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Differential geometry
MTH3110
Synopsis
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.
Sourced from the Monash Handbook 2026.
Quick facts
- Credit points
- 6
- Level
- 3
- Audience
- Undergraduate
- Type
- Coursework
- School
- Faculty of Science
- Faculty
- School of Mathematics
- Handbook year
- 2026
Prerequisites (5)
What it unlocks (5)
- Topology: The mathematics of shapeMTH3130
- Network mathematicsMTH3170
- Network mathematics (Advanced)MTH3175
- Algebraic topologyMTH4115
- Algebraic topologyMTH5115
Offerings (1)
- First semesterClayton · ON-CAMPUS
Listed in 7 areas of study
- Applied mathematicsLevel 3 units
- Applied mathematicsAdditional elective unit
- MathematicsMathematics elective units
- MathematicsMathematics elective units
- Pure mathematicsPure mathematics elective units
- Pure mathematicsPure mathematics elective units
- Mathematical statisticsAdditional elective units