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Subject: COMPLEX SYSTEMS (A.A. 2021/2022)

master degree course in MATHEMATICS

Course year 2
CFU 6
Teaching units Unit Sistemi complessi
Related or Additional Studies (lesson)
  • TAF: Supplementary compulsory subjects SSD: INF/01 CFU: 6
Teachers: Marco VILLANI
Exam type oral
Evaluation final vote
Teaching language Italiano
Contents download pdf download

Teachers

Marco VILLANI

Overview

The study of complex systems has acquired a leading role not only in scientific activities, but also in companies and organizations active on the market and in society. In the scientific field, it provides a new and complementary point of view compared to those of traditional disciplines, while in the corporate and organizational sphere it provides both fundamental conceptual tools for management in a period of rapid changes, and operational tools to decipher the dynamics of processes, markets, finance.
In this field the use of IT tools is a necessary step, both to simulate complex dynamics and to analyse the results of the simulations, so it is advisable for the IT specialists to know the main elements of this new approach and to be able to dialogue with both specialists and users.

Results.

The study of complex systems is oriented to the research of organizational principles in systems composed of different elements interacting in a non-linear way. It has been shown that some behaviours are more influenced by the properties of interactions than by the nature of the elements of the system, and this allows to apply, with the due rigor, similar concepts and methods in different systems.

At the end of the course the student:
• will have acquired the main concepts relating to complex systems;
• will know the main mathematical and computational tools of complex systems;
• will know the applications of the Science of Complexity.

Admission requirements

None

Course contents

Emerging phenomena and their models
Cellular Automata
Self-reproducing systems
Structure and dynamics of complex networks
Multigraphs, Hypergraphs
Self-organising complexity (SOC)
Robustness, degeneracy

Teaching methods

Teaching is based, on an ordinary basis, on lectures and optional projects. Student questions and interventions are welcome and encouraged. Attendance is not compulsory, but strongly recommended. The course is delivered in Italian. All technical and organizational information on teaching, as well as teaching material, will be uploaded to the Dolly platform. The student is invited to register and consult this platform regularly

Assessment methods

The verification is based on a written exam with open answers (2 questions chosen from 4-5 questions regarding the topics discussed in class, it is necessary to have enough in both answers for the task to be sufficient). This test is aimed at verifying the learning of the main topics of the course and the reasoning skills acquired by the students. For those students who wish, it is possible to prepare a one-hour lesson on a monographic topic (which contributes 1/3 to the final grade). Furthermore, those who prefer can take an oral exam instead of the written exam.

Learning outcomes

Knowledge and understanding:
At the end of the course the student will have acquired the main concepts related to complex systems, will know the main mathematical and computational tools and will be able to understand part of the current scientific literature.
Ability to apply knowledge and understanding:
Thanks to the variety of examples considered, the student will be able to apply the most appropriate methods for the different cases he faces
Autonomy of judgment:
Thanks to the variety of examples considered, the student will be able to identify the most effective approaches for different cases, and identify their limits
Communication skills:
The student will acquire the language of the science of complexity, and will demonstrate its mastery during the exam and the possible lesson to the companions
Learning ability:
Several cases will be examined, going from a phenomenological description to mathematical modelling and related analysis tools. This experience will expand the learning ability of new cases and tools, and the ability to model complex phenomena