MTH3110 Differential geometry
Faculty of Science
MTH3110 Differential geometry is a level 3, 6-credit-point, undergraduate unit from the Faculty of Science, offered in 2027 in Semester 1 at Clayton. It has no prerequisites and unlocks 4 units, leading on to 8 units in all.
- Credit points
- 6
- Offered in 2027
- Semester 1
- Clayton
- Assessment
- Exam 50%
- and 1 other task
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Requisites
Before MTH3110
No prerequisites or corequisites besides the enrolment rules below.
After MTH3110
4 units list MTH3110 as a prerequisite or corequisite.
Enrolment rules
PREREQUISITE: You must have passed one unit from MTH2010 or MTH2015 or ENG2005 and one unit from MTH2021or MTH2025, or be enrolled in the Master of Mathematics..
PROHIBITION: MTH3132
Equivalent units
The same content under another code. Only one of them counts.
Overview
This unit will explore the metric structure of curves and surfaces, primarily in 3-dimensional Euclidean space. The major focus is on the various concepts of curvature and related notions, and the relationships between them. Curvature and torsion of a curve. First and second fundamental forms of a surface. Geodesic and normal curvatures of a curve on a surface. Gaussian, mean and principal curvatures of a surface. Important theorems relating these concepts. Links will be drawn with many other areas of mathematics, including real and complex analysis, linear algebra, differential equations, and general relativity.
Offerings in 2027
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.
Learning outcomes
When you finish this unit, you should be able to:
- 1
Explain the significance of intrinsic measures of curvature, for curves and surfaces in 3-dimensional space.
- 2
Perform calculations of curvature and related quantities for curves and surfaces in 3-dimensional spaces.
- 3
Explain and apply important concepts and theorems about the geometry of curves and surfaces in 3-dimensional space.
- 4
Apply results about differential geometry to write proofs and solve problems about curves and surfaces in 3-dimensional space.
- 5
Recognise many of the links between differential geometry and other areas of mathematics and physics, such as real and complex analysis, linear algebra, differential equations, and general relativity.
- 6
Communicate mathematical ideas relating to differential geometry in a clear, precise and rigorous manner.
Workload and teaching
- Seminars36 hours
- Applied sessions22 hours
- Three 1-hour seminars;
- One 2-hour applied class (in weeks 2-12) and
- 7 hours of independent study per week.
Contacts
- Chief Examiners
- Associate Professor Daniel Mathews
- Unit Coordinators
- Associate Professor Daniel Mathews
Common questions
What are the prerequisites for MTH3110?
MTH3110 has no prerequisites, but enrolment rules apply.
What can I take after MTH3110?
MTH3110 is a prerequisite or corequisite for 4 units, including MTH3130, MTH3170, MTH3175 and MTH5115. Those lead on to 8 units in all.
When is MTH3110 offered?
In 2027, MTH3110 runs in Semester 1 at Clayton.
Does MTH3110 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.