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 2020 in Semester 1 at Clayton. It has no prerequisites and unlocks 6 units, leading on to 10 units in all.
- Credit points
- 6
- Offered in 2020
- Semester 1
- Clayton
This is the 2020 handbook entry. See the 2027 entry.
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Requisites
Before MTH3110
No prerequisites or corequisites besides the enrolment rules below.
After MTH3110
6 units list MTH3110 as a prerequisite or corequisite.
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 2020
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
| First semester (Fully flex) | Clayton | Flexible |
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
Three hours of lectures and one 2-hour applied class per week
Where it fits
MTH3110 is part of 6 areas of study in the 2020 handbook.
- APPLMTH07Additional extended major elective unitsApplied mathematicsNo reviews yet
- MTHSTAT07Mathematical statistics elective unitsMathematical statisticsNo reviews yet
- MATHS05Additional mathematics unitMathematicsNo reviews yet
- MATHS06Additional mathematics unitsMathematicsNo reviews yet
- MATPURE05Pure mathematics elective unitsPure mathematicsNo reviews yet
- MATPURE07Pure mathematics elective unitsPure mathematicsNo reviews yet
Contacts
- Unit Coordinators
- Dr Daniel Mathews
- Chief Examiners
- Dr 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 6 units, including MTH3130, MTH3170, MTH4115, MTH4121, MTH5115 and MTH5121. Those lead on to 10 units in all.
When is MTH3110 offered?
In 2020, MTH3110 runs in Semester 1 at Clayton.
Which majors and minors include MTH3110?
MTH3110 is part of Applied mathematics, Mathematical statistics, Mathematics and Pure mathematics.