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Araceli Queiruga-Dios1, Gerardo Rodríguez Sánchez1, Ascensión Hernández Encinas1, Ángel Martín del Rey1, Jesús Martín-Vaquero1, Luis Hernández-Encinas2
1Department of Applied Mathematics University of Salamanca, Salamanca, Spain
2Spanish National Research Council (CSIC), Madrid, Spain
The smart phones, tablets and laptops are important part of our daily life. Students are everyday and every moment using their mobile phones. Sometimes it is difficult that they disconnect from those devices and pay attention to teachers and lecturers. Mathematical classes need a special attention to get the explanations and not to spend too much time looking for understanding basic concepts.
We have proposed our undergraduate engineering students a Realistic Mathematics Education (RME) based on Internet of Things (IoT) and malware propagation.
Engineering students have to handle a lot of simulation problems using numerical methods: magnetic shield, airflow around an obstruction, car deforms in a crash, etc. Differential Equations and Partial Differential Equations are topics that will be part of their life for finding solutions to many problems. They learn mathematics solving real problems with the help of the already acquired competences and skills. We have proposed the students the adaptation of the mathematical competences to the engineering context: modeling mathematically the dissemination of any virus (biological o computational); thinking mathematically on their mobile devices; handling mathematical symbols and formalism, and solving mathematical problems using the needed tools.
The progressive implementation of the IoT makes the malware a real threat. We are all connected. We found the malware as one of the most important security threats against mobile devices. Mobile devices play an important role in the development, management, monitoring, and control of the critical infrastructures. Critical infrastructure sectors include energy, public health, telecommunications, transportation, nuclear safety, emergency services, industry, etc. They are essential for the maintenance of the basic social requirements, and are managed by information and telecommunication technologies.
From the simulations shown in some films or videos published in YouTube, students could understand how the virus spread works. There are several simulations available at the Internet and also some developments at Wolfram Community for example.
From the classical model of Kermack and McKendrick to the Random Constant-Spread Model that describes the outbreak of the code-red worm in 2001, students can work on the model expressing the equations whose solutions will be found using different technological tools. They will describe the behavior of the phenomenon and determine the efficiency of the mathematical model developed. We proposed the students this process to acquire the competences related to Differential Equations, and we made a statistical analysis from their answers to a reliable survey.