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Geometry (MAST30024)
Undergraduate level 3Points: 12.5Dual-Delivery (Parkville)
From 2023 most subjects will be taught on campus only with flexible options limited to a select number of postgraduate programs and individual subjects.
To learn more, visit COVID-19 course and subject delivery.
About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)
Contact information
Semester 2
Overview
| Availability | Semester 2 - Dual-Delivery |
|---|---|
| Fees | Look up fees |
This subject introduces three areas of geometry that play a key role in many branches of mathematics and physics. In differential geometry, calculus and the concept of curvature will be used to study the shape of curves and surfaces. In topology, geometric properties that are unchanged by continuous deformations will be studied to find a topological classification of surfaces. In algebraic geometry, curves defined by polynomial equations will be explored. Remarkable connections between these areas will be discussed.
Topics include: Topological classification of surfaces, Euler characteristic, orientability.Introduction to the differential geometry of surfaces in Euclidean space:smooth surfaces, tangent planes, length of curves, Riemannian metrics, Gaussian curvature, minimal surfaces, Gauss-Bonnet theorem.Complex algebraic curves, including conics and cubics, genus.
Intended learning outcomes
On completion of this subject, students should
Have an understanding of:
- Euler characteristic and the topological classification of surfaces;
- how surfaces arise as complex algebraic curves.
- Riemannian metrics and curvature for surfaces;
- the Gauss-Bonnet theorem;
Be able to:
- calculate Euler characteristic and identify surfaces described combinatorially;
- compute lengths, angles, areas for a given Riemannian metric;
- apply the Gauss-Bonnet theorem;
- compute principal curvatures, mean curvature, Gaussian curvature for surfaces in Euclidean space;
- do simple calculations with algebraic plane curves.
Generic skills
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- collaborative skills: the ability to work in a team;
- time-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 3 June 2023
Eligibility and requirements
Prerequisites
One of
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST20009 | Vector Calculus |
Semester 2 (Dual-Delivery - Parkville)
Semester 1 (Dual-Delivery - Parkville)
|
12.5 |
| MAST20032 | Vector Calculus: Advanced | Semester 1 (Dual-Delivery - Parkville) |
12.5 |
AND
One of
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST10009 | Accelerated Mathematics 2 | Semester 2 (Dual-Delivery - Parkville) |
12.5 |
| MAST20026 | Real Analysis |
Semester 2 (Dual-Delivery - Parkville)
Semester 1 (Dual-Delivery - Parkville)
|
12.5 |
| MAST20033 | Real Analysis: Advanced | Semester 1 (Dual-Delivery - Parkville) |
12.5 |
Corequisites
None
Non-allowed subjects
None
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 3 June 2023
Assessment
| Description | Timing | Percentage |
|---|---|---|
Two or three written assignments due at regular intervals amounting to a total of up to 50 pages
| During the teaching period | 20% |
A written examination
| During the examination period | 80% |
Additional details
This Dual-Delivery subject has On Campus assessment components.
Last updated: 3 June 2023
Dates & times
- Semester 2
Coordinator Diarmuid Crowley Mode of delivery Dual-Delivery (Parkville) Contact hours 3 x one hour lectures per week, 1 x one hour practice class per week Total time commitment 170 hours Teaching period 25 July 2022 to 23 October 2022 Last self-enrol date 5 August 2022 Census date 31 August 2022 Last date to withdraw without fail 23 September 2022 Assessment period ends 18 November 2022 Semester 2 contact information
Time commitment details
Estimated total time commitment of 170 hours
Additional delivery details
This Dual-Delivery subject has On Campus assessment components.
Last updated: 3 June 2023
Further information
- Texts
Prescribed texts
Recommended texts and other resources
N. Hitchin, Geometry of surfaces, Oxford University lecture notes, available online.
M. do Carmo, Differential geometry of curves and surfaces, Prentice-Hall, 1976.
F. Kirwan, Complex algebraic curves, Cambridge University Press, 1992.
- Subject notes
This subject is available for science credit to students enrolled in the BSc (both pre-2008 and new degrees), BASc or a combined BSc course.
- Related Handbook entries
This subject contributes to the following:
Type Name Informal specialisation Science Discipline subjects - new generation B-SCI Informal specialisation Pure Mathematics specialisation - Breadth options
This subject is available as breadth in the following courses:
- Bachelor of Commerce
- Bachelor of Environments
- Bachelor of Fine Arts (Acting)
- Bachelor of Fine Arts (Animation)
- Bachelor of Fine Arts (Dance)
- Bachelor of Fine Arts (Film and Television)
- Bachelor of Fine Arts (Music Theatre)
- Bachelor of Fine Arts (Production)
- Bachelor of Fine Arts (Screenwriting)
- Bachelor of Fine Arts (Theatre)
- Bachelor of Fine Arts (Visual Art)
- Bachelor of Music
- Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
- Available to Study Abroad and/or Study Exchange Students
This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.
Last updated: 3 June 2023