Track 12. Educational innovation Authors: Araceli Queiruga Dios, Angel Martin Del Rey, Ascensión Hernández, Jesus Martin-Vaquero, Luis Hernandez Encinas and Gerardo Rodriguez Sanchez

1. CASE STUDY: MALWARE PROPAGATION MODELS FOR
UNDERGRADUATE ENGINEERING STUDENTS
A. Queiruga Dios1, A. Hernández Encinas1, J. Martín Vaquero1, Á. Martín del Rey1,
G. Rodríguez Sánchez1, and L. Hernández Encinas2
1Department of Applied Mathematics. University of Salamanca, Salamanca, Spain.
2Institute of Physical and Information Technologies, Spanish National Research Council,
Madrid, Spain

2. TEEM’16 - International Conference Technological Ecosystems for Enhancing Multiculturality
 Introduction
 Mathematical models and malware spreading
o Internet of Things
o Solving differential equations to model malware spreading
 Case study: Undergraduate engineering students
o Realistic Mathematics Education
o Case study: malware spreading in mobile devices
o Assessing mathematical competencies
 Conclusions
MALWARE PROPAGATION MODELS FOR UNDERGRADUATE ENGINEERING STUDENTS
OUTLINE
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3. TEEM’16 - International Conference Technological Ecosystems for Enhancing Multiculturality
 The smart phones, tablets and laptops are important part of our daily
life.
 We have proposed our undergraduate engineering students a Realistic
Mathematics Education (RME) based on Internet of Things (IoT) and
malware spreading.
 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. Ordinary Differential Equations and Partial
Differential Equations are topics that will be part of their lives for finding
solutions to many problems.
 They learn Mathematics solving real problems with the help of the
already acquired competencies and skills.
 The progressive implementation of the IoT makes the malware a real
threat. We are all connected.
MALWARE PROPAGATION MODELS FOR UNDERGRADUATE ENGINEERING STUDENTS
INTRODUCTION
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4. TEEM’16 - International Conference Technological Ecosystems for Enhancing Multiculturality
MALWARE PROPAGATION MODELS FOR UNDERGRADUATE ENGINEERING STUDENTS
INTRODUCTION: COMPETENCIES
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5. TEEM’16 - International Conference Technological Ecosystems for Enhancing Multiculturality
MALWARE PROPAGATION MODELS FOR UNDERGRADUATE ENGINEERING STUDENTS
INTRODUCTION: MALWARE SPREADING
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 From the simulations shown in some films or videos published in
YouTube, students could understand how the virus spread works.
 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.
 We proposed the students this process to acquire the competencies
related to Differential Equations.

6. TEEM’16 - International Conference Technological Ecosystems for Enhancing Multiculturality
MATHEMATICS
AM
CAM
Malware
spreading
MALWARE PROPAGATION MODELS FOR UNDERGRADUATE ENGINEERING STUDENTS
MATHEMATICAL MODELS AND MALWARE SPREADING
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 A mathematical model (a set of mathematical symbols, relations and
functions) allows the transformation from a real world situation to a
mathematical problem.
 Mathematical models are idealized (simplified) representations of the
basic characteristics of the real situations.
 They allow the transformation from a real world situation to a
mathematical problem.
 We have proposed our undergraduate engineering students to solve a
real malware spreading problem.
Pollack's circle of modelling:
CAM: Classical Applied Mathematics
AM: Applicable Mathematics

7. TEEM’16 - International Conference Technological Ecosystems for Enhancing Multiculturality
MALWARE PROPAGATION MODELS FOR UNDERGRADUATE ENGINEERING STUDENTS
INTERNET OF THINGS (IoT)

8. TEEM’16 - International Conference Technological Ecosystems for Enhancing Multiculturality
MALWARE PROPAGATION MODELS FOR UNDERGRADUATE ENGINEERING STUDENTS
SOLVING DIFFERENTIAL EQUATIONS TO MODEL MALWARE SPREADING
 Mathematical tools has made accessible for treatment several realistic
applications.
 Engineer students should be able to recognize the same mathematical
model (structure) in different applications that could be modeled using
Differential Equations.

9. TEEM’16 - International Conference Technological Ecosystems for Enhancing Multiculturality
MALWARE PROPAGATION MODELS FOR UNDERGRADUATE ENGINEERING STUDENTS
SOLVING DIFFERENTIAL EQUATIONS TO ACQUIRE MATHEMATICAL COMPETENCIES
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Thinking
mathematically
Reasoning
mathematically
Posing and solving
mathematical
problems
Modelling
mathematically
Representing
mathematical
entities
Handling
mathematical
symbols and
formalism
Communicating in,
with, and about
Mathematics
Making use of aids
and tools for
mathematical
activity

10. TEEM’16 - International Conference Technological Ecosystems for Enhancing Multiculturality
The RME method describes the mathematical concepts from their relation
to the phenomena that originated them, and considering Mathematics as a
human activity.
MALWARE PROPAGATION MODELS FOR UNDERGRADUATE ENGINEERING STUDENTS
REALISTIC MATHEMATICS EDUCATION
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•Students are treated as active participants in their learning process,
and they learn Mathematics doing Mathematics.Activity:
•It is related to apply Mathematics in solving real-life problems.Reality:
•Learning Mathematics means that students pass various levels of
understanding until being able to see the overall problem.Level principle:
•Mathematical topics are not isolated curriculum chapters but as
heavily integrated.Intertwinement:
•Learning Mathematics is a social activity and not only an individual
task.Interactivity:
•It is related to the proactive role of the teachers, as guides of long-
term teaching-learning trajectories.Guidance principle:

11. TEEM’16 - International Conference Technological Ecosystems for Enhancing Multiculturality
MALWARE PROPAGATION MODELS FOR UNDERGRADUATE ENGINEERING STUDENTS
CASE STUDY: MALWARE SPREADING IN MOBILE DEVICES
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Before starting the subject related to differential equations, and before
the proposal of other examples and applications, we conducted a survey
about the knowledge of malware spreading.

12. TEEM’16 - International Conference Technological Ecosystems for Enhancing Multiculturality
MALWARE PROPAGATION MODELS FOR UNDERGRADUATE ENGINEERING STUDENTS
ASSESSMENT AND CONCLUSIONS
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 The way to assess the acquisition of the different competencies varies
depending on the competence itself.
 The assessment include to characterize what you are looking for, to
identify if what you are looking for is included in the situations involved
in the assessment, and to judge the identified.
 It is expected that students work deeper to understand the situations
and problems that they will find in their daily work.
 This paper outlines the mathematical competencies, knowledge and
tools that an engineer must put into practice in a specific field.
 This study has analyzed the problem of malware spreading, that is
modeled by a system of ordinary differential equations. The application
of a Realistic Mathematics Education allows students to pay attention to
real problems like the malware threat.
 In future works, we plan to get some results after using this proposal in
some engineering undergraduate degree classes.

13. CASE STUDY: MALWARE PROPAGATION MODELS FOR
UNDERGRADUATE ENGINEERING STUDENTS
A. Queiruga Dios1, A. Hernández Encinas1, J. Martín Vaquero1, Á. Martín del Rey1,
G. Rodríguez Sánchez1, and L. Hernández Encinas2
1Department of Applied Mathematics. University of Salamanca, Salamanca, Spain.
2Institute of Physical and Information Technologies, CSIC, Madrid, Spain