Teaching plan for the course unit



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General information


Course unit name: Complex Systems

Course unit code: 572561

Academic year: 2020-2021

Coordinator: Marian Boguńa Espinal

Department: Department of Condensed Matter Physics

Credits: 3

Single program: S



Estimated learning time

Total number of hours 75


Face-to-face and/or online activities



-  Lecture

Face-to-face and online




-  Seminar

Face-to-face and online



Supervised project


Independent learning




Competences to be gained during study



CB6 – Having knowledge and understanding that provides a basis or opportunity for originality in developing and/or applying ideas, often in a research context.

CB7 - That the students can apply their knowledge and their ability to solve problems in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their field of study.

CB8 - That students are able to integrate knowledge and handle complexity and formulate judgments based on information that, although incomplete or limited, includes reflections on social and ethical responsibilities linked to the application of their knowledge and judgments.

CB9 - That students can communicate their conclusions and the underpinning knowledge and rationale to specialists and non-specialists in a clear and unambiguous manner.

CB10 - Students must possess the learning skills that enable them to continue studying in a way that will be largely self-directed or autonomous.


CG1 - Know how to evaluate and select the appropriate scientific theory and precise methodology of their field of study to make judgments based on incomplete or limited information including, where necessary and appropriate, reflections on the social and ethical responsibilities linked to the solution that is proposed in each case.

CG2 - Being able to check the scientific literature, databases and analyze scientific and technical documents in English.

CG3 – Being able to prepare reports, presentations and scientific publications.

CG4 – Being able to conceive and design a research process.

CG5 – Being able to predict and control the evolution of complex situations by developing new and innovative working methodologies adapted to specific scientific / research, technological or professional contexts, usually multidisciplinary, where his/her activity is developed.

CG6 - Develop sufficient autonomy to participate in research projects and scientific and technological collaboration within their subject area, in interdisciplinary contexts and, where appropriate, with a high component of knowledge transfer.


CT1 – To be autonomous, dynamic and organized, with analytical and synthesis capacity, critical thinking skills and ability to be prospective.

CT3 - Being able to work in a team and adapt to multidisciplinary and international teams on different scales.

CT5 - Having the ability to make decisions and adapt to new situations.


CE3 - Being able to write programs in high-level programming languages and knowing the basics of parallelization and optimization that enable parallel execution of tasks in the context of the atomistic and multiscalecomputational modeling.

CE6 - Understanding the different time and length scales in nature and the physical-mathematical formalisms that can be applied in each of them.

CE10 - Understanding the physical laws that govern the behavior of nonequilibrium systems: relaxation processes and transport phenomena.

CE11 - Understanding the physical laws that govern the behavior of nonequilibrium systems: chemical reactivity, reaction-diffusion processes and phase changes in physicochemical and biochemical systems.

CE13 - Given a material, physical or chemical phenomenon or complex system to be modeled, being able to evaluate and select the time and length scales in which this phenomenon occurs.





Learning objectives


Referring to knowledge

  • Understand the stability of systems of differential equations representing the dynamics of coupled systems
  • Understand the importance and ubiquity of free scaling behaviors
  • Being able to understand generalization of dynamic system to consider spatial dependencies , and structures emerging and characterize a system as complex .
  • Have an overview of the modern theory of networks and provide some applications to different fields.



Teaching blocks


1. Introduction to complex systems. Dynamical systems and scaling laws

2. Spatio temporal structures

3. Introduction to complex networks: structure and applications



Teaching methods and general organization


- Lectures: Lectures are taught orally by the teacher without the active participation of the students.
- Group work: Learning activity that must be done through collaboration between the members of a group.
- Written work: A consistent activity in the presentation of a written document.
- Application activities: With the application activities it is possible to contextualize the theoretical learning through its application to a fact, event, situation, data or specific phenomenon selected to facilitate learning.
- Problem solving: In the problem-solving activity, teachers present a complex issue that students must solve, whether working individually or in a team.
- Practical exercises: activity based on practical exercises consists in the formulation, analysis, resolution or debate of a problem related to the topic of the subject. This activity is aimed at learning through the practice of knowledge or programmed abilities.
- Practices: They allow to apply and configure, at a practical level, the theory of a field of knowledge in a specific context.



Official assessment of learning outcomes


- Written tests: case study, problem solving (45%)
- Oral tests: exhibitions (20%)
- Work done by the student: memoirs, projects (35%)


Examination-based assessment

The students that request it will be evaluated with a single global proof that represents 100% of the total grade. To give up on the continuous assessment, and request the single assessment, the student must present to the teacher the instance that exists to this effect on the faculty website, before the first test of continuous assessment of the subject.

Students who have been qualified with a minimum grade of 3.5 can be re-evaluated. The re-evaluation consists of a written synthesis test that includes the whole program of the subject. The re-evaluation is done on the dates determined by the Board of Studies. The final grade is the most favorable of the two, the one of the single evaluation or the one of the re-evaluation. The student who, having passed the subject, wants to improve the grade for the re-assessment, must give up the qualification by means of a written presentation to the teacher with a copy to the Secretariat of the center.

These tests can consist of several short questions, topics, questions with related exercises and problems. The score of each question, question or problem is indicated in the statement of the exam.