A METHOD TO CONNECT MATHEMATICS AND SCIENCES USING A COMPUTER ALGEBRA SYSTEM
Résumé
The paper presents an experience driven over twenty years in an Institute of Technology. The two first authors are mathematicians, the third one is teaching automatic control and the last is a specialist in digital electronics. The authors have worked, discussed and shared their common teaching experience on how to restore the vanishing student motivation mainly due to the running and efficient technology. As the powerful software in any domain are getting higher, their use in education seem unavoidable. The paper deals with the use of a computer algebra system in a closed connection and applications to the above scientific domains. A computer algebra system is a software that eases the calculation in a way closed to the same as hand calculation. They are used in mathematics and sciences. Their main features are given in the following. A user friendly interface eases the symbolic manipulations. All numerical operations can be done in an arbitrary-precision. The sketch of curves and surfaces is possible in any representation mode. Some systems offers more features first in additional library then included later in the software after users comments and feedback. For a pedagogical purpose, the well-built on line help is one of the first criterion to choose a computer algebra system rather another one. Nowadays, in higher education, the curriculum of some course includes their natural use in mathematics classrooms. To make mathematics more attractive, to apply them to different technologies and to do an effective scientific work with pleasure, the authors have adjusted a method that has proved its efficiency for many years. The method is based on the use of a computer algebra system. The paper details this new method. The method is illustrated by three examples in different domains. The method is now denoted as the DARe method. It holds three major steps. The first one called Discovering is devoted to a direct use of the computer algebraic software to measure its effect in the mathematical background. The second point is called Applying. It focuses on the way to translate the mathematical information in the specific language of the software. The last point called Resolving is mixing the practical acquired knowledge in order to model and solve a scientific problem by the use of the computer algebraic software. The public concerned with the method is composed of groups of twelve students in the bachelor of technology domain with electrical engineering as speciality. The syllabus is proposing about fifty hours of practical mathematical works. About one thousand students have applied this method. Thanks to their direct comments, discussions and answers to a final questionnaire, the method has been improved since many years. The last release is presented here through some examples taken from automatic control and electronics. Even if the last step, of the method, "to model a problem ", is rising up the difficulties, the students mention that they are doing rather listening mathematics. The computer algebraic system free them of calculus and prevent them from errors. The three steps method has been applied with success in a computer science course. It is also extended for experiments to other subjects such as robotics, electronics and mechanics.
Domaines
Mathématiques [math]
Origine : Fichiers éditeurs autorisés sur une archive ouverte
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