The overall aim of the course is to encourage reflection on mathematical modelling, on

the current uses and applications of mathematics and to create mathematical models. In

the subject, mathematical models of physics and biology will be studied, together with

applications of mathematics in the present-day information and image society. The

subject will also have a practical side. Various situations will be proposed that need to

be translated into mathematical language, which will then be modelled and resolved to

obtain a solution. It therefore combines questions of a general nature on mathematical

modelling with the study of operational models, through the construction and analysis

of models. Emphasis will be placed on the fact that models are justified by their

adaptation to the experimental data of the phenomenon they are describing, or due to

practical validity in terms of the need that they set out to satisfy.



Particular importance will also be paid to the historical aspects of the formulation of the

different mathematical models.



In the subject, mathematical models applied to problems are presented, whose solutions

or approximations can be found using specially studied techniques in the subjects

Numerical Methods I and II, Differential Equations, Codes and Cryptography,

Extension of Numerical Methods and Mathematical Programming.

MC07CM01 - Acquire a vision on the capacity and power of mathematics to solve practical

problems, and of its applications in a wide variety of areas.

M07CM02 - Develop the ability to find solutions, take decisions and propose operational methods

to other sciences or engineering disciplines.

M07CM03 - Foster the ability to use mathematics. Mathematics are also a tool that students need to

learn how to use.

- Learn about interactions between different parts of mathematics towards achieving a common objective.

- Know real situations, practical problems and their mathematical modeling.

- Learn about modeling models, including their origin and their own history.

- Gain experience in decision-making when approaching a practical situation and accepting the model.

1. INTRODUCTION TO MATHEMATICAL MODELLING.

2. MATHEMATICS IN THE PRESENT-DAY SOCIETY OF INFORMATION AND IMAGES.

Corrective codes. Applications of Perron Theorem. Linear programming. Cellular Automaton.

3. MODELS IN BIOLOGY.

Growth models in a population. Interaction models between species. Health-based

models.

4. MODELS IN PHYSICS.

Control theory. Graphs and molecules.

5. PRACTICAL WORK.



Practical work is done with computers, implementing and applying the algorithms

studied and described in the theoretical part of the subject.

The theoretical content will be explained in lectures, following basic references that

appear in the Bibliography and material of compulsory use. Lectures are complemented

with problem-solving classes (practical sessions) in which students will be asked to

solve questions where the knowledge acquired in the theoretical classes will be applied.

Representative questions and examples of the subject content will be worked on

seminars. These will usually be notified in advance so that the students can work on

them with a view to later reflection and discussion in a dedicated session. Practical work

with computers aimed at acquiring skills in the subject will also be done.



Students will do individual work on theory and problems in periodic seminars with the

support of the professor.



An important part of the student's work is of an individual nature. The professors will

provide guidance for this work and will encourage students to do it with regularity and

enthusiasm. Students are also encouraged to make use of one-to-one tutorials to clarify

any doubt of difficulty they may encounters in the subjects.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • See orientations. (%): 100

CRITERIA FOR CONTINUOUS ASSESSMENT



Written exam: 60%



Computational exercises: 20%. They can be evaluated by an exam or by performance in computer practice sessions.



Active methodologies: 20%. It will consist of one or more of the following activities: e-gela quizzes, out-of-class work, oral presentations and discussions with the teacher. These activities may be individual or in groups.



Specific details will be provided on the first day of class.



In order to pass the course at least a 4.5 out of 10 is required in both the written exam and the computational exercises.





CRITERIA FOR FINAL ASSESSMENT

A student who does not wish to participate in continuous assessment may officially

withdraw from it in writing to the professor responsible for his/her subject, within 9

weeks of the start of the term. The evaluation will consist of a written exam and a computational exercise's exam. In order to pass the course, a 4.5 out of 10 must be obtained in both exams. Likewise, the student may be required to submit a work or give an oral presentation during the exam period to evaluate the competencies worked on through active methodologies.

The evaluation criteria will be the same as the final evaluation ones in the ordinary call.

- The teachers will upload useful material in the eGela virtual classroom.
- Information obtained from Internet.
- Scientific software as Microsoft Excel, Wolfram Mathematica, MatLab and Pyhton.

Basic bibliography

F. BRAUER Y C. CASTILLO-CHÁVEZ: Mathematical Models in Population, Biology and Epidemiology, Text in Applied Mathematics, Springer, 2001

M. BRAUN: Differential Equations and Their Applications: An Introduction to Applied Mathematics, 4th ed, Springer, 1992.

J. M. CORON, Control and Nonlinearity, American Mathematical Society, 2007 (available in

https://www.ljll.fr/~coron/Documents/Coron-book.pdf)

L. EDELSTEIN-KESHET: Mathematical Models in Biology, SIAM, 2005.

R. HABERMAN: Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow, SIAM, 1998.

K. P. HADELER, Topics in Mathematical Biology, Springer, 2017

M. MARTCHEVA, An Introduction to Mathematical Epidemiology, Springer, 2015

J.D. MURRAY: Mathematical Biology,Springer-Verlag, 1989

O. PAPINI Y J WOLFMAN: Algèbre discréte et codes correcteurs, Springer-Verlag, 1995.

C. ROBINSON. Dynamical systems: stability, symbolic dynamics, and chaos. CRC press, 1998.

E. TRÉLAT, Contrôle optimal: théorie & applications, Vuibert, Collection "Mathématiques Concrètes", 2005 (available in https://www.ljll.math.upmc.fr/trelat/fichiers/livreopt2.pdf)

S. WAGNER, H. WANG: Introduction to Chemical Graph Theory, CRC Press, 2019

Web addresses

Programa "dfield" para representacion de soluciones de EDO:
http://www.cs.unm.edu/%7Ejoel/dfield/dfield.jar