Before moving on to another topic with a different pattern, let me just follow up with some thoughts about goals and progress in the GR/cosmology-focused interest in mathematics.

Unlike wine or music theory, it may seem like there's not as obvious a progression or end-goal, but for me I think there actually is.

For quite a number of years, I've had in the back of my mind a possible (albeit challenging even if just from a lifestyle point of view) goal of doing Part III of the Cambridge Mathematical Tripos. It's a very difficult, taught-Masters course that allows for a focus specifically on GR / cosmology (as well as many other alternatives) at pretty much exactly the level I'd eventually like to get to. (I've long abandoned doing a *PhD* in theoretical physics.)

Even if I never actually do the Part III, I can use it as the basis for my own private study and progression. It's possible to work backwards through the course prerequisites to a set of Part II courses, then Part IB courses, then Part IA courses.

What's particularly neat about this is I can construct a pyramid of interests so the foundation is fairly broad (although still not all of 1st-year mathematics) and narrows to the specialization I'm interested in as you go up.

Here's what a possible progression might look like based on the current Cambridge Mathematical Tripos:

### Part IA (1st term)

- Vectors & Matrices
- Differential Equations
- Groups

### Part IA (2nd term)

- Vector Calculus
- Dynamics & Relativity
- Analysis I

### Part IB (1st term)

- Methods
- Quantum Mechanics
- Linear Algebra

### Part IB (2nd term)

- Complex Methods
- Electromagnetism
- Geometry
- Groups, Rings and Modules
- Variational Principles

### Part II Michaelmas (1st term)

- Classical Dynamics
- Electrodynamics
- Principles of Quantum Mechanics
- Cosmology

### Part II (2nd term)

- Statistical Physics
- General Relativity
- Further Complex Methods

### Part III (1st term)

- Cosmology
- General Relativity
- Quantum Field Theory
- (
*possibly*) Symmetries, Fields and Particles

### Part III (2nd term)

- Advanced Cosmology
- Black Holes

It's possible to get a syllabus, recommended readings and, in some cases, lecture notes for these.