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Mathematical Sciences Institute · ANU College of Systems and Society
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.
3 written graduate assignments involving problem-solving, proofs of theorems, and the extension of theory (20% each)
Learning outcomes 1, 2, 3
Workshop problems
Learning outcomes 1, 2, 3
Subject-specific project applying differential geometry to an area of interest (hurdle)
Learning outcomes 3, 4
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.
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.