Course: MTH6107/MTH727U/ MTH727P-Chaos and Fractals-2025/26

Section outline

Select section General

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General

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- Select activity General Module Announcements
  
  General Module Announcements Forum
  
  Students must
  
  Mark as done
  
  View all general news and announcements from the your module leaders.
- Select activity Student Forum
  
  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.
Select section Exam Preparation - Past exam papers

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Exam Preparation - Past exam papers
- Select activity 2024-25 exam
  
  2024-25 exam File
  
  131.6 KB
- Select activity 2024-25 Exam Solutions
  
  2024-25 Exam Solutions File
  
  147.6 KB
- Select activity 2023-24 exam
  
  2023-24 exam File
  
  127.6 KB
- Select activity 2023-24 exam SOLUTIONS
  
  2023-24 exam SOLUTIONS File
  
  153.9 KB
- Select activity 2022-23 exam
  
  2022-23 exam File
  
  132.8 KB
- Select activity 2016-17 exam
  
  2016-17 exam File
  
  92.6 KB
- Select activity 2016-17 exam SOLUTIONS
  
  2016-17 exam SOLUTIONS File
  
  137.0 KB
- Select activity 2021-22 exam
  
  2021-22 exam File
  
  120.3 KB
- Select activity 2015-16 exam
  
  2015-16 exam File
  
  106.0 KB
- Select activity 2015-16 exam SOLUTIONS
  
  2015-16 exam SOLUTIONS File
  
  138.9 KB
- Select activity 2014-15 exam
  
  2014-15 exam File
  
  135.9 KB
- Select activity 2014-15 exam SOLUTIONS
  
  2014-15 exam SOLUTIONS File
  
  157.2 KB
- Select activity 2013-14 exam
  
  2013-14 exam File
  
  137.0 KB
- Select activity 2013-14 exam SOLUTIONS
  
  2013-14 exam SOLUTIONS File
  
  166.1 KB
Select section Week 1: Dynamical systems

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Week 1: Dynamical systems
- Select activity Exercise Sheet 1
  
  Exercise Sheet 1 File
  
  76.8 KB
- Select activity Solution sheet 1
  
  Solution sheet 1 File
  
  244.9 KB
- Select activity Lecture Notes Week 1
  
  Lecture Notes Week 1 File
  
  1.5 MB
Select section Week 2: Basin of attraction, attracting and repelling periodic points

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Week 2: Basin of attraction, attracting and repelling periodic points
- Select activity Lecture Notes Week 2
  
  Lecture Notes Week 2 File
  
  2.4 MB
Select section Week 3: Diffeomorphisms of R

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Week 3: Diffeomorphisms of R
- Select activity Lecture Notes Week 3
  
  Lecture Notes Week 3 File
  
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Select section Module Description

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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.
Select section Week 4: Fixed points and periodic orbits of diffeomorphisms

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Week 4: Fixed points and periodic orbits of diffeomorphisms
- Select activity Exercise Sheet 2
  
  Exercise Sheet 2 File
  
  101.1 KB
- Select activity Solution Sheet 2
  
  Solution Sheet 2 File
  
  133.8 KB
- Select activity Lecture Notes Week 4
  
  Lecture Notes Week 4 File
  
  2.4 MB
Select section Week 5: Sharkovskii's Theorem, Logistic maps, period-doubling

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Week 5: Sharkovskii's Theorem, Logistic maps, period-doubling
- Select activity Lecture Notes Week 5
  
  Lecture Notes Week 5 File
  
  2.1 MB
Select section Week 6: Topological conjugacy, symbolic dynamics

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Week 6: Topological conjugacy, symbolic dynamics
- Select activity Exercise Sheet 3
  
  Exercise Sheet 3 File
  
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- Select activity Solution sheet 3 (full solutions)
  
  Solution sheet 3 (full solutions) File
  
  118.9 KB
- Select activity Solution sheet 3 (topological conjugacy)
  
  Solution sheet 3 (topological conjugacy) File
  
  85.9 KB
- Select activity Lecture Notes Week 6
  
  Lecture Notes Week 6 File
  
  2.1 MB
Select section Week 7: Coursework

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Week 7: Coursework
- Select activity 001 - Coursework - 20% - Submission Portal [Deadline: 13 November 2025 at 1300]
  
  001 - Coursework - 20% - Submission Portal [Deadline: 13 November 2025 at 1300] Assignment
  
  All questions carry equal marks.
  
  Your solutions must be handwritten (with a proper pen on proper paper).
  
  Please include your name and student ID number.
  
  The submission deadline is 1pm on Thursday 13th November.
  
  Please scan and submit your answer file in 1 single file in PDF format.
  
  The file size limit is 50MB.
  
  7-Day late submission window runs from 13 November 2025 at 1300 to 20 November 2025 at 1300.
  
