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Unit outline_

MATH4412: Advanced Methods in Applied Mathematics

Semester 2, 2021 [Normal day] - Camperdown/Darlington, Sydney

Mathematical approaches to many real-world problems are underpinned by powerful and wide ranging mathematical methods and techniques that have become standard in the field and should be in the toolbag of all applied mathematicians. This unit will introduce you to a suite of those methods and give you the opportunity to engage with applications of these methods to well-known problems. In particular, you will learn both the theory and use of asymptotic methods which are ubiquitous in applications requiring differential equations or other continuous models. You will also engage with methods for probabilistic models including information theory and stochastic models. By doing this unit you will develop a broad knowledge of advanced methods and techniques in applied mathematics and know how to use these in practice. This will provide a strong foundation for using mathematics in a broad sweep of practical applications in research, in industry or in further study.

Unit details and rules

Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Assumed knowledge

A thorough knowledge of vector calculus (e.g., MATH2X21) and of linear algebra (e.g., MATH2X22). Some familiarity with partial differential equations (e.g., MATH3X78) and mathematical computing (e.g., MATH3X76) would be useful.

Available to study abroad and exchange students


Teaching staff

Coordinator Geoffrey Vasil,
Lecturer(s) Geoffrey Vasil,
Type Description Weight Due Length
Online task Worked presentation
12 recorded presentations.
100% Weekly 20 min each.
Outcomes assessed: LO1 LO2 LO3 LO4 LO5

Assessment summary

Each week, students are required to submit two 10-min (maximum) recordings of their solution to two assigned questions. 

I will flip a coin each week to decide which question to mark. 

There will be 12 total submissions throughout the semester. The top 8 will count toward the final mark.

The submissions will be due on Sunday night each week. Because you are allowed to drop the lowest 4 marks, there will be no late submissions, nor special considerations. 

Assessment criteria

Assessment grading information.

  • Each question will be marked 0-5, with the following scoring guidelines:

0: Did not submit

1: Submitted, but with minimal demonstrated understanding.

2: Some understanding, with significant errors

3: Mostly accurate understanding of problem steps. Perhaps a correct solution with some misunderstanding or a close-to-correct solution. 

4: Demonstrated understanding of each essential problem element. A possibly incorrect solution for minor reasons. 

5: Demonstrated mastery of each essential problem element. Must present a correct solution for correct reasons. Must be able to say why the solution checks out. E.g., mentioning special cases that clearly make sense. 

Half points: In any category, an honest and introspective assessment of how you think a calculation is incorrect or how you think you are stuck can earn an extra 0.5 mark.  


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:

No late submissions.

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 Orthogonal vectors, dual vectors, bases. Lecture (3 hr)  
General theory of orthogonal polynomials. Lecture (3 hr)  
Theory of classical OPs (continuous and discrete) Lecture (3 hr)  
Stochastic methods: General framework Lecture (3 hr)  
Stochastic methods: Applications to birth-death process. sampling, asymptotic. Lecture (3 hr)  
Applications to geometry. Spherical Harmonics, representation of functions, operations on functions. Lecture (3 hr)  
Weekly Tutorial and/or computer lab on weekly topic Tutorial (1 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 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 broad understanding of key concepts in applied mathematics​
  • LO2. Create models and solve qualitative and quantitative problems in scientific contexts, using appropriate mathematical and computing techniques as necessary​
  • LO3. Use the principles of applied mathematics to analyse and explore deterministic and stochastic systems​
  • LO4. Evaluate the accuracy of approximate methods and assess their applicability​
  • LO5. Communicate mathematical information deeply and coherently, both orally and through written work to a variety of audiences​​

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.

This is the 2nd time this unit has been offered.


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

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