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Unit of study_

MATH5411: Special Topics in Applied Mathematics (Alt)

Semester 1, 2024 [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 than 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 MATH5411
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Prohibitions
? 
None
Prerequisites
? 
None
Corequisites
? 
None
Assumed knowledge
? 

None

Available to study abroad and exchange students

Yes

Teaching staff

Coordinator Holger Dullin, holger.dullin@sydney.edu.au
Type Description Weight Due Length
Assignment Assignment 2
2 seminar presentations, slides to be handed in
30% Multiple weeks approx. 10 slides each
Outcomes assessed: LO1 LO2 LO4 LO5 LO6
Assignment Assignment 1
Problem set
30% Week 09
Due date: 28 Apr 2024 at 23:59
5-10 pages
Outcomes assessed: LO2 LO1 LO6 LO5 LO4 LO3
Assignment Assignment 3
Written report on a research topic related to the lecture
30% Week 13
Due date: 26 May 2024 at 23:59
10-20 latex pages
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6
Participation Class Participation
Participation in in-class discussions
10% Weekly 13 Weeks
Outcomes assessed: LO1 LO6 LO5 LO4 LO3 LO2

Assessment summary

Detailed information for each assessment can be found on Canvas.

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

When you don’t meet 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.

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.

Support for students

The Support for Students Policy 2023 reflects the University’s commitment to supporting students in their academic journey and making the University safe for students. It is important that you read and understand this policy so that you are familiar with the range of support services available to you and understand how to engage with them.

The University uses email as its primary source of communication with students who need support under the Support for Students Policy 2023. Make sure you check your University email regularly and respond to any communications received from the University.

Learning resources and detailed information about weekly assessment and learning activities can be accessed via Canvas. It is essential that you visit your unit of study Canvas site to ensure you are up to date with all of your tasks.

If you are having difficulties completing your studies, or are feeling unsure about your progress, we are here to help. You can access the support services offered by the University at any time:

Support and Services (including health and wellbeing services, financial support and learning support)
Course planning and administration
Meet with an Academic Adviser

WK Topic Learning activity Learning outcomes
Multiple weeks Classical integrable Hamiltonian systems and isospectral deformations Lecture (6 hr) LO1 LO2 LO5 LO6
Geodesics on an ellipsoid and the mechanical system of C. Neumann Lecture (6 hr) LO1 LO2 LO3 LO4 LO5 LO6
The Schrödinger equation for almost periodic potentials Lecture (6 hr) LO1 LO2 LO5 LO6
Finite band potentials Lecture (8 hr) LO1 LO2 LO3 LO4 LO5 LO6
Weekly Weeks 2- 13. Tutorial Tutorial (12 hr) LO1 LO2 LO3 LO4 LO5 LO6
Weekly seminar presented by students Seminar (12 hr) LO1 LO2 LO3 LO4 LO5 LO6

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

Integrable Hamiltonian Systems and Spectral Theory by J. Moser

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 a coherent and advanced understanding of key concepts in a specific area of applied mathematics.
  • LO2. Apply fundamental principles and methods of applied mathematics to solve given problems in a specific area of mathematical application.
  • LO3. For a given real world system, determine the type of mathematical representation and model assumptions required to represent or approximate the system correctly by a mathematical model.
  • LO4. Formulate models and determine the appropriate mathematical approach to solve them.
  • LO5. Devise solutions to complex problems using the methods of applied mathematics.
  • LO6. Communicate coherent mathematical arguments appropriately to student and expert audiences, both orally and through written work.

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
GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

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

This is the first time this unit has been offered.

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.