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Unit of study_
MATH4068: Differential Geometry
2025 unit information
This unit is an introduction to Differential Geometry, one of the core pillars of modern mathematics. Using ideas from calculus of several variables, we develop the mathematical theory of geometrical objects such as curves, surfaces and their higher-dimensional analogues. For students, this provides the first taste of the investigation on the deep relation between geometry and topology of mathematical objects, highlighted in the classic Gauss-Bonnet Theorem. Differential geometry also plays an important part in both classical and modern theoretical physics. The unit aims to develop geometrical ideas such as curvature in the context of curves and surfaces in space, leading to the famous Gauss-Bonnet formula relating the curvature and topology of a surface. A second aim is to remind the students about all the content covered in the mathematical units for previous years, most importantly the key ideas in vector calculus, along with some applications. It also helps to prepare the students for honours courses like Riemannian Geometry. By doing this unit you will further appreciate the beauty of mathematics which originated from the need to solve practical problems, develop skills in understanding the geometry of the surrounding environment, prepare yourself for future study or the workplace by developing advanced critical thinking skills and gain a deep understanding of the underlying rules of the Universe.
Unit details and rules
Managing faculty or University school:
Science
| Study level | Undergraduate |
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| Academic unit | Mathematics and Statistics Academic Operations |
| Credit points | 6 |
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Prerequisites:
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(A mark of 65 or greater in 12 credit points of MATH2XXX units of study) or [12 credit points from (MATH3061 or MATH3066 or MATH3063 or MATH3076 or MATH3078 or MATH3961 or MATH3962 or MATH3963 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3978 or MATH3979)] |
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Corequisites:
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None |
| Prohibitions:
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MATH3968 |
| Assumed knowledge:
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Vector calculus, differential equations and real analysis, for example MATH2X21 and MATH2X23 |
At the completion of this unit, you should be able to:
- LO1. demonstrate knowledge and understanding of fundamental concepts and theorems in differential geometry.
- LO2. apply fundamental theorems and concepts of differential geometry in order to solve geometric problems
- LO3. understand and apply geometric concepts to analyse examples to draw conclusions
- LO4. evaluate geometric quantities such as torsion and curvature
- LO5. Synthesise knowledge across a range of topics and write novel mathematical proofs.
Unit availability
This section lists the session, attendance modes and locations the unit is available in. There is a unit outline for each of the unit availabilities, which gives you information about the unit including assessment details and a schedule of weekly activities.
The outline is published 2 weeks before the first day of teaching. You can look at previous outlines for a guide to the details of a unit.
| Session | MoA ? | Location | Outline ? |
|---|---|---|---|
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Semester 2 2025
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Normal day | Camperdown/Darlington, Sydney |
Outline unavailable
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Modes of attendance (MoA)
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