This course is self-contained so there is no need to have studied previously any contents related to this subject.
As a general enrollment requirement, the provisions of RD 1393/2007, as amended by RD 861/2010, were taken into account in order to define the entry requirements for the Master. Candidates must certify that they hold a bachelor's degree or equivalent in order to be eligible for admission to the master. International students from outside the EHEA must certify that they are qualified for admission to postgraduate courses.
Students admitted to this degree program are required to hold a bachelor's degree or equivalent in Mathematics or Physics. Other graduates with knowledge and skills of a level equivalent to holders of bachelor of engineering or science degrees are also eligible for admission to this master's degree.
Nowadays, we can observe a clear tendency for interdisciplinary studies.The mathematical notions of complex networks have fruitful applications to other fields of knowledge. The understanding of reality through models based on networks is used, for example, in Engineering, Computation, Medicine, Biology, Ecology or Social Sciences. One of the aims of this course is to provide the basics that could be developped later depending on the interests of the students.
The topics of this course include: neural, biology, social and economic networks, useful in many branches of knowledge.
The course is also guided by the idea that students at this level must be able to become autonomous learners taking into account their future prospects to undertake research.
Course competences | |
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Code | Description |
CB06 | Possess and understand knowledge that provides a basis or opportunity to be original in the development and / or application of ideas, often in a research context. |
CB07 | Apply the achieved knowledge and ability to solve problems in new or unfamiliar environments within broader (or multidisciplinary) contexts related to the area of study |
CB08 | Be able to integrate knowledge and face the complexity of making judgments based on information that, being incomplete or limited, includes reflections on social and ethical responsibilities linked to the application of knowledge and judgments |
CB09 | Know how to communicate the conclusions and their supported knowledge and ultimate reasons to specialized and non-specialized audiences in a clear and unambiguous way |
CB10 | Have the learning skills which allow to continue studying in a self-directed or autonomous way |
CE01 | Solve physical and mathematical problems, planning their solutions based on the available tools and time and resource constraints |
CE02 | Develop the ability to decide the appropriate techniques to solve a specific problem with special emphasis on those problems associated with the Modeling in Science and Engineering, Astrophysics, Physics, and Mathematics |
CE03 | Have the ability to build and develop advanced mathematical reasoning, and delve into the different fields of mathematics |
CE04 | Have the ability to build and develop advanced physical reasoning, and delve into the various fields of physics and astrophysics |
CE05 | Know how to obtain and interpret physical and/or mathematical data that can be applied in other branches of knowledge |
CE06 | Prove the necessary capacity to perform a critical analysis, evaluation and synthesis of new and complex results and ideas in the field of astrophysics, physics, mathematics and biomathematics |
CE07 | Ability to understand and apply advanced knowledge of mathematics and numerical or computational methods to problems of biology, physics and astrophysics, as well as to build and develop mathematical models in science, biology and engineering |
CE08 | Ability to model, interpret and predict from experimental observations and numerical data |
CG01 | Know how to work in a multidisciplinary team and manage work time |
CG02 | Ability to generate and independently develop innovative and competitive proposals in research and professional activity in the scientific field of Physics and Mathematics |
CG03 | Present publicly the research results or technical reports, to communicate the conclusions to a specialized court, interested persons or organizations, and discuss with their members any aspect related to them |
CG04 | Know how to communicate with the academic and scientific community as a whole, with the company and with society in general about Physics and/or Mathematics and its academic, productive or social implications |
CG05 | Gain the ability to develop a scientific research work independently and in its entirety. Be able to search and assimilate scientific literature, formulate hypotheses, raise and develop problems and draw conclusions from the obtained results |
CG06 | Gain the capacity for dialogue and cooperation with scientific and business communities from other fields of research, including social and natural sciences |
CT01 | Promote the innovative, creative and enterprising spirit |
CT02 | Guarantee and promote respect for Human Rights and the principles of equality, universal accessibility, non-discrimination and democratic values and the culture of peace |
CT03 | Develop critical reasoning and the ability to criticize and self-criticize |
CT04 | Understand and reinforce the ethical and deontological responsibility and commitment in the performance of the professional and research activity and as a citizen |
CT05 | Autonomous learning and responsibility (analysis, synthesis, initiative and teamwork) |
Course learning outcomes | |
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Description | |
Understand the dynamics of complex networks generated by preferential attachment | |
Understand the underlying physics and emerging phenomena in complex neural networks | |
Understand the underlying physics and emerging phenomena in other complex networks such as trophic networks and metabolic networks | |
Understand the underlying physics and emerging phenomena in complex social networks. Understand the dynamics of the structure of social networks | |
Understanding of the concept of probability distribution of nodes and of correlations between nodes in complex networks | |
Understanding of the complex network concept in physics and mathematics, in particular the concept of random graph, scale invariant network, small world network and multiplex networks | |
Ability to simulate different types of complex networks by computer and to study their emerging properties | |
Additional outcomes | |
Not established. |
Training Activity | Methodology | Related Competences (only degrees before RD 822/2021) | ECTS | Hours | As | Com | Description | |
Class Attendance (theory) [ON-SITE] | Combination of methods | CB06 CB07 CB09 CB10 CE01 CE02 CE05 CE07 CE08 CT03 CT05 | 1.48 | 37 | Y | N | ||
Class Attendance (practical) [ON-SITE] | Combination of methods | CB06 CB07 CB09 CB10 CE01 CE02 CE05 CE07 CE08 CT03 CT05 | 0.16 | 4 | Y | N | ||
Workshops or seminars [ON-SITE] | Workshops and Seminars | CE06 CG06 | 0.04 | 1 | Y | N | ||
Writing of reports or projects [OFF-SITE] | Individual presentation of projects and reports | CB07 CB08 CB09 CB10 CG01 CG02 CG03 CG04 CG05 CT01 CT02 CT03 CT04 CT05 | 2.16 | 54 | Y | Y | ||
Study and Exam Preparation [OFF-SITE] | Self-study | CB06 CB07 CB08 CB09 CB10 CE01 CE02 CE04 CE05 CE06 CE07 CG01 CG02 CG05 CT01 CT03 CT04 CT05 | 2.16 | 54 | Y | N | ||
Total: | 6 | 150 | ||||||
Total credits of in-class work: 1.68 | Total class time hours: 42 | |||||||
Total credits of out of class work: 4.32 | Total hours of out of class work: 108 |
As: Assessable training activity Com: Training activity of compulsory overcoming (It will be essential to overcome both continuous and non-continuous assessment).
