MATH5320: Semester 1, 2026

Units MATH5320 Semester 1 2026 [Normal day]

Unit outline_

MATH5320: Topics in Analysis

Semester 1, 2026 [Normal day] - Camperdown/Darlington, Sydney

Overview

Differential equations and the notion of convergence are ubiquitous within the natural sciences, engineering and mathematics. Analysis has, thus, far reaching applications, and it is a major discipline in its own right. The origins of many major areas such as topology, functional and harmonic analysis have their roots in real and complex analysis. Analysis makes unexpected appearances in other areas such as number theory, where it played a key role in a recent breakthrough on arithmetic progression of prime numbers by Fields medalist Terrence Tao. Analysis deals with any kind of limit process, notions of distance, measure, continuity or differentiability. It makes up a crucial part of diverse areas in mathematics. The fields of application of analysis that you will encounter in this unit may include partial differential equations, differential geometry, harmonic analysis, topological groups, optimal control, scattering theory, ergodic theory, differential topology or mathematical physics. The selection of topics in this unit is guided by their relevance for applications and current research. In this unit, you will gain an understanding of the systematic, abstract foundations of a branch of analysis and develop tools needed to get to the present frontiers.

Unit details and rules

Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prerequisites ?	None
Corequisites ?	None
Prohibitions ?	None
Assumed knowledge ?	Familiarity with metric spaces (e.g., MATH4061 or equivalent) and higher analysis (e.g., MATH4313 or MATH4315 or equivalent). Please consult with the coordinator for further information
Available to study abroad and exchange students	No

Teaching staff

Coordinator	Jiakun Liu, jiakun.liu@sydney.edu.au

Assessment

The census date for this unit availability is 31 March 2026

Details
Criteria

Type	Description	Weight	Due	Length	Use of AI
Written exam	Final exam Final exam consisting of extended answer questions	60%	Formal exam period	2 hours	AI prohibited
Outcomes assessed:
Written work	Assignment 1 Written assignment	12.5%	Week 05 Due date: 27 Mar 2026 at 23:59 Closing date: 06 Apr 2026	3-5 pages	AI allowed
Outcomes assessed:
In-person written or creative task	Quiz Written test	15%	Week 08 Due date: 23 Apr 2026 at 09:00 Closing date: 23 Apr 2026	45 minutes	AI prohibited
Outcomes assessed:
Written work	Assignment 2 Written assignment	12.5%	Week 11 Due date: 15 May 2026 at 23:59 Closing date: 25 May 2026	3-5 pages	AI allowed
Outcomes assessed:

Assessment summary

Assignment 1: Work individually on about 3-5 questions regarding the content of the course from weeks 1-4. Type the answers into a pdf file to be submitted at the end of week 5. Detailed information for each assessment can be found on Canvas in week 4.
Assignment 2: Work individually on about 3-5 questions regarding the content of the course from weeks 1-10. Type the answers into a pdf file to be submitted at the end of week 11. Detailed information for each assessment can be found on Canvas in week 10.
Quiz: In-class, closed-book test consisting of approximately 2-3 questions, with a duration of 45 minutes. Answers must be handwritten and submitted by the end of the class.

Assessment criteria

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name	Mark range	Description
High distinction	85 - 100
Distinction	75 - 84
Credit	65 - 74
Pass	50 - 64
Fail	0 - 49	The learning outcomes of the unit of study have not been met to a satisfactory standard.

For more information see guide to grades.

Use of generative artificial intelligence (AI)

You can use generative AI tools for open assessments. Restrictions on AI use apply to secure, supervised assessments used to confirm if students have met specific learning outcomes.

Refer to the assessment table above to see if AI is allowed, for assessments in this unit and check Canvas for full instructions on assessment tasks and AI use.

If you use AI, you must always acknowledge it. Misusing AI may lead to a breach of the Academic Integrity Policy.

Visit the Current Students website for more information on AI in assessments, including details on how to acknowledge its use.

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 University expects students to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

Our website provides information on academic integrity and the resources available to all students. This includes advice on how to avoid common breaches of academic integrity. Ensure that you have completed the Academic Honesty Education Module (AHEM) which is mandatory for all commencing coursework students

Penalties for serious breaches can significantly impact your studies and your career after graduation. It is important that you speak with your unit coordinator if you need help with completing assessments.

Visit the Current Students website for more information on AI in assessments, including details on how to acknowledge its use.

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.

Support for students

The Support for Students Policy 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. 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

Weekly schedule

WK	Topic	Learning activity
Week 01	Laplace and Poisson equations	Lecture (3 hr)
Week 02	Calculus of variation, and boundary problems	Lecture (3 hr)
Week 03	Mean value property and Harnack inequality	Lecture (3 hr)
Week 04	Gradient estimate and Liouville Theorem	Lecture (3 hr)
Week 05	Maximum Principle and applications	Lecture (3 hr)
Week 06	Green function and singularity	Lecture (3 hr)
Week 07	Eigenvalue problems	Lecture (3 hr)
Week 08	General elliptic equations and extensions	Lecture (2 hr)
Week 09	Heat equation and Cauchy problem	Lecture (3 hr)
Week 10	Fourier transform and properties	Lecture (3 hr)
Week 11	Weak and strong maximum principles	Lecture (3 hr)
Week 12	Energy method and ancient solutions	Lecture (3 hr)
Week 13	General parabolic equations and recap	Lecture (3 hr)
Weekly	Weekly problem solving relating to the previous week's theory	Tutorial (13 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 a coherent and advanced understanding of key concepts in analysis
LO2. utilise fundamental analytic principles and results to determine solutions to given problems
LO3. Distinguish and compare the properties of different spaces and maps between them
LO4. formulate mathematical problems using terminology from analysis and justify the use of select frameworks in solving them
LO5. determine the principles inherent to complex problems from analysis, and devise strategies to solve the given problems
LO6. compose correct proofs of unfamiliar general results in analysis
LO7. 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
Learning outcomes

Responding to student feedback

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

This section outlines changes made to this unit following staff and student reviews. This is the first time this unit has been offered.

Disclaimer

Important: the University of Sydney regularly reviews units of study and reserves the right to change the units of study available annually. To stay up to date on available study options, including unit of study details and availability, refer to the relevant handbook.

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

Use of generative artificial intelligence (AI)

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Disclaimer

On this page

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