Studying [Academic Advise Needed] Math and coding in Astrophysics

[warhammer]

Hi everyone,

I'm currently doing my Master's in Astrophysics, and during my research in observational stellar and galactic physics I’ve noticed that a lot of the work relies on strong foundations in certain mathematical areas such as statistics, Bayesian inference, polynomial fitting, and linear algebra, among others.

However, I’ve realized that I have some gaps in these foundational concepts, which is affecting my ability to fully grasp the coding strategies used in research (e.g., MCMC sampling, curve fitting, modeling, etc.). So the challenge is twofold: the math itself, and then how it's applied programmatically.

I’m looking for resources (books, courses, online material) that can serve as a refresher for these mathematical concepts but preferably with a focus on or examples from astrophysics or astronomy. If anyone here has found a textbook, lecture series, or online course that helped bridge this gap, I’d really appreciate your suggestions.

 

[TensorCalculus]

How much would you say you already know about these concepts (e.g. I cannot imagine you have taken a whole astrophysics degree and never come across any linear algebra)? Do you already know them to a certain depth and need to deepen your understanding, did you once know everything and need to revisit the concepts again as they've faded in your mind over time, or have you never come across them before? This may help determine what sort of book (or other resource) would be best - some books are made for learning whereas others are best kept as reference to come back and refresh knowledge.

 

[warhammer]

How much would you say you already know about these concepts (e.g. I cannot imagine you have taken a whole astrophysics degree and never come across any linear algebra)? Do you already know them to a certain depth and need to deepen your understanding, did you once know everything and need to revisit the concepts again as they've faded in your mind over time, or have you never come across them before? This may help determine what sort of book (or other resource) would be best - some books are made for learning whereas others are best kept as reference to come back and refresh knowledge.

Thank you for responding. I did my undergrad in Physics and currently smack in the middle of the Astrophysics masters - so I would say I know some to a certain depth and some I practically know all there is to know about but need a refresher. But I think I hinge more on the refresher because those concepts "seem" faded and I feel like I need to get in touch with them again

 

[TensorCalculus]

No problem! So you are looking for a refresher on these concepts.
I'm definitely not the best person to answer your question since I'm not very experienced with the sort of mathematics that would come up in an astrophysics masters, but here are some more general suggestions for books and resources you could look at...

A nice book for reviewing/keeping as reference for things like linear algebra and statistics (at least in my experience) might be Riley, Hobson and Bence - I don't know if it would go into the kind of depth that you are looking for, but at least for the concepts that come up in physics undergrad, it should be helpful. I'm not sure what would be good for Bayesian Inference, but a bit of digging led me to find Bayesian Data Analysis by Andrew Gelman, which seems a popular book on these matters. Perhaps for statistics you might benefit from Statistical Methods for the Physical Sciences by Robert D. Cowan.
You could also check out some sites for courses on these concepts like OCW, though I haven't found much that would be particularly helpful - there are Statistics and Linear Algebra courses but they look to be more on the introductory side.
For polynomial fitting I doubt you will be able to find many books/courses that would be specifically helpful, but maybe books on numerical methods of data analysis would cover it.

What programming language are you using to implement these programmatically?

 

[warhammer]

No problem! So you are looking for a refresher on these concepts.
I'm definitely not the best person to answer your question since I'm not very experienced with the sort of mathematics that would come up in an astrophysics masters, but here are some more general suggestions for books and resources you could look at...

A nice book for reviewing/keeping as reference for things like linear algebra and statistics (at least in my experience) might be Riley, Hobson and Bence - I don't know if it would go into the kind of depth that you are looking for, but at least for the concepts that come up in physics undergrad, it should be helpful. I'm not sure what would be good for Bayesian Inference, but a bit of digging led me to find Bayesian Data Analysis by Andrew Gelman, which seems a popular book on these matters. Perhaps for statistics you might benefit from Statistical Methods for the Physical Sciences by Robert D. Cowan.
You could also check out some sites for courses on these concepts like OCW, though I haven't found much that would be particularly helpful - there are Statistics and Linear Algebra courses but they look to be more on the introductory side.
For polynomial fitting I doubt you will be able to find many books/courses that would be specifically helpful, but maybe books on numerical methods of data analysis would cover it.

What programming language are you using to implement these programmatically?

Thank you so much for your exhaustive response! Will definitely check out these books and resources (have used RHB during my undergrad as well!).

I am currently using Python and C (very sparingly) for these tasks. But some SMBH codes use C++ so might have to bridge my gaps!

 

[Muu9]

"Statistics, Data Mining, and Machine Learning in Astronomy" by Željko Ivezić, VanderPlas et al.

For more mathematical detail, check out these handouts by Andrew Ng and the YouTube playlist of lectures from the same course

 

[MidgetDwarf]

For probability, I found Hossein to be an excellent text.

For polynomial curve fitting, have a look at numerical methods books.
I took two classes in numerical (Did pure math), and I do not have any recommendations. We used a run of the mill book for numerical. Decent, but I’m not familiar with the books.

If you are looking for matrix methods, then Watkins : Fundamental of Matrix Computations. If you want something more concise, but a but more dense than Trefethen. I enjoyed Watkins more, since it was more explanatory, but it’s a bit dense. Trefethen is a great book, but found it a bit hard to read .