Teaching
Teaching history
- 2023 Semester 2
- Partial Differential Equations
- 2023 Semester 2
- Calculus 2: Advanced
- 2022 Semester 2
- Differential Geometry
- 2022 Semester 2
-
Calculus 2: Advanced
- 2021 Semester 2
- Partial Differential Equations
- 2021 Semester 2
- Calculus 2: Advanced
- 2020 Semester 2
- Calculus 2: Advanced
- 2019 Semester 1
- Measure Theory
Students
- 2025 2022
-
Louie Bernhardt
PhD
- 2023 2022
-
Daniel Traicos
MSc
- Thesis title: “Global Solutions of Semilinear Wave Equations Satisfying the Null Condition”
- 2022 2021
-
Sean Wynn
MSc
- Thesis title: “On the non-relativistic limit of crystalline solids in a fully geometric theory of continuum mechanics”
- 2020 2019
-
Caelan Turvey
MSc
- Thesis title: “The wave equation on neutron star spacetimes”
- 2020 2019
-
Madeleine Johnson
MSc
- Thesis title: “On the notion of global hyperbolicity in Lorentzian geometry”
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)
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”.