Students	MSc Theses
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”	If you are a Master’s student, and trying to get an idea what a thesis under my supervision would look like, you should: Have a look at the titles of recent theses on the timeline on the left, Come to the analysis seminar, and subscribe to the list, Look at the reading list below, which are examples of reading material in the given direction, Talk to me. 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)

Students

MSc Theses

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

2020 2019

Madeleine Johnson

MSc

If you are a Master’s student, and trying to get an idea what a thesis under my supervision would look like, you should:

Have a look at the titles of recent theses on the timeline on the left,
Come to the analysis seminar, and subscribe to the list,
Look at the reading list below, which are examples of reading material in the given direction,
Talk to me.

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)

This course is offered annually for first year students in Semester 2.
I have developed it in the years from 2020 to 2023.

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”.