Course: Complex System

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Course title Complex System
Course code KMA/KS
Organizational form of instruction Lecture
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 2
Language of instruction Czech, English
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
  • Fürst Tomáš, RNDr. Ph.D.
Course content
1. The age of complexity. Internet, telephone networks, power grids, transportation network, biochemical and neural networks. Why to be interested in networks? It's a small world. 2. The mathematics of networks ... is linear algebra in disguise. Measures, metrics and structures. 3. Algorithms for network analysis 4. Network models and processes. Network formation, percolation, basic epidemiology. 5. Dynamical systems, stability, chaos and bifurcations. The language of complex systems. 6. Synchronisation. Pendulums, fire-bugs, and human hearts. 7. Self-organisation and emergent phenomena. The new mathematics of life.

Learning activities and teaching methods
Lecture, Demonstration
  • Attendace - 26 hours per semester
  • Preparation for the Exam - 34 hours per semester
Learning outcomes
To understand the mathematics of complex networks. To understand models of network processes.
Comprehension Comprehension of complex networks, ability to solve practical problems.
Some linear algebra, basic ordinary and partial differential equations, programming (MatLab, SciLab or Octave are preferred), English (all course materials are in English).

Assessment methods and criteria
Oral exam, Seminar Work

Exam: a working sotware code and demostrated comprehension of basic principles.
Recommended literature
  • Newman, M. (2010). Networks. An Introduction. Oxford.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Applied Mathematics (2014) Mathematics courses 1 Summer