## APP MTH 7045 - Applied Mathematics Topic B

### North Terrace Campus - Semester 1 - 2024

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 7045 Applied Mathematics Topic B Mathematical Sciences Semester 1 Postgraduate Coursework North Terrace Campus 3 Y Ongoing assessment, exam
##### Course Staff

Course Coordinator: Professor Matthew Roughan

##### Course Timetable

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

• Learning Outcomes
##### Course Learning Outcomes
Complex network modelling and inference.

Syllabus:

Networks are all around us -- friend networks, communications networks, and transportation networks to name but three. There is a need to both understand these to improve our lives and relationships, and to better engineeer components to make our critical infrastructure more reliable and efificient.

This course will study graphs and networks, and their generalisations as applied to modelling of complex systems of interacting components or actors with the view of achieving improve behaviour.

We'll go somewhat beyond standard graph theory in that we will consider how quantities associated with links affect real network problems. In particular, we will consider how to statistically infer properties of networks from realistically obtainable metrics when the networks are large, and we cannot query the network directly, but must use indirect measurement strategies. Applications range from management of computer networks to analysis of social phenomenon, such as memes that "go viral".

Learning Outcomes:

1. Modelling: model a problem
- Take a problem stated in words, and convert it into mathematical form
- Consider assumptions and approximations
- Deal with incomplete information/ideas by asking questions, and investigation

2. Analysis: analyse the problem using diverse tools
- Analysis (mathematical solution of problems)
- Statistics (incorporating data)
- Simulation
- Algorithms

3. Critically examine results:
- Sanity checking
- Close the loop between modelling->analysis->output
- Sensitivity analysis

4. Communicate results
- Mathematical exposition skills

Pre-requisites and assumed knowledge:

Mathematics up to second year level will be required, including

- Probability and Statistics II,
- Scientific Computing or equivalent.

In particular, this project will require some programming in the Julia programming language, which is similar to Matlab. Solid experience with any of Python, Matlab, R or Julia should be sufficient background.

Some knowledge of graph theory and/or Discrete Maths would be useful.
##### 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 4: Professionalism and leadership readiness

Graduates engage in professional behaviour and have the potential to be entrepreneurial and take leadership roles in their chosen occupations or careers and communities.

all

Attribute 7: Digital capabilities

Graduates are well prepared for living, learning and working in a digital society.

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
Most course materials are available online either through MyUni or https://roughan.info/notes/network_modelling/
##### Recommended Resources
Resources will be provided through MyUni.

##### 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 written and/or online assignments provides assessment opportunities for students to gauge their progress and understanding.
##### Workload

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   24   72
Assignments/assessment   8   48
Mini-Project 1 36
Total   156
##### Learning Activities Summary
1. Mathematical Modelling
2. Graph and Network Theory
3. Statistical Inference of Networks
4. Graph Algorithms
5. Network Data Science
• 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 Mini-project 30% all Competition 10% all Test 30% all
##### Assessment Related Requirements
An aggregate score of 50% is required to pass the course.
##### Assessment Detail

No information currently available.

##### Submission
Homework assignments must either be given to the lecturer in person or submitted via MyUni by the given due time.  Failure to meet the deadline without reasonable and verifiable excuse may result in a significant penalty for that assignment.
##### 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 (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.

```
```