MATH4413: Semester 1, 2020

University home

Library

Current students

Staff intranet

Find an event

Give

Current students

Units MATH4413 Semester 1 2020 [Normal day]

Unit outline_

MATH4413: Applied Mathematical Modelling

Semester 1, 2020 [Normal day] - Camperdown/Darlington, Sydney

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

Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prerequisites ?	None
Corequisites ?	None
Prohibitions ?	None
Assumed knowledge ?	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.
Available to study abroad and exchange students	Yes

Teaching staff

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

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	Question and answer
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.

For more information see guide to grades.

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.

Academic integrity

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.

Use of generative artificial intelligence (AI) and automated writing tools

You may only use generative AI and automated writing tools in assessment tasks if you are permitted to by your unit coordinator. If you do use these tools, you must acknowledge this in your work, either in a footnote or an acknowledgement section. The assessment instructions or unit outline will give guidance of the types of tools that are permitted and how the tools should be used.

Your final submitted work must be your own, original work. You must acknowledge any use of generative AI tools that have been used in the assessment, and any material that forms part of your submission must be appropriately referenced. For guidance on how to acknowledge the use of AI, please refer to the AI in Education Canvas site.

The unapproved use of these tools or unacknowledged use will be considered a breach of the Academic Integrity Policy and penalties may apply.

Studiosity is permitted unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission as detailed on the Learning Hub’s Canvas page.

Outside assessment tasks, generative AI tools may be used to support your learning. The AI in Education Canvas site contains a number of productive ways that students are using AI to improve their learning.

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
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.

Outcomes
Graduate qualities

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.

Graduate qualities

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

Learning outcomes	Graduate qualities
Learning outcomes

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..

Additional information

Disclaimer

The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

To help you understand common terms that we use at the University, we offer an online glossary.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Weekly schedule

Weekly schedule

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Disclaimer

On this page

Useful links

Media

Student links

About us

Connect