  For every period of 24 hours, or part thereof, that an assignment is overdue there shall be a deduction of five per cent of the total marks available (i.e. five marks for an assessment marked out of 100). After seven calendar days (168 hours or more late) the mark shall be reduced to zero, and recorded as 0FL (zero, fail, late).
Select section Week 8: Symbolic coding

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Week 8: Symbolic coding
- Select activity Exercise sheet 4
  
  Exercise sheet 4 File
  
  70.3 KB
- Select activity Solution sheet 4
  
  Solution sheet 4 File
  
  87.6 KB
- Select activity Week 8 Lecture Notes
  
  Week 8 Lecture Notes File
  
  2.6 MB
Select section Week 9: Chaos, Cantor sets, Non-escaping sets

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Week 9: Chaos, Cantor sets, Non-escaping sets
- Select activity Exercise Sheet 5
  
  Exercise Sheet 5 File
  
  87.7 KB
- Select activity Solution Sheet 5
  
  Solution Sheet 5 File
  
  113.5 KB
- Select activity Week 9 Lecture Notes
  
  Week 9 Lecture Notes File
  
  2.4 MB
Select section Week 10: Cantor sets and fractals

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Week 10: Cantor sets and fractals
- Select activity Exercise sheet 6
  
  Exercise sheet 6 File
  
  114.6 KB
- Select activity Solution sheet 6
  
  Solution sheet 6 File
  
  140.6 KB
- Select activity Week 10 Lecture Notes
  
  Week 10 Lecture Notes File
  
  2.7 MB
Select section Week 11: Fractals and Dimension, Iterated Function Systems

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Week 11: Fractals and Dimension, Iterated Function Systems
- Select activity Exercise Sheet 7
  
  Exercise Sheet 7 File
  
  104.4 KB
- Select activity Solution sheet 7
  
  Solution sheet 7 File
  
  118.8 KB
- Select activity Week 11 Lecture Notes
  
  Week 11 Lecture Notes File
  
  1.3 MB
Select section Week 12: Dimension

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Week 12: Dimension
Select section Syllabus

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Syllabus

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Select section Module aims and learning outcomes

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Module aims and learning outcomes

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Select section assessment

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assessment

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Select section teaching team

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teaching team

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Select section hints and tips

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hints and tips

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Select section where to get help

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where to get help

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Select section module handbook

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module handbook

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Select section general course materials

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general course materials

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Select section coursework

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coursework

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Select section exam papers

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exam papers

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Select section Early feedback questionnaire

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Early feedback questionnaire

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Select section Assessment information

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Assessment information
- Select activity ASSESSMENT PATTERN - The assessment pattern of thi...
  
  Assessment Pattern - The assessment pattern of this module is 20% coursework + 80% final exam.
  
  Format and dates for the in-term assessments - The coursework will assess material covered in the first 6 weeks of lectures, and will be available by the end of week 6 (i.e. 31st October). You will have approximately 2 weeks to work on the coursework - the deadline will be in week 8 (currently scheduled to be 13th November, but the exact date will be confirmed on the coursework).
  
  Starting this year, a no-discount policy is in effect for approved Extenuating Circumstances claims (EC). This means that if a student
  cannot sit an in-term assessment for valid reasons, and has an approved EC claim for that missed assessment, they will have to sit that
  assessment at the next available opportunity. This will usually be arranged in Week 12 of the same semester where the in-term assessment
  was originally due, in the form of a different assignment covering broadly the same content of the original in-term assessment.
  
  Format of final assessment - Your final examination will be on campus. It will be 2 hours (MTH6107) or 3 hours (MTH727U/P) 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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  Assessment Portal Linked to SITS MTH6107
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  Assessment Portal Linked to SITS MTH727P
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  Assessment Portal Linked to SITS MTH727U
Select section Generated by Assessment Information block

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Generated by Assessment Information block

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Select section Reading List Online

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Reading List Online
- Select activity Some books related to Chaos & Fractals
  
  Some books related to Chaos & Fractals File
  
  36.1 KB
Select section New section

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New section

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Select section Q-Review

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Q-Review
- Select activity Q-Review Recordings
  
  Q-Review Recordings External tool
Select section Skills Journey

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Skills Journey
- Select activity [365_25%20QM%20EMPLOYABILTY%20AND%20SKILLS%20FRAME...
  
  In this module you will develop the following graduate attributes, which you will evidence through the following skills.
  
  Communicate effectively in a range of formats for different purposes with a diverse range of people.
  
  Respect, listen to, and value others and their opinions.
  
  Identify clear personal, study and career goals, taking responsibility for your own growth and development.
  
  Apply a resilient and flexible approach to your life.
  
  Recognise and value your individual worth and identify the contributions you can make.
  
  Apply your disciplinary expertise to broader contexts and society.
  
  Engage critically and reflectively with knowledge.
  
  Demonstrate an innovative and creative approach to problem solving.
  
  Participate effectively and inclusively in different roles as part of a team, including as a leader.
  
  Act honestly, fairly and ethically, including in academic conduct.