The use of mathematical models has grown rapidly in recent years, owing to the advent of cheap and powerful computers, expanding from applications in the physical and earth sciences to the biological and environmental sciences, and now into industry and commerce.

In this course we study:

• The process of starting with an initial succinct non-mathematical description of a problem
  Formulate associated mathematical models.
• Introduce new mathematical techniques and then determine and interpret solutions that are useful in a real life context.
• General computational and mathematical techniques and strategies will be introduced by examining specific scientific and industrial problems.

The topics to be covered in this course include:

• Model type selection and formulation
• Data analysis techniques (time/space and frequency domain)
• State Space and Transfer Function Models
• Model Structure Identification
• Testing and Sensitivity Analysis

Computations will be done using modern high level scientific computing environments such as SCILAB or PYTHON. 

Note: Graduate students attend joint classes with undergraduates but are assessed separately.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Design a model based on the basic processes and behaviour of a system and different ways of representing them
2. Evaluate the issues in building and evaluating models, taking into account their purpose and prior knowledge
3. Explain and use some important modelling tools (transfer function, state space, frequency-domain and DE-based models as well as data analysis techniques)
4. Discuss the role of modelling in both industry and science
5. Explain sensitivity and uncertainty analysis techniques

Research-Led Teaching

This course develops the ability to take real world problems, produce associated mathematical models, and then use mathematical and computational techniques to produce an understanding of the properties of the original problem.

Recommended Resources

Texts:

• Industrial Mathematics: Modeling in Industry, Science, and Government, by C. R. MacCluer
• The pleasures of probability, by Richard Isaac
• Mathematical modelling with case studies : a differential equation approach using Maple / Belinda Barnes and Glenn R. Fulford

Staff Feedback

Students will be given feedback in the following forms in this course:

• written comments
• verbal comments
• feedback to whole class, groups, individuals, focus group etc

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Infectious Disease and Epidemic modelling	Matlab Computer Lab
2	Infectious Disease and Epidemic modelling	Workshop/Computer Lab
3	Infectious Disease and Epidemic modelling	Workshop/Computer Lab
4	Tsunami and Flood Modelling. Conservation Laws	Assignment 1 Due Workshop/Computer Lab
5	Shallow water equations	Workshop/Computer Lab
6	Riemann Solution of Shallow Water equations	Workshop/Computer Lab
7	Data and Fourier Analysis	Assignment 2 Due Workshop/Computer Lab
8	Statistical Modelling	Assignment 3 Due Workshop/Computer Lab
9	Monte-Carlo methods and Optimization	Workshop/Computer Lab
10	Uncertainty Quantification	Assignment 4 Due Workshop/Computer Lab
11	High Dimensional Approximation	Workshop/Computer Lab
12	Student Project Presentations	Assignment 5 Due Workshop/Computer Lab

Tutorial Registration

Workshops will begin in Week 2. See Wattle for essential information about registration.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Infectious Disease and Epidemic Modelling Assignment.	7 %	19/08/2019	26/08/2019	1,2,3,4
Conservation Laws and Tsunami and Flood Modelling Assignment	7 %	16/09/2019	23/09/2019	1,2,3,4
Data and Fourier Analysis Assignment	7 %	23/09/2019	30/09/2019	1,2,3,4
Statistical Modelling and Monte-Carlo Methods Assignment	7 %	11/10/2019	18/10/2019	1,2,3,4
Uncertainty Quantification and Optimization Assignment	7 %	25/10/2019	28/10/2019	1,2,3,4,5
Reflection on Student Presentations	2 %	21/10/2019	25/10/2019	1,2,3,4,5
Modelling Project	15 %	25/10/2019	28/11/2019	1,2,3,4,5
Final Exam	48 %	31/10/2019	28/11/2019	1,2,3,4,5

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Policy and General Information 
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure

Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the ANU Online website. In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Participation

We believe that discussing mathematics is one of the best ways to master the material. Students are expected to engage actively and respectfully in cooperative problem-solving during the workshops and laboratories. Students are strongly encouraged to attend lectures and ask questions!

Examination(s)

The date range in the Assessment Summary indicates the start of the end of semester exam period and the date official end of semester results are released on ISIS. Please check the ANU final Examination Timetable http://www.anu.edu.au/students/program-administration/assessments-exams/examination-timetable to confirm the date, time and location exam.

Assessment Task 1

Infectious Disease and Epidemic Modelling Assignment.

Use the techniques from the lectures to analyse an SIR epidemic model.

Assessment Task 2

Conservation Laws and Tsunami and Flood Modelling Assignment

Will investigate the solution of scalar conservation equation via the method of characteristics, as well as shocks and rarefaction solutions. The Riemann problem for the Shallow water equations will be investigated. Combination of theoretical and computational investigation.

Assessment Task 3

Data and Fourier Analysis Assignment

The task is to analyse a recording (a sample) of a note played by an oboe and produce a synthetic version of the note. Combination of theoretical and computational investigation.

Assessment Task 4

Statistical Modelling and Monte-Carlo Methods Assignment

The main task is to optimize a problem (such as a Call centre allocation of operators, or machines in a factory) using statistical modelling. Combination of theoretical and computational investigation.

Assessment Task 5

Uncertainty Quantification and Optimization Assignment

Investigate the effect of uncertainty on the predicted outcome of a model. Also will consider the determination of optimal parameter choice for high dimensional parameter problems, and will look at the sensitivity of parameters.

Assessment Task 6

Reflection on Student Presentations

Attend and provide feedback and peer assessment of student presentations in week 12.

Assessment Task 7

Modelling Project

Students need to produce a research report and present their work on the application or solution techniques of a mathematical model. Projects can be motivated by applications, mathematical theory, implementations or any combination. They can be application based, showing how mathematical models can be used to obtain interesting understanding or predictive ability. They can also be about mathematical techniques which can be used in a range of modelling situations. The report and presentation should demonstrate an understanding of the context of the problem, a description of the mathematical model and mathematical techniques required, the results from the model, with a reflection on the applicability of the model.

Assessment Task 8

Final Exam

The final exam will be a cumulative assessment of the material covered in the entire course, although the emphasis will be on material not yet assessed.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.

The ANU commits to assisting all members of our community to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to be familiar with the academic integrity principle and Academic Misconduct Rule, uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with.

The Academic Misconduct Rule is in place to promote academic integrity and manage academic misconduct. Very minor breaches of the academic integrity principle may result in a reduction of marks of up to 10% of the total marks available for the assessment. The ANU offers a number of online and in person services to assist students with their assignments, examinations, and other learning activities. Visit the Academic Skills website for more information about academic integrity, your responsibilities and for assistance with your assignments, writing skills and study.

Online Submission

You will be required to electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin.

Hardcopy Submission

For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.

Late Submission

Individual assessment tasks may or may not allow for late submission. Policy regarding late submission is detailed below:

• Late submission permitted. Late submission of assessment tasks without an extension are penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of assessment tasks is not accepted after the date specified in the course outline for the return of the assessment item (after the next workshop after the due date). Late submission is not accepted for take-home examinations.

Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

Returning Assignments

Assignment and Project assessment will be returned via wattle.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. The Course Convener may grant extensions for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Resubmission of Assignments

Assignments cannot be resubmitted after the due date.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Diversity and inclusion for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents undergraduate and ANU College students
• PARSA supports and represents postgraduate and research students