Math needed for researching Cosmology?

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In summary: 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,
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m_x_a
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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
 
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  • #2
m_x_a said:
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.
 
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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.
 
  • #4
m_x_a said:
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?
 
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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.
 
  • #6
m_x_a said:
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.
 
  • #7
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.
 
  • #8
m_x_a said:
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?
 
  • #9
Once I feel that I have the math I need to approach cosmology confidently.
 
  • #10
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
MATH106Functions of a Complex Variable3
MATH113Linear Algebra and Matrix Theory3
MATH116Complex Analysis3
PHYSICS111Partial Differential Equations of Mathematical Physics4
PHYSICS112Mathematical Methods for Physics4

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.
 
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  • #11
gwnorth said:
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
MATH106Functions of a Complex Variable3
MATH113Linear Algebra and Matrix Theory3
MATH116Complex Analysis3
PHYSICS111Partial Differential Equations of Mathematical Physics4
PHYSICS112Mathematical Methods for Physics4

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.
 
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  • #12
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.
 
  • #13
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.
 
  • #14
m_x_a said:
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:cool:
 
  • #15
Many thanks, that’s helpful.

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

Related to Math needed for researching Cosmology?

1. What specific branches of math are important in researching cosmology?

The most important branches of math in cosmology are calculus, differential equations, linear algebra, and statistics. These branches are used to model and analyze the behavior of particles, light, and energy in the universe.

2. How is calculus used in cosmology research?

Calculus is used to study the movement and behavior of objects in the universe, such as the motion of planets and stars. It is also used to study the curvature of space-time and to solve equations related to the Big Bang theory and general relativity.

3. Why is linear algebra important in cosmology?

Linear algebra is used to represent and manipulate large sets of data, such as observations of galaxies and other celestial objects. It is also used in computer simulations of the evolution of the universe.

4. How does differential equations play a role in cosmology research?

Differential equations are used to describe and model physical phenomena in the universe, including the behavior of matter and energy. They are also used to study the dynamics of the expanding universe and the formation of structures such as galaxies and galaxy clusters.

5. Is statistics used in cosmology research?

Yes, statistics is an essential tool in cosmology research. It is used to analyze and interpret large datasets, to test hypotheses, and to make predictions about the properties and behavior of the universe. It is also used to quantify uncertainties and to make statistical inferences about the nature of the universe.

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