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I'm looking for a cool and interesting subject in mathematical astrophysics to study for my master's project. What I really aim for is certain processes in the cosmos (multiple body-problem, black holes, asteroid belts, colliding stellar objects, etc...), but my background is not very much on the physics side, unfortunately. However, I read about special relativity, gravitational waves and how to measure in space, but not in a very mathematical way.

I would like to hear from someone whether they know similar subjects like the above that are reachable for a graduate math student, like me, to study for their master's project.

My background is mainly in algebra (Galois, Geometry, crypto), but I also have done statistical data analysis courses and (P)DE courses; thus I have seen a rich part of mathematics, but my specialty is really in abstract algebra. However, especially now, I would like to get to know subjects that are not mainly abstract algebra, but more PDE, for example.

I'm ready to dive into depths of mathematical physics if necessary. Thanks for any suggestions!

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    $\begingroup$ low N-body systems (e.g. 3 or 4 masses) are a lot of fun to explore and there are still many interesting questions to be asked - they're chaotic but in the limit of extreme mass ratios (as you get for planetary systems for example) may be semi-analytic - learning to code one up and visualising it is a great project, even just for learning the skills $\endgroup$
    – zephyr
    Commented Jun 6, 2020 at 19:15
  • $\begingroup$ I'm not really sure why nobody else is mentioning this - but if you're interested in PDE's in mathematical astrophysics, then why not study solutions to Einstein's field equations? After all, they are just a set of nonlinear PDEs; if you're interested in the numerical side, people run simulations to determine things about e.g. gravitational waves emitted from black hole merger events. If you're interested more in theory, then there are important questions about existence/behaviour of solutions, for example the issues surrounding cosmic censorship $\endgroup$
    – QCD_IS_GOOD
    Commented May 23, 2021 at 5:40

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As a first step Newtonian Mechanics is very important. Both at an undergrad level and graduate level. So a calculas based first course is very important. Also very useful is a source on undergrad Atomic Physics and a course in Nuclear Physics. There are several others besides these. I would recommend the series of courses in a Halliday and Resnick type of text as a start. This will help set you up for many other courses in Physics. IMHO.

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One area where PDEs may be useful in astrophysics is the thermal evolution of various objects, especially inhomogeneous things like planets and asteroids. Another example, as one of my many side-projects I have been modelling the evolution of the number of stellar objects in late eras using the Smoluchowski coagulation equation to model mergers. I know that approach is also sometimes used for asteroid belt evolution and planet formation.

Statistical data analysis is also useful and likely in high demand.

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