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Unit of study_

MATH5410: Special Topics in Applied Mathematics

Semester 1, 2023 [Normal day] - Camperdown/Darlington, Sydney

In his book on Applied Mathematics, Alain Goriely states There is great beauty in mathematics and great beauty in the world around us. Applied Mathematics brings the two together in a way that is not always beautiful, but is always interesting and exciting. In this unit you will explore classic problems in Applied Mathematics and their solutions or investigate an area of Applied Mathematics that is currently the focus of active research. You will delve deeply into powerful mathematical methods and use this mathematics to investigate and resolve problems in the real world, whether that is in computation, the social sciences or the natural sciences. You will learn how the synergies between mathematics and real world problems that are found throughout Applied Mathematics both drive the creation of new mathematical methods and theory, and give powerful insights into the underlying problems, resulting in new ways of seeing the world and new types of technology. By doing this unit you will grow in your appreciation of the links between mathematical theory and its practical outcomes in other disciplines and learn to use mathematics in deeply profound ways in one or more areas of application.

Unit details and rules

Unit code MATH5410
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Assumed knowledge

Familiarity with the methods of classical applied mathematics (e.g., MATH4412) and the ability to write code and numerical schemes to solve standard applied mathematical problems (e.g., MATH4411 or equivalent). Please consult with the coordinator for further information

Available to study abroad and exchange students


Teaching staff

Coordinator Nalini Joshi,
Lecturer(s) Nalini Joshi,
Tutor(s) Nalini Joshi,
Type Description Weight Due Length
Assignment Assignment 1
See Canvas for more details
25% -
Due date: 27 Mar 2023 at 23:59
See Canvas for more details
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7
Assignment Assignment 2
See Canvas for details.
25% -
Due date: 08 May 2023 at 23:59
See Canvas for details.
Outcomes assessed: LO4 LO5 LO6 LO7
Supervised exam
Final exam
Written exam
40% Formal exam period 2 hours
Outcomes assessed: LO1 LO2 LO4 LO5 LO6 LO7
Participation Tutorial participation
In-class participation during tutorials
10% Weekly Ongoing participation
Outcomes assessed: LO1 LO7 LO6 LO5 LO4 LO3 LO2

Assessment summary

  • Tutorial Participation: Selected exercises from the lectures and lecture notes will be highlighted each week for the weekly tutorial. They are designed to help you understand the new topics.  The approach of the tutorial is based on participation, that is, making verbal suggestions and trying out calculations. The maximum mark is based on active participation in at least 10 tutorials.
  • Assignments: Two assignments will be distributed approximately in Weeks 4 and 9. These are designed to develop your methodological skills. They must be submitted electronically on Canvas through TurnItIn by the deadline.
  • Final exam: There will be a 2-hour supervised/monitored exam. If a second replacement exam is required, this exam may be delivered via an alternative assessment method, such as a viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The format of the alternative assessment will be determined by the unit coordinator.


Assessment criteria

Result name Mark range Description
High distinction 85–100 For demonstrating an exceptionally high level of mastery of the learning outcomes for the unit, by being able to identify, apply and interpret the methods and ideas in the unit at a very high level and providing evidence of ability to extend advanced methods and/or ideas to applications beyond those available in references.
Distinction 75–84 For demonstrating a very high level of mastery of the learning outcomes for the unit, by being able to identify, apply and interpret  the methods and ideas in the unit to several examples and providing evidence of attempts to extend the advanced methods and/or ideas to applications beyond those available in references.
Credit 65–74 For demonstrating a good standard of mastery of the learning outcomes for the unit, by being able to identify, apply and interpret  the methods and ideas in the unit to more than one setting.
Pass 50–64 For demonstrating an acceptable standard of mastery of the learning outcomes for the unit, by being able to identify, apply and interpret  the methods and ideas in the unit in at least one setting.
Fail 0–49 For not demonstrating an acceptable standard of mastery of the learning outcomes for the unit.


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:

Late submissions will not be accepted.

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.

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.

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.

WK Topic Learning activity Learning outcomes
Multiple weeks Random matrix theory; universal results for ensembles of matrices; properties of families of orthogonal polynomials; differential and difference equations for these families Lecture and tutorial (10 hr) LO2 LO3
Symmetry properties of mathematical models Lecture and tutorial (12 hr) LO4 LO5
Riemann-Hilbert problems and solutions Lecture and tutorial (12 hr) LO3 LO6 LO7
Asymptotic and numerical analysis of solutions of models Lecture and tutorial (10 hr) LO4 LO7
Week 01 Introduction to preliminary ideas, basic terminology and methods; difference between discrete and continuum models; boundary value problems and eigenfunctions. Lecture and tutorial (4 hr) LO1 LO2

Attendance and class requirements

You are expected to attend and participate in at least 10 tutorials, as participation in tutorials will count for 10% of your total mark.

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.

Required readings

  • MATH5410 Lecture notes – to be distributed on Canvas.

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. Recognize and apply previous learned methods to describe solutions of mathematical models in mathematics.
  • LO2. demonstrate a coherent and advanced understanding of key concepts in a specific area of applied mathematics.
  • LO3. for a given real world system, analyze the mathematical representation and model assumptions required to represent or approximate the system correctly by a mathematical model.
  • LO4. communicate coherent mathematical arguments appropriately to student and expert audiences, both orally and through written work.
  • LO5. evaluate models and determine the appropriate mathematical approach to solve them.
  • LO6. apply fundamental principles and methods of applied mathematics to solve given problems in a specific area of mathematical application.
  • LO7. devise solutions to complex problems using the methods of applied mathematics.

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

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

No changes have been made since this unit was last offered.


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