This course 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: Graduate students attend joint classes with undergraduates but are assessed separately.
Learning Outcomes
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
- Apply problem-solving with differential geometry to diverse situations in physics, engineering or other mathematical contexts
- Apply differential geometry techniques to specific research problems in mathematics or other fields
Indicative Assessment
- 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 x short in-class quizzes (20) [LO 1,2,3]
- Subject-specific project applying differential geometry to an area of interest (40) [LO 3,4]
The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.
Workload
The expected workload will consist of approximately 130 hours throughout the semester including:
- Face-to-face component consisting of 3 one-hour lectures per week, plus 10 one 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.
Inherent Requirements
To be determined
Requisite and Incompatibility
You will need to contact the Mathematical Sciences Institute to request a permission code to enrol in this course.
Prescribed Texts
Lecture notes provided
Preliminary Reading
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.
Assumed Knowledge
Students should have a strong understanding of calculus and linear algebra, including calculus of several variables, and be familiar with the concepts of metric space theory such as convergence, completeness and compactness. Successful prior completion of MATH6110 or equivalent is preferred, but students can discuss their specific background with the lecturer to obtain permission to enrol.
Fees
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:
- 1
- 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.
Where there is a unit range displayed for this course, not all unit options below may be available.
| Units | EFTSL |
|---|---|
| 6.00 | 0.12500 |
Course fees
- Domestic fee paying students
| Year | Fee |
|---|---|
| 2024 | $4440 |
- International fee paying students
| Year | Fee |
|---|---|
| 2024 | $6360 |
Offerings, Dates and Class Summary Links
ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.
First Semester
| Class number | Class start date | Last day to enrol | Census date | Class end date | Mode Of Delivery | Class Summary |
|---|---|---|---|---|---|---|
| 2719 | 19 Feb 2024 | 26 Feb 2024 | 05 Apr 2024 | 24 May 2024 | In Person | View |
