This is a special topics course which introduces students to the key concepts and techniques of Differential Geometry. Possible topics include:
Surfaces in Euclidean space, general differentiable manifolds, tangent spaces and vector fields, differential forms, Riemannian manifolds, Gauss-Bonnet theorem.
Note: This is an Honours Pathway course. It emphasises mathematical rigour and proof and develops the fundamental ideas of differential geometry from an abstract viewpoint.
Upon successful completion, students will have the knowledge and skills to:
- Explain the concepts and language of differential geometry and its role in modern mathematics
- Analyse and solve complex problems using appropriate techniques from differential geometry with mathematical rigour
- Apply problem-solving with differential geometry to diverse situations in physics, engineering or other mathematical contexts
- 3 written assignments involving problem-solving, proofs of theorems and extension of theory (10% each) (30) [LO 1,2,3]
- Workshop participation and presentation (10) [LO 1,2,3]
- Lecture participation and 10 in-class (5 minute) quizzes (20) [LO 1,2,3]
- Take home final exam (40) [LO 1,2,3]
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The expected workload will consist of approximately 130 hours throughout the semester including:
- Face-to-face component consisting of 3 x 1 hour lectures per week, plus 10 x 1 hour workshops over the semester.
- Approximately 45 hours of self directed study including preparation for lectures, workshops and quizzes.
- Approximately 39 hours of study towards assignments.
To be determined
Requisite and Incompatibility
Lecture notes provided
- John M. Lee, Introduction to smooth manifolds. 2nd ed., Graduate Texts in Mathematics, vol. 218, Springer, New York, 2013.
- Manfredo Perdigao do Carmo, Riemannian geometry. Mathematics: Theory & Applications, Birkh ¨auser Boston, Inc., Boston, MA, 1992. Translated from the second Portuguese edition by Francis Flaherty.
Tuition fees are for the academic year indicated at the top of the page.
Commonwealth Support (CSP) Students
If you have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). More information about your student contribution amount for each course at Fees.
- Student Contribution Band:
- Unit value:
- 6 units
If you are a domestic graduate coursework student with a Domestic Tuition Fee (DTF) place or international student you will be required to pay course tuition fees (see below). Course tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.
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