## APP MTH 7087 - Applied Mathematics Topic E

### North Terrace Campus - Semester 2 - 2022

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.

• General Course Information
##### Course Details
Course Code APP MTH 7087 Applied Mathematics Topic E School of Mathematical Sciences Semester 2 Postgraduate Coursework North Terrace Campus 3 Y 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 Staff

Course Coordinator: Dr Judith Bunder

##### 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.

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
##### Recommended Resources
L. Edelstein-Keshet, Mathematical Models in Biology, SIAM Classics in Applied Mathematics, 2005.

J. P. Keener and J. Sneyd, Mathematical Physiology, Springer 2008.

J. D. Murray, Mathematical Biology (two volumes), Springer, 2002.
##### 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:
• 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.

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
1. Enzyme catalysed reactions, the Law of Mass Action, Michaelis-Menten kinetics
2. Ion transport, excitable systems, the Hodgkin-Huxley equations
3. Conservation laws, cell movement, reaction-advection diffusion equations, age-structured models
4. Fisher's equation, travelling waves
5. Pattern formation, Keller-Segel model, linear stability analysis, Turing patterns, diffusion-driven instability
6. Domain growth, free boundary problems, avascular tumour models, development of the necrotic core
• 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 at least 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 13 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.

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

M10 (Coursework Mark Scheme)
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 (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 studentâ€™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.

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