Handbook home
Geometry (MAST30024)
Undergraduate level 3Points: 12.5On Campus (Parkville)
About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)
Contact information
Semester 2
Email: craigdh@unimelb.edu.au
Overview
Availability | Semester 2 |
---|---|
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;
- Riemannian metrics and curvature for surfaces;
- the Gauss-Bonnet theorem;
- how surfaces arise as complex algebraic curves.
Be able to:
- calculate Euler characteristic and identify surfaces described combinatorially;
- compute lengths, angles, areas for a given Riemannian metric;
- compute principal curvatures, mean curvature, Gaussian curvature for surfaces in Euclidean space;
- apply the Gauss-Bonnet theorem;
- 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: 15 February 2024
Eligibility and requirements
Prerequisites
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST20009 | Vector Calculus |
Semester 1 (On Campus - Parkville)
Semester 2 (On Campus - Parkville)
|
12.5 |
and one of
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST20026 | Real Analysis |
Semester 2 (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
|
12.5 |
MAST10009 | Accelerated Mathematics 2 | Semester 2 (On Campus - 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: 15 February 2024
Assessment
Additional details
Two or three written assignments due at regular intervals during semester amounting to a total of up to 50 pages (20%), and a 3-hour written examination in the examination period (80%).
Last updated: 15 February 2024
Dates & times
- Semester 2
Principal coordinator Craig Hodgson Mode of delivery On Campus (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 24 July 2017 to 22 October 2017 Last self-enrol date 4 August 2017 Census date 31 August 2017 Last date to withdraw without fail 22 September 2017 Assessment period ends 17 November 2017 Semester 2 contact information
Email: craigdh@unimelb.edu.au
Time commitment details
Estimated total time commitment of 170 hours
Last updated: 15 February 2024
Further information
- Texts
Prescribed texts
None
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 Pure Mathematics Informal specialisation Science-credited subjects - new generation B-SCI and B-ENG. Informal specialisation Selective subjects for B-BMED - Breadth options
This subject is available as breadth in the following courses:
- 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: 15 February 2024