Unit of study_

# MATH4413: Applied Mathematical Modelling

## Overview

Applied Mathematics harnesses the power of mathematics to give insight into phenomena in the wider world and to solve practical problems. Modelling is the key process that translates a scientific or other phenomenon into a mathematical framework through applying suitable assumptions, identifying important variables and deriving a well-defined mathematical problem. Mathematicians then use this model to explore the real-world phenomenon, including making predictions. Good mathematical modelling is something of an art and is best learnt by example and by writing, refining and analysing your own models. This unit will introduce you to some classic mathematical models and give you the opportunity to analyse, explore and extend these models to make predictions and gain insights into the underlying phenomena. You will also engage with modelling in depth in at least one area of application. By doing this unit you will develop a broad knowledge of advanced mathematical modelling methods and techniques and know how to use these in practice. This will provide a strong foundation for applying mathematics and modelling to many diverse applications and for research or further study.

### Unit details and rules

Unit code MATH4413 Mathematics and Statistics Academic Operations 6 None None None MATH2X21 and MATH3X63 or equivalent. That is, a knowledge of linear and simple nonlinear ordinary differential equations and of linear, second order partial differential equations. Yes

### Teaching staff

Coordinator Marek Rutkowski, marek.rutkowski@sydney.edu.au

## Assessment

Type Description Weight Due Length
Assignment Final take home exam
Take home written exam
50% Formal exam period 16 pages
Outcomes assessed:
Presentation Presentation
Online presentation
20% Week 06
Due date: 02 Apr 2020 at 00:00
See Canvas
Outcomes assessed:
Assignment Assignment
Written assignment
20% Week 13
Due date: 28 May 2020 at 23:59
Outcomes assessed:
Participation Tutorial Participation
Participation in discussion questions in online chat or zoom tutorial.
10% Weekly Weekly
Outcomes assessed:

### Assessment summary

• In the written assignments, students will be required to solve mathematical problems and write code in Matlab to simulate relevant PDE systems.
• In the prespentation assignment, students will select a current research article in mathematical biology and give an in-class presentation on the paper.
• For the participation mark, students will contribute to discussions of quetions in online chat and mathematical problems provided in zoom tutorial classes.
• In the final exam, students will complete a take home exam covering material from the course.

### Assessment criteria

 Result name Mark range Description High distinction 85-100 Representing complete or close to complete mastery of the material. Distinction 75-84 Representing excellence, but substantially less than complete mastery. Credit 65-74 Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence. Pass 50-64 Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course. Fail 0-49 Not meeting the learning outcomes of the unit to a satisfactory standard.

### Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

• Deduction of 5% of the maximum mark for each calendar day after the due date.
• After ten calendar days late, a mark of zero will be awarded.

This unit has an exception to the standard University policy or supplementary information has been provided by the unit coordinator. This information is displayed below:

Please discuss any issues with submitting assignments on time with Peter Kim or Robert Marangell.

The Current Student website  provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

## Learning support

### Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

### Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

### Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

## Weekly schedule

WK Topic Learning activity Learning outcomes
Week 01 Age-structured models Lecture and tutorial (4 hr)
Week 02 Diffusion and Turing patterns Lecture and tutorial (4 hr)
Week 03 Chemotaxis models Lecture and tutorial (4 hr)
Week 04 Fisher's equation Lecture and tutorial (4 hr)
Week 05 Travelling waves/fronts Lecture and tutorial (4 hr)
Week 06 Connecting PDEs to agent-based models Lecture and tutorial (4 hr)
Week 07 BZ Models Lecture and tutorial (4 hr)
Week 08 Relaxation oscillations Lecture and tutorial (4 hr)
Week 09 KdV Lecture and tutorial (4 hr)
Week 10 Gibbs Phenomenon Lecture and tutorial (4 hr)
Week 11 Turing Bifurcations Lecture and tutorial (4 hr)
Week 12 NLS and optics Lecture and tutorial (4 hr)

### Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

## Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

At the completion of this unit, you should be able to:

• LO1. Demonstrate an understanding of key concepts in mathematical modelling and the associated mathematical theory with an in-depth understanding of modelling and analysis in at least one field.
• LO2. Critically analyse suitable mathematical frameworks to model real-world problems, produce suitable models and interpret the results of this modelling.
• LO3. Find and critically evaluate information about area of modelling applications and judge its reliability and significance.
• LO4. Synthesise theory from this unit, theory from other units, the research literature or other written resources, and numerical calculations to generate solutions to complex problems in mathematical modelling.
• LO5. Communicate clearly and appropriately, in both formal and informal contexts, both orally and through written work.
• LO6. Contribute to team and group work to develop mathematical models and to perform analyses and interpretation and for the process of learning.
• LO7. Demonstrate a sense of responsibility, ethical behaviour and independence as a learner and as an applied mathematician.

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

 GQ1 Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline. GQ2 Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem. GQ3 Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context. GQ4 Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies. GQ5 Inventiveness Generating novel ideas and solutions. GQ6 Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues. GQ7 Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries. GQ8 Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context. GQ9 Influence Engaging others in a process, idea or vision.

### Outcome map

GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

## Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

This is the first time this unit is being offered..