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Unit of study_

MATH5330: Topics in Geometry

Semester 2, 2023 [Normal day] - Camperdown/Darlington, Sydney

Geometry, as one of the most ancient branches of pure mathematics, arose from the necessity and desire to describe and thoroughly understand the surrounding world and the universe. The development of geometry substantially contributes to the evolution of mathematics as a whole subject through the concepts and notions of axiom and manifold, which lays the foundation of modern mathematics. Despite the abstract appearance of modern geometry, the objects and problems of modern geometry can usually be traced back to practical situations. A good example is the recent breakthrough in image identification technology, which is rooted in differential geometry. From both a research and an educational perspective, geometry provides perfect opportunities for the implementation and interaction of ideas and techniques from other branches of mathematics like algebra, analysis, topology and probability, and other subjects like chemistry, finance and physics through topics including financial derivatives, Einstein Equations and black holes, which have attracted enormous public attention in recent years. You will learn to approach questions initially through intuition and then make this rigorous using mathematical tools. Through the selection of topics in this unit, you will train your mathematical imagination to discover the geometric framework of a complex problem.

Unit details and rules

Unit code MATH5330
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Prohibitions
? 
None
Prerequisites
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None
Corequisites
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None
Assumed knowledge
? 

Familiarity with metric spaces (e.g., MATH4061 or equivalent) and differential geometry (e.g., MATH4068 or equivalent). Please consult with the coordinator for further information

Available to study abroad and exchange students

Yes

Teaching staff

Coordinator Zhou Zhang, zhou.zhang@sydney.edu.au
Type Description Weight Due Length
Supervised exam
? 
Final Exam
Final Exam
40% Formal exam period 2 hours
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7
Assignment Assignment 1
written assignment
15% Week 05
Due date: 03 Sep 2023 at 23:59

Closing date: 10 Sep 2023
2 weeks
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7
Presentation Seminar Presentation
presentation on topics assigned at the beginning of the semester
15% Week 10
Due date: 13 Oct 2023 at 13:00

Closing date: 20 Oct 2023
one lecture (about 50 minutes)
Outcomes assessed: LO1 LO7 LO6 LO5 LO4 LO3 LO2
Assignment Assignment 2
written assignment
15% Week 10
Due date: 15 Oct 2023 at 23:59

Closing date: 22 Oct 2023
2 weeks
Outcomes assessed: LO1 LO7 LO6 LO5 LO4 LO3 LO2
Small continuous assessment Presentation Notes Submission
typed notes for student presentation
15% Week 12
Due date: 27 Oct 2023 at 13:00

Closing date: 03 Nov 2023
2 weeks
Outcomes assessed: LO1 LO7 LO6 LO5 LO4 LO3 LO2

Assessment summary

2 assignments with 15% weight each. 

1 presentation with 15% weight. 

1 submssion of typed presentation notes for 15% weight. 

Final Exam for 40% weight. 

Final 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

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, an HD indicates work of an exceptional standard, a D a very high standard, a CR a good standard, and a P an acceptable standard.

Result Mark% Description
HD 85-100

representing complete or close to complete mastery of the material

D 75-84

representing excellence but substantially less than complete mastery

CR 65-74

representing a creditable performance that goes beyond routine knowledge and understanding but less than excellence

P 50-64

representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course

F 0-49 not meeting the learning outcomes of the unit to a satisfactory standard

For more information see sydney.edu.au/students/guide-to-grades.

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:

For late submission of assignment, every day costs 20% of the original weight.  For late submission of notes from presentation, every day costs 5% of the original weight. 

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 differential geometry, Riemannian geometry, Kahler geometry and relevant geometric flows Lecture (26 hr) LO1 LO2 LO3 LO4 LO5 LO6 LO7
differential geometry, Riemannian geometry, Kahler geometry and relevant geometric flows Tutorial (13 hr) LO1 LO2 LO3 LO4 LO5 LO6 LO7
student presentations on topics relevant to the unit which will be announced at the beginning of the semester with references provided by the instructor Presentation (13 hr) LO1 LO2 LO3 LO4 LO5 LO6 LO7

Attendance and class requirements

Lecture, tutorial and student presentation attendance will be taken, but not counted directly into the final grade.

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

Learning material is provided at the beginning of the semester.

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 geometry.
  • LO2. Apply fundamental principles and results in geometry to solve given problems.
  • LO3. Distinguish and compare the properties of different types of spaces and maps between them.
  • LO4. Formulate geometric problems in terms of invariants and determine the appropriate framework to solve them.
  • LO5. Devise geometric solutions to complex problems.
  • LO6. Compose correct proofs of unfamiliar general results in geometry.
  • 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
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 and we get prepared for a hybrid mode. The remote student needs will be accommodated in reasonable ways.

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Additional costs

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Disclaimer

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