If I want to learn about astrophysics, should I study up on mathematics?
I am currently reading A Brief History of Time and while the book itself does not contain much mathematics in it, I want to learn more about the concepts Prof. Hawkings talks about more in-depth.
Now I am aware that I will never get the expansive knowledge that a university tuition in the field would give me, but I have already branched off into something else that does not allow me to pursue that field even if I really wanted to so I want to make do. (I also understand that any knowledge I do get will be basically useless to me, but I love space that much that, in spirit, the knowledge would feel useful to me.)
My question is, before I read books more technical, should I brush up on my math? I am aware that a more applicable subject like physics has more correlation with what I am interested in, but I don't want to read about physics if I have little to no knowledge what the hell each equation means. (Also, how I will learn is through online courses/websites/books. I know it is not the ideal way to go about it, but again, I will do what I can.)
Of course, if you believe I should somehow go back a few years and try my hardest at physics and follow the most tried path, I am all ears. It is just that I am now going to a technical college for IT and if I want to leave, I would have to spend a lot more time in education than most - meaning (as I live in the UK) will probably have to pay extra when I pass a certain age.
I know this question is not exactly linked to astrophysics, but I do not know where else to ask it. If I had read A Brief History of Time earlier in my life, I would not be in this sticky situation. Thanks in advance.
(ADDITION: I have always had a love for space and I was interested in physics, but my teacher was uninspiring and I was going through a tough period in my life. I am willing to work towards it now, even if my teacher is the worse thing to ever exist.)
Basic maths skills like basic calculus would be "enough" to help. But basic physics is an absolute essential. You don't need the mathematics as much as you do the concepts - an intuitive sense of how things work and the core "rules", like the laws of thermodynamics. You might consider Leonard Susskind's "The Theoretical Minimum" books. Minimal maths and mostly concepts.
Can you clarify: what do you mean by "books more technical". Can you give examples? What level of maths have you reached? Do you understand fractions? algebra? calculus? topology? For the question to be clear you need to specify where you are now, and where exactly you want to go.
@JamesK What I mean are books that properly going into subjects like universe expansion and red-shifting. My mathematics level is GCSEs (sort of pre-calculus stuff), but I've forgotten a good chunk of it. I guess I want to go on a knowledge quest of some kind - if I wasn't in my situation now, I would definitely pursue a university/college degree in astrophysics/astronomy.
You can use pauls math notes to get comfortable with calculus and differential equations btw.
Yes, absolutely. At bare minimum, you'll need to study some geometry to understand how distances are calculated and how the shapes of orbits are related. Next, you'll want to study some algebra, so you can understand the likes of the inverse square law for how the intensity of light drops off as you move away from an object emitting light equally in all directions. Algebra also helps in understanding the magnitude system astronomers use to describe how bright objects are in the night sky.
After geometry and algebra comes trigonometry, especially spherical trigonometry, because of its use in dealing with how we describe the location of objects in the sky, and how to relate positions in one coordinate system to positions in another.
Finally, if you want the really deep understanding, you'll want to go for integral and differential calculus. As my high school physics teacher used to say, the difference between an ordinary formula and one that uses calculus is like the difference between prose and poetry - the calculus encodes deeper meaning and is applicable in more situations than any single formula that can be derived from it.