Math needed for researching Cosmology?

[m_x_a]

Greetings everyone,

I'm looking for ideas about what areas of math I should do to prepare for a PhD in Cosmology. (So far I have an undergrad math & stats degree).

I personally love pure math and view it as a series of puzzles; but somehow cosmology sounds more "applied". Anyway there are so many experts here that I'm sure I'll get plenty of directional ideas.

Cheers

Max

 

[PeroK]

Greetings everyone,

I'm looking for ideas about what areas of math I should do to prepare for a PhD in Cosmology. (So far I have an undergrad math & stats degree).

I personally love pure math and view it as a series of puzzles; but somehow cosmology sounds more "applied". Anyway there are so many experts here that I'm sure I'll get plenty of directional ideas.

Cheers

Max

If you've done a maths degree, then aren't the missing prerequisites for a cosmology PhD likely to be physics? SR, GR, QM, particle physics, thermodynamics?

Your biggest issue mathematically might be to learn a new style of using mathematics (fast and loose or wild and woolly). That should come with studying physics topics.

 

[m_x_a]

Thanks. It's sounds reasonable that they're likely to be physics but of course until I've studied physics, I can't be sure. If SR, GR, QM, particle physics and thermodynamics are what they study in cosmology, then I guess that's what I'll need to study.

 

[PeroK]

Thanks. It's sounds reasonable that they're likely to be physics but of course until I've studied physics, I can't be sure. If SR, GR, QM, particle physics and thermodynamics are what they study in cosmology, then I guess that's what I'll need to study.

How far have you got in your PhD application?

 

[m_x_a]

There's no particular hurry I already have one PhD. But that said, I'm keen to get going by learning as much as I can before registering.

 

[Vanadium 50]

There's no particular hurry I already have one PhD.

You should tell us your background rather than making us squeeze it out of you one drop at a time.

It is rare for a university to award a second PhD. Your options may be limited.

 

[m_x_a]

Since I’ve never done physics before, I have no idea what information is relevant. I know people with two PhDs.

But my question is simply asking what math would be useful to study for a background in cosmology. If it’s too complicated or you need more information, just ask.

 

[PeroK]

But my question is simply asking what math would be useful to study for a background in cosmology.

At what point do you plan to study any cosmology?

 

[m_x_a]

Once I feel that I have the math I need to approach cosmology confidently.

 

[gwnorth]

Have you looked at the requirements programs are looking for for admission to Cosmology PhDs? Many of them post them on their admissions websites.

As an example Stanford's Physics PhD program says:

All Ph.D. candidates must have math proficiency equivalent to the following Stanford MATH courses:

	Units
		Course List
MATH106	Functions of a Complex Variable	3
MATH113	Linear Algebra and Matrix Theory	3
MATH116	Complex Analysis	3
PHYSICS111	Partial Differential Equations of Mathematical Physics	4
PHYSICS112	Mathematical Methods for Physics	4

https://bulletin.stanford.edu/programs/PHYS-PHD

With an undergraduate degree in Math and Stats you most likely already have the requisite math background to be admitted to a PhD in Cosmology. Your limiting factor is most likely to be whether or not you have a sufficient background in Physics.

 

[m_x_a]

Have you looked at the requirements programs are looking for for admission to Cosmology PhDs? Many of them post them on their admissions websites.

As an example Stanford's Physics PhD program says:

All Ph.D. candidates must have math proficiency equivalent to the following Stanford MATH courses:

	Units
		Course List
MATH106	Functions of a Complex Variable	3
MATH113	Linear Algebra and Matrix Theory	3
MATH116	Complex Analysis	3
PHYSICS111	Partial Differential Equations of Mathematical Physics	4
PHYSICS112	Mathematical Methods for Physics	4

https://bulletin.stanford.edu/programs/PHYS-PHD

With an undergraduate degree in Math and Stats you most likely already have the requisite math background to be admitted to a PhD in Cosmology. Your limiting factor is most likely to be whether or not you have a sufficient background in Physics.

Thank you so much - that's a really helpful list. I haven't found lists like this on UK sites because I think they tend to be "research-based" rather than taught.

I have written to a couple of professors and while their advice varies depending on their area of interest, below is one helpful reply I just received.

Cosmology these days is not monolithic. Some theoretical subfields still use GR and numerical methods associated with solving gravity situations, so that's pure math.

Similarly for world models and speculations about dark matter and dark energy, that's in the realm of extensions to the standard model of particle physics, so gauge theory and pretty much pure math.

Increasingly, numerical and computational methods are dominant, so those skills sets are in high demand. That's a relatively new trend.

Little of the cosmology research I'm aware of uses applied math as such, expect in limited situations.

So I guess the answer is pure math is the best route to cosmology, although the PhD programs in astronomy/astrophysics include other courses that are very useful to a working cosmologist, and you'd miss those doing pure math.

 

[gwnorth]

I think part of the confusion here lies in the difference in structure of PhD programs in the UK vs the US. In which country are you wishing to study?

US Physics PhD programs are designed to be entered straight from undergraduate studies and as such incorporate 1-2 years of additional course work at the beginning before formal PhD research begins. Many UK PhD programs (but not all) require you to have a Master's degree first during which those courses are completed. What math you "require" depends on the admissions requirements of the specific programs you're considering, a bachelor's degree or a master's degree.

 

[m_x_a]

Many thanks. Chances are I'll study in the UK which is why it would help for me to know as much about the field before I actually start (no sense in doing my basic learning once the PhD has started which is a mistake i made last time). I find that if you can demonstrate Masters-level subject knowledge (even without a Masters), you can probably get in.

Anyway the way it works in the UK is that everyone starts on something called an MPhil where they watch you develop your research. You then apply for an upgrade to PhD which you may or may not get.

 

[f95toli]

Anyway the way it works in the UK is that everyone starts on something called an MPhil where they watch you develop your research. You then apply for an upgrade to PhD which you may or may not get.

No, that is not quite how it works,
There are several parallel system in the UK. The two "main" ones are either going straight into a research project (typically 3.5 years) OR doing a PhD via Centre for Doctoral training (CDT). In the latter case you do 1 year of coursework and projects and are then awarded what is usually called an MRes (not an MPhil); some people do leave after this.

In either case you do need a Masters of some sort before you can apply (MPhil or MSc).

Sometimes they do make exceptions to this and you can e.g. apply with a BSc plus relevant experience, but this is quite rare.
I do know that MPhils are sometimes seen as "short PhDs", but as far as I am aware that is not very common in physics. I don't know of any programs where you start an MPhil and is then "upgraded" to a PhD, although this doesn't mean that it doesn't happen; there are -as mentioned above- several coexisting systems.

Note that if you get your PhD from a CDT you will actually have several degrees: BSc (or equivalent), an MPhil/MSc, a MRes and a PhD (or a DEng if you work in a an engineering focused area)
Useful if you like adding letters to the end of your name

 

[m_x_a]

Many thanks, that’s helpful.

My PhD is from the University of London so I converted my MPhil to a PhD.