Evaluation System | Continuous assessment | Non-continuous evaluation * | Description |
Assessment of problem solving and/or case studies | 80.00% | 80.00% | Students must solve individually some problems related with the contents of the course. |
Theoretical papers assessment | 10.00% | 10.00% | Students must write individually a report about some topics of the course. |
Other methods of assessment | 10.00% | 10.00% | Attendance and participation in the possible seminars of the course will be taken into account. |
Total: | 100.00% | 100.00% |
Not related to the syllabus/contents | |
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Hours | hours |
Workshops or seminars [PRESENCIAL][Workshops and Seminars] | 1 |
Unit 1 (de 5): Introduction to complex networks | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Combination of methods] | 13 |
Class Attendance (practical) [PRESENCIAL][Combination of methods] | 1 |
Writing of reports or projects [AUTÓNOMA][Individual presentation of projects and reports] | 17 |
Study and Exam Preparation [AUTÓNOMA][Self-study] | 17 |
Teaching period: Weeks 1-5 |
Unit 2 (de 5): Neural networks | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Combination of methods] | 4 |
Writing of reports or projects [AUTÓNOMA][Individual presentation of projects and reports] | 9 |
Study and Exam Preparation [AUTÓNOMA][Self-study] | 9 |
Teaching period: Weeks 6-7 |
Unit 3 (de 5): Networks in systems biology. Boolean networks | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Combination of methods] | 5 |
Class Attendance (practical) [PRESENCIAL][Combination of methods] | 1 |
Writing of reports or projects [AUTÓNOMA][Individual presentation of projects and reports] | 7 |
Study and Exam Preparation [AUTÓNOMA][Self-study] | 7 |
Teaching period: Weeks 8-9 |
Unit 4 (de 5): Networks in ecology | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Combination of methods] | 5 |
Class Attendance (practical) [PRESENCIAL][Combination of methods] | 1 |
Writing of reports or projects [AUTÓNOMA][Individual presentation of projects and reports] | 7 |
Study and Exam Preparation [AUTÓNOMA][Self-study] | 7 |
Teaching period: Weeks 10-11 |
Unit 5 (de 5): Social and economic networks | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Combination of methods] | 10 |
Class Attendance (practical) [PRESENCIAL][Combination of methods] | 1 |
Writing of reports or projects [AUTÓNOMA][Individual presentation of projects and reports] | 14 |
Study and Exam Preparation [AUTÓNOMA][Self-study] | 14 |
Teaching period: Weeks 12-15 |
Global activity | |
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Activities | hours |
General comments about the planning: | Teaching period may vary due to unexpected circumstances. |
Author(s) | Title | Book/Journal | Citv | Publishing house | ISBN | Year | Description | Link | Catálogo biblioteca |
---|---|---|---|---|---|---|---|---|---|
Juan A. Aledo, S. Martínez and Jose C. Valverde | Parallel Dynamical Systems over Graphs and related topics: A survey | 2015 | http://dx.doi.org/10.1155/2015/594294 | ||||||
R. Rodeva | Algebraic and Discrete Mathematical Methods for Modern Biology | Academic Press | 2015 | ||||||
E. Bujalance y otros | Elementos de matemática discreta | Sanz y Torres | 84-96094-61-8 | 2005 | |||||
J.A. Aledo, J. Penabad, J.C. Valverde y J.J. Villaverde | Ejercicios de Álgebra y Matemática Discreta I | Alpeviva | 2001 | ||||||
J.A. Aledo, J. Penabad, J.C. Valverde y J.J. Villaverde | Álgebra y Matemática Discreta | Alpeviva | 2002 | ||||||
Jordán Lluch, Cristina | Introducción a la teoría de grafos y sus algoritmos | Reverté Universidad Politécnica de Valencia | 84-7721-438-7 | 1996 | |||||
K. Erciyes | Complex networks. An algorithmic perspective | CRC Press | 978-1-4665-7167-9 | 2015 | |||||
Ricardo Vicente Solé, Susanna C. Manrubia | Orden y caos en sistemas complejos, Volumen 2 | Univ. Politèc. de Catalunya | 84-8301-431-9 | 2009 |