Journeyman of Some

102 thoughts
last posted Jan. 12, 2018, 11:11 a.m.

86 earlier thoughts


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.

15 later thoughts