Abstract:

The Spanish Naval Academy (ENM) is in charge of the education of future Navy officers. During such period they must complete their studies in the Mechanical Engineering Degree. In this context, this teaching innovation project proposes a pedagogical strategy in which Algebra and Statistics are presented as modeling tools for situations that arise outside their mathematical scope, such as Physics or Manufacturing Engineering. This approach first presents basic theory concepts and, then, a typical real-life problem where these ideas apply. Our learning strategy is intended to establish the connection between basic and applied subject contents, which is often missed by engineering undergraduate students.

The linear Algebra subject is instrumental in the development of engineers. In particular, linear equations systems appear in many problems in science, or more distant subjects like Economics. To facilitate the analysis of this type of system, the Rouché-Frobenius theorem classifies them according to their mathematical features. To connect this high-level procedure with a practical problem, we have utilized these techniques in the subject of Physics I, and in particular in problems of dynamics, where we study the behavior of systems consisting of two blocks of a certain mass joined by a flexible and inextensible thread passing through a fixed pulley without friction and mass. It is interesting to investigate in which situations the system initiates motion, depending on the variables involved. Once the corresponding equations have been posed, they can be studied as a system of linear equations, where the methods contained in the Algebra course are useful to reach the desired conclusions.

This activity was presented during the theory sessions of the Algebra course, and it was developed later by the students. They have been provided with two different situations and their corresponding analysis. Subsequently, a questionnaire was sent to the students so that they could evaluate the usefulness and convenience of the proposed workshop.

The focus of Statistics is on regression models, focusing on linear regression, which is the simplest technique to obtain the relationship between two variables, but it is widely used in sociological, economic, or scientific studies.

The students were provided with a self-explanatory document so that they could familiarize themselves with the deduction of the equation of the line of best fit, the correlation coefficient, and the limitations in its application and interpretation. At the same time, they were introduced to the Excel tool. Next, the students performed an activity related to Ohm's law and platinum resistance thermometers to study the linear and nonlinear relationship between temperature (Kelvin degrees) and resistance (ohms). The platinum resistance thermometer is an electronic device used inside circuits to determine the temperature of a system through its electrical resistance. Its purpose is to evaluate the changes that can occur in the amount of electrical resistance of a material in cases of extreme temperatures. It is known that the resistivity of a metallic material increases with increasing temperature because the ions of the conductor vibrate with greater amplitude, which makes it more likely that a moving electron collides with an ion; this prevents the drag of electrons through the conductor, and, therefore, also the current.

Keywords:

Algebra and Statistics, education, workshop.