APP MTH 4051 - Applied Mathematics Topic E - Honours

North Terrace Campus - Semester 2 - 2022

This course is available for students taking an honours degree in Mathematical Sciences. The course will cover an advanced topic in applied mathematics. For details of the topic offered this year please refer to the Course Outline.

  • General Course Information
    Course Details
    Course Code APP MTH 4051
    Course Applied Mathematics Topic E - Honours
    Coordinating Unit School of Mathematical Sciences
    Term Semester 2
    Level Undergraduate
    Location/s North Terrace Campus
    Units 3
    Contact Up to 2.5 hours per week
    Available for Study Abroad and Exchange Y
    Restrictions Honours students only
    Course Description This course is available for students taking an honours degree in Mathematical Sciences. The course will cover an advanced topic in applied mathematics. For details of the topic offered this year please refer to the Course Outline.
    Course Staff

    Course Coordinator: Dr Judith Bunder

    This is the same course as APP MTH 7087 - Applied Mathematics Topic E
    Course Timetable

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

  • Learning Outcomes
    Course Learning Outcomes
    In 2022 the topic of this course is Modelling Emergent Dynamics in Complex Systems.

    Synopsis
    In applying mathematics we have to choose a level ofdescription, of modelling.  This course explores thesurprisingly subtle theoretical and practical connectionsbetween highly detailed, complicated, 'microscale' modelsand coarse, simple, 'macroscale' models. Further, much ofthe world around us evolves so that patterns emerge overtime, whether coherent (stripes on a tiger, orquasi-stationary distributions) or incoherent (turbulence).We seek to find ways to mathematically model the macroscalecoherent or incoherent behaviour that we see arising frommicroscale dynamics, and the relationship between them. What is the aggregate behaviour? How can the whole be morethan the sum of its parts?  This course explores how longlasting dynamics emerge after the decay of negligibletransients. We find that coordinate transforms clearlyseparate transients from long-lasting dynamics, evenstochastic.  A range of examples illustrate that 'longlasting' and 'transient' are subjective decisions to takedepending upon the application. Computer algebra handles thealgebraic complexity. Starting from basic asymptoticperturbation methods, this course establishes theory andtechniques of dimensional reduction for dynamical systems,and develops how these are applied in modelling dynamics invarious scenarios.

    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)

    Attribute 1: Deep discipline knowledge and intellectual breadth

    Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.

    all

    Attribute 2: Creative and critical thinking, and problem solving

    Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.

    all

    Attribute 3: Teamwork and communication skills

    Graduates convey ideas and information effectively to a range of audiences for a variety of purposes and contribute in a positive and collaborative manner to achieving common goals.

    all

    Attribute 8: Self-awareness and emotional intelligence

    Graduates are self-aware and reflective; they are flexible and resilient and have the capacity to accept and give constructive feedback; they act with integrity and take responsibility for their actions.

    all
  • Learning Resources
    Required Resources
    Access to the internet and University intranet.
    Recommended Resources
    1. A. J. Roberts. Model emergent dynamics in complex systems. SIAM, Philadelphia, Jan 2015.
    Online Learning
    This course uses MyUni for providing electronic resources, such as assignments and handouts, and for making course announcements. It is recommended that students make appropriate use of these resources. Link to MyUni login page:
    https://myuni.adelaide.edu.au/webapps/login/
  • Learning & Teaching Activities
    Learning & Teaching Modes
    Students work through the course material with support from the lecturer. Fortnightly homework assignments help students strengthen their understanding of the theory and their skills in applying it, and allow them to gauge their progress.
    Workload

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



    Activity   Quantity Workload Hours
    Study 30 90
    Assignments 5 66
    Total 156
    Learning Activities Summary

    Learning activities summary

    1. basic asymptotic perturbation methods,
    2. theory and techniques of dimensional reduction for dynamical systems, and
    3. applications in modelling dynamics on a continuum and on network hierarchies.
  • 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
    Component Weighting Objective assessed
    Assignments 30% all
    Exam 70% all
    Assessment Related Requirements
    An aggregate score of 50% is required to pass the course.
    Assessment Detail
    Assessment item Distributed Due date Weighting
    Assignment 1 Week 2 Week 4 6%
    Assignment 2 Week 4 Week 6 6%
    Assignment 3 Week 6 Week 8 6%
    Assignment 4 Week 8 Week 10 6%
    Assignment 5 Week 10 Week 12 6%
    Submission
    All written assignments are to be submitted via MyUni. 

    Students requiring an extension or exemption for an assignment for medical or compassionate reasons should contact the lecturer as early as possible, and certainly before the deadline for the assignment in question.
    Course Grading

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

    M11 (Honours Mark Scheme)
    GradeGrade reflects following criteria for allocation of gradeReported on Official Transcript
    Fail A mark between 1-49 F
    Third Class A mark between 50-59 3
    Second Class Div B A mark between 60-69 2B
    Second Class Div A A mark between 70-79 2A
    First Class A mark between 80-100 1
    Result Pending An interim result RP
    Continuing Continuing CN

    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 (http://www.adelaide.edu.au/policies/101/) 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

    Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's student’s disciplinary procedures.

The University of Adelaide is committed to regular reviews of the courses and programs it offers to students. The University of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.