APP MTH 7044 - Applied Mathematics Topic C

North Terrace Campus - Semester 1 - 2020

Please contact the School of Mathematical Sciences for further details, or view course information on the School of Mathematical Sciences web site at

  • General Course Information
    Course Details
    Course Code APP MTH 7044
    Course Applied Mathematics Topic C
    Coordinating Unit Mathematical Sciences
    Term Semester 1
    Level Postgraduate Coursework
    Location/s North Terrace Campus
    Units 3
    Available for Study Abroad and Exchange Y
    Assessment Ongoing assessment, Exam
    Course Staff

    Course Coordinator: Professor Anthony Roberts

    Course Timetable

    The full timetable of all activities for this course can be accessed from Course Planner.

  • Learning Outcomes
    Course Learning Outcomes
    In 2020, the topic of this course is Modelling Emergent Dynamics in Complex Systems

    In applying mathematics we have to choose a level of description, of modelling. This course explores the surprisingly subtle theoretical and practical connections between highly detailed, complicated, 'microscale' models and coarse, simple, 'macroscale' models. Further, much of the world around us evolves so that patterns emerge over time, whether coherent (stripes on a tiger, or quasi-stationary distributions) or incoherent (turbulence). We seek to find ways to mathematically model the macroscale coherent or incoherent behaviour that we see arising from microscale dynamics, and the relationship between them. What is the aggregate behaviour? How can the whole be more than the sum of its parts? This course explores how long lasting dynamics emerge after the decay of negligible transients. We find that coordinate transforms clearly separate transients from long-lasting dynamics, even stochastic. A range of examples illustrate that 'long lasting' and 'transient' are subjective decisions to take depending upon the application. Computer algebra handles the algebraic complexity. Starting from basic asymptotic perturbation methods, this course establishes theory and techniques of dimensional reduction for dynamical systems, and develops how these are applied in modelling dynamics in various scenarios. The detailed syllabus will be chosen interactively with students to reflect student projects and interests.

    Assumed knowledge: Modelling with ODEs; PDEs & Waves is useful; linear algebra.

    Learning outcomes

    On successful completion of this course students will be able to

    1. use deep discipline knowledge of mathematical modelling to create asymptotic solutions;
    2. critically invoke theory and techniques of dimensional reduction for modelling to explore and solve problems in dynamical systems.
    3. interpret and communicate the modelling and analysis of systems.
    4. use paradoxes in modelling to become aware of subjectivity in modelling.
    5. develop knowledge of dynamics on networks and its potential implication for social networks.
    University Graduate Attributes

    This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

    University Graduate Attribute Course Learning Outcome(s)
    Deep discipline knowledge
    • informed and infused by cutting edge research, scaffolded throughout their program of studies
    • acquired from personal interaction with research active educators, from year 1
    • accredited or validated against national or international standards (for relevant programs)
    Critical thinking and problem solving
    • steeped in research methods and rigor
    • based on empirical evidence and the scientific approach to knowledge development
    • demonstrated through appropriate and relevant assessment
    Teamwork and communication skills
    • developed from, with, and via the SGDE
    • honed through assessment and practice throughout the program of studies
    • encouraged and valued in all aspects of learning
    Self-awareness and emotional intelligence
    • a capacity for self-reflection and a willingness to engage in self-appraisal
    • open to objective and constructive feedback from supervisors and peers
    • able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate
  • Learning Resources
    Required Resources
    Access to the intranet.
    Recommended Resources
    1. A. J. Roberts. Model emergent dynamics in complex systems. SIAM, Philadelphia, Jan 2015.
    Online Learning
    This course uses MyUni exclusively for providing electronic  resources, such as lecture notes, assignment papers, and sample  solutions.  Students should make appropriate use of these  resources.
  • Learning & Teaching Activities
    Learning & Teaching Modes
    This course relies on lectures and exercises as the primary learning mechanism for the material. A sequence of homework, written, and/or online assignments provides assessment opportunities for students to gauge their progress and understanding.

    The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

    The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
    ActivityQuantityWorkload Hours
    Lecture classes 30 100
    Assignments/assessment 5 56
    Total 156
    Learning Activities Summary
    1. develop models for real world applications;
    2. introductory perturbation methods;
    3. asymptotic techniques;
    4. multi-scale modelling and homogenisation theory.
  • Assessment

    The University's policy on Assessment for Coursework Programs is based on the following four principles:

    1. Assessment must encourage and reinforce learning.
    2. Assessment must enable robust and fair judgements about student performance.
    3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
    4. Assessment must maintain academic standards.

    Assessment Summary
    ComponentWeightingObjective assessed
    Assignments 30% all
    Exam 70% all
    Assessment Related Requirements
    Aggregate score of at least 50%.
    Assessment Detail
    Assessment itemDistributedDue dateWeighting
    Assignment 1 week 2 week 3 6%
    Assignment 2 week 4 week 5 6%
    Assignment 3 week 6 week 7 6%
    Assignment 4 week 8 week 9 6%
    Assignment 5 week 10 week 11 6%
    Homework assignments must either be given to the lecturer in person or left in the box outside the lecturer's office by the given due time. Failure to meet the deadline without reasonable and verifiable excuse may result in a significant penalty for that assignment. The last day on which a miniproject may be submitted is the last teaching day of the semester.
    Course Grading

    Grades for your performance in this course will be awarded in accordance with the following scheme:

    M10 (Coursework Mark Scheme)
    Grade Mark Description
    FNS   Fail No Submission
    F 1-49 Fail
    P 50-64 Pass
    C 65-74 Credit
    D 75-84 Distinction
    HD 85-100 High Distinction
    CN   Continuing
    NFE   No Formal Examination
    RP   Result Pending

    Further details of the grades/results can be obtained from Examinations.

    Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

    Final results for this course will be made available through Access Adelaide.

  • Student Feedback

    The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

    SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy ( course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

  • Student Support
  • Policies & Guidelines
  • Fraud Awareness

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