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    • General Module Announcements Forum
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    • Student Forum
      Forum Description: This forum is available for everyone to post messages to. Students can raise questions or discuss issues related to the module. Students are encouraged to post to this forum and it will be checked daily by the module leaders. Students should feel free to reply to other students if they are able to.

  • Week 1: Dynamical systems

  • Week 2: Basin of attraction, attracting and repelling periodic points

  • Week 3: Diffeomorphisms of R

  • Module Description

    Chaos theory is an area of mathematics that studies dynamical systems that are highly sensitive to changes on their conditions. Chaotic systems exhibit, among others, underlying patterns, feedback loops, repetitions, and fractals.
    The main aims of this module are twofold:
    To illustrate (rigorously) how simple deterministic dynamical systems are capable of extremely complicated or chaotic behaviour.
    To make contact with real systems by considering a number of physically motivated examples and defining some of the tools employed to study chaotic systems in practice.
    In our study we will encounter concepts such as, discrete, and continuous dynamical systems, repellers and attractors, Cantor sets, symbolic dynamics, topological conjugacy for maps, fractals, iterated function systems and Julia sets. Ideas and techniques from calculus and geometry will be important tools.

  • Week 4: Fixed points and periodic orbits of diffeomorphisms

  • Week 5: Sharkovskii's Theorem, Logistic maps, period-doubling

  • Week 6: Topological conjugacy, symbolic dynamics

  • Week 7: Test & consolidation week

  • Week 8: Symbolic coding

    • Exercise sheet 4 File
      Available from 21 November 2024, 10:50 AM
      61.1 KB

  • Week 9: Chaos, Cantor sets, Non-escaping sets

    • Solution sheet 5 File
      Available from 28 November 2024, 6:00 PM
      98.0 KB

  • Week 10: Cantor sets and fractals

    • Solution Sheet 6 File
      Available from 5 December 2024, 6:00 PM
      122.3 KB

  • Week 11: Fractals and Dimension, Iterated Function Systems

  • Week 12: Dimension

  • Assessment information

    • Assessment Pattern -  The assessment pattern of this module is 20% in-term test + 80% final exam.

      Format and dates for the in-term assessments - TBA

      Format of final assessment - Your final examination will be on campus.  It will be 3 hours in duration with SpLD accommodations handled separately.  You will not be allowed a calculator. 

      link to past papers - 

      Exam papers from previous years can be found here:

      https://qmplus.qmul.ac.uk/mod/data/view.php?id=2443216

      Description of Feedback - 

      It is very important that you participate actively in the module by staying on top of your work, asking questions and seeking feedback for your work continuously.  However, it is totally normal to get stuck while doing your coursework, watching a recording or during live sessions.

      Here are some avenues of support and feedback available to you:

      • Ask questions  during or after live lectures,
      • Participate actively in the problem-solving sessions/tutorials,
      • Visit me in office hours for more personalised feedback
      • Query your peers and the lecturer (me!) using the student forum.


      You can also contact me by email with any queries you might have, but please do consider posting to the Student Forum first, as this will benefit everybody.

      Your feedback comes in many forms.  It is not just written comments on a piece of homework. Please make sure that you actively engage with all these opportunities, as they are there to help you learn and gain confidence in learning new mathematics!

       

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