Teaching
MSc Courses
Differential Geometry (MAST90143)
This course is offered biennially (every two years). I am teaching it for the first time in Semester 2, 2022.
Partial Differential Equations (MAST90133)
This course is offered biennially (every two years). I have taught it for the first time in Semester 2, 2021.
Measure Theory (MAST90012)
This course is offered biennially. I taught it in Semester 1, 2019.
Syllabus (2019), Course material (2019).
MSc Theses
If you are a student in the Master’s program of the School of Mathematics and currently looking for a supervisor, then the following topics give you an idea what I have currently in mind:
- Topics in relativistic elasticity. Flavour: Differential Geometry. Literature: Christodoulou & Kaelin (2012)
- Asymptotics for semi-linear wave equations. Flavour: Functional Analysis, PDE. Literature: Luk (2012), Lindblad & Rodnianski (2003), Lindblad & Schlue (2020)
- Waves in de Sitter and Schwarzschild de Sitter. Flavour: General Relativity, PDE. Literature: Dafermos and Rodnianski (2008), Schlue (2012)
Lecture Notes
Undergraduate Courses
Calculus 2: Advanced (MAST10021)
This course is offered annually for first year students in Semester 2.
I have been teaching it every year since 2020 when it was first introduced.
FAQ about this course:
- What is the difference between Calculus 2: Advanced and Calculus 2?
I would say, while the topics covered in this course are broadly the same as in MAST10006 Calculus 2, the material is more “advanced” in the sense that you will see more proofs and concepts, and fewer examples with “ad hoc” solutions. Here we aim to strike a balance between the theoretical underpinnings of Calculus and its practical applications, which also prepares you to take other classes is mathematics & physics. - What is the difference between Calculus 2: Advanced and Accelerated Mathematics 2?
In comparison to Calculus 2 the course Accelerated Mathematics 2 proceeds quicker, but not at a deeper level. The idea of the new courses in the Advanced stream is to offer solid entry courses in mathematics, where the foundations of these subjects are developed with more care, and more emphasis on the underlying proofs is given, both in the presentation of the material, and the skills acquired by the student. - How do I enroll?
Please contact ms-mslc-approvals@ms.unimelb.edu.au for all questions related to enrollment. - Is there a book you recommend?
I like Spivak‘s “Calculus” which gives a beautiful introduction to Calculus at the intended level for this course. In fact, large parts of this course are based on Spivak‘s text. I also recommend Folland‘s “Advanced Calculus”.