea como el primer paso hacia el álgebra escolar'.

Resumen basado en el de la publicación

Integrating control systems defined on the frame bundles of the space forms

This paper considers left-invariant control systems defined on the orthonormal frame bundles of simply connected manifolds of constant sectional curvature, namely the space forms Euclidean space E-3, the sphere S-3 and Hyperboloid H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1, 3). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to left-invariant control systems defined on Lie groups. In this paper a method for integrating these systems is given where the controls are time-independent. In the Euclidean case the elements of the Lie algebra se(3) are often referred to as twists. For constant twist motions, the corresponding curves g(t) is an element of SE(3) are known as screw motions, given in closed form by using the well known Rodrigues' formula. However, this formula is only applicable to the Euclidean case. This paper gives a method for computing the non-Euclidean screw motions in closed form. This involves decoupling the system into two lower dimensional systems using the double cover properties of Lie groups, then the lower dimensional systems are solved explicitly in closed form.

Monte Carlo numerical treatment of large linear algebra problems

In this paper we deal with performance analysis of Monte Carlo algorithm for large linear algebra problems. We consider applicability and efficiency of the Markov chain Monte Carlo for large problems, i.e., problems involving matrices with a number of non-zero elements ranging between one million and one billion. We are concentrating on analysis of the almost Optimal Monte Carlo (MAO) algorithm for evaluating bilinear forms of matrix powers since they form the so-called Krylov subspaces. Results are presented comparing the performance of the Robust and Non-robust Monte Carlo algorithms. The algorithms are tested on large dense matrices as well as on large unstructured sparse matrices.

Integrable quadratic Hamiltonians on the Euclidean group of motions

In this paper, we discuss the problem of globally computing sub-Riemannian curves on the Euclidean group of motions SE(3). In particular, we derive a global result for special sub-Riemannian curves whose Hamiltonian satisfies a particular condition. In this paper, sub-Riemannian curves are defined in the context of a constrained optimal control problem. The maximum principle is then applied to this problem to yield an appropriate left-invariant quadratic Hamiltonian. A number of integrable quadratic Hamiltonians are identified. We then proceed to derive convenient expressions for sub-Riemannian curves in SE(3) that correspond to particular extremal curves. These equations are then used to compute sub-Riemannian curves that could potentially be used for motion planning of underwater vehicles.