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Mathematical Sciences Institute · ANU College of Systems and Society
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.
3 written 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
Take home final exam
Learning outcomes 1, 2, 3
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.
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.