APP MTH 7044 - Applied Mathematics Topic C
North Terrace Campus - Semester 1 - 2022
General Course Information
Course Code APP MTH 7044 Course Applied Mathematics Topic C Coordinating Unit School of Mathematical Sciences Term Semester 1 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Available for Study Abroad and Exchange Y Course Description This course is available for students taking a Masters 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 Coordinator: Professor Anthony Roberts
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning OutcomesIn 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.
On successful completion of this course students will be able to
- use deep discipline knowledge of mathematical modelling to create asymptotic solutions;
- critically invoke theory and techniques of dimensional reduction for modelling to explore and solve problems in dynamical systems.
- interpret and communicate the modelling and analysis of systems.
- use paradoxes in modelling to become aware of subjectivity in modelling.
- 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.
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.
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.
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.
Required ResourcesAccess to the intranet.
- A. J. Roberts. Model emergent dynamics in complex systems. SIAM, Philadelphia, Jan 2015.
Online LearningThis 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 ModesThis 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.
Activity Quantity Workload Hours Lecture classes 30 100 Assignments/assessment 5 56 Total 156
Learning Activities Summary
- develop models for real world applications;
- introductory perturbation methods;
- asymptotic techniques;
- multi-scale modelling and homogenisation theory.
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
Component Weighting Objective assessed Assignments 30% all Exam 70% all
Assessment Related RequirementsAggregate score of at least 50%.
Assessment item Distributed Due date Weighting 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%
SubmissionHomework 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.
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.
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.
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