MTH4110 Differential geometry
Faculty of Science
MTH4110 Differential geometry is a level 4, 6-credit-point, undergraduate and postgraduate unit from the Faculty of Science, offered in 2027 in Semester 1 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2027
- Semester 1
- Clayton
- Assessment
- Exam 50%
- and 1 other task
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Requisites
Before MTH4110
No prerequisites or corequisites besides the enrolment rules below.
After MTH4110
No unit lists MTH4110 as a prerequisite in the 2027 handbook.
Enrolment rules
You must be enrolled in the Graduate Certificate in Mathematics or the Master of Mathematics
PROHIBITION: MTH3110
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 - Examination (3 hours 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
Critically analyse the significance and implications of intrinsic measures of curvature, for curves and surfaces in 3-dimensional space
- 2
Perform calculations to determine curvature and related quantities for curves and surfaces in 3-dimensional space.
- 3
Synthesise and apply advanced concepts and theorems regarding the geometry of curves and surfaces in 3-dimensional space, demonstrating a deep understanding.
- 4
Formulate and prove theorems, and solve complex problems about curves and surfaces in 3-dimensional space using differential geometry techniques.
- 5
Evaluate and explore the intricate connections between differential geometry and other advanced areas of mathematics and physics, such as real and complex analysis, abstract linear algebra, differential equations, and general relativity.
- 6
Articulate complex mathematical ideas and findings related to differential geometry with clarity, precision, and rigour, suitable for academic and professional audiences
Workload and teaching
- Applied sessions22 hours
- Seminars36 hours
- Teaching approachActive learning
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 MTH4110?
MTH4110 has no prerequisites, but enrolment rules apply.
When is MTH4110 offered?
In 2027, MTH4110 runs in Semester 1 at Clayton.
Does MTH4110 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.