||Teaching Commutative Algebra and Algebraic Geometry using Computer Algebra Systems
We present a new approach to the teaching of Synthetic Geometry in schools and universities with the help of DGS. The introduction of new elements into DGS helps to optimize the teaching process. These new elements are infinite points in the extended Euclidean plane and the “Swap finite & infinite points” In teaching a mathematics course in commutative algebra and algebraic geometry, we would like to equip students with a computer algebra system so they can solve problems that they might encounter in their own research or in industry. The purpose of this paper is to firstly describe how we use computer algebra in the course that we teach and secondly, to share with the reader a list of applications which make use of the computer that we have found to be suitable for such a course. We give examples of the usage of these new elements in Projectivity, Homology, Conic Sections, Plane Sections of Polyhedra, and in the application of Pappus’ Theorem and Desargues’ Theorem. These new features increase the benefits of DGS in teaching and learning Geometry. We optimize the education process by saving time involved in drawing, generalizing large groups of problems, stimulating and helping investigations, and forming a creative style of thinking.