I loved maths at school and was always good at it, but incompetent teaching meant that nobody in my class got a good grade at 6th form. I've not really studied maths since. I've always thought that was a shame.
Similarly, I've always liked physics. I enjoy reading layman's articles and books on the subject, as well as following if not necessarily participating in the discussions here. But it's often said that you can't properly understand various branches of physics unless you can do the maths. This seems trivially true to me.
So what I want to know is - what specific branches of maths do I need to learn to have a good understanding of various types of physics? I know that various different types will require different branches (probability will be required for quantum mechanics, probably some geometry for relativity, etc.) but is it possible to boil it down to a key few disciplines where I'd have a good chance at being able to grapple with most things that cross my paths? Also, more specifically, I'd quite like to work my way up to properly understanding quantum field theory (even though I've heard it say that it's probably the most difficult branch of physics to fully understand), so can anybody tell me what I'd need to understand that, as well as the disciplines I'd need to understand first (i.e., if it's necessary for me to understand a different branch of physics before I could get to QFT, then I'll obviously need the maths for that, too).
And, as one last question, does anybody know of any good, preferably free, resources for studying maths to these kinds of levels? Ditto for a basic refresher course in the A-Level maths I didn't pass back in the day. I can remember doing differential equations (and being good at doing them, as well as enjoying doing them), but I can't remember how or why one would solve a differential equation. So anything which could briefly give me pointers on that kind of thing would also be good.
Similarly, I've always liked physics. I enjoy reading layman's articles and books on the subject, as well as following if not necessarily participating in the discussions here. But it's often said that you can't properly understand various branches of physics unless you can do the maths. This seems trivially true to me.
So what I want to know is - what specific branches of maths do I need to learn to have a good understanding of various types of physics? I know that various different types will require different branches (probability will be required for quantum mechanics, probably some geometry for relativity, etc.) but is it possible to boil it down to a key few disciplines where I'd have a good chance at being able to grapple with most things that cross my paths? Also, more specifically, I'd quite like to work my way up to properly understanding quantum field theory (even though I've heard it say that it's probably the most difficult branch of physics to fully understand), so can anybody tell me what I'd need to understand that, as well as the disciplines I'd need to understand first (i.e., if it's necessary for me to understand a different branch of physics before I could get to QFT, then I'll obviously need the maths for that, too).
And, as one last question, does anybody know of any good, preferably free, resources for studying maths to these kinds of levels? Ditto for a basic refresher course in the A-Level maths I didn't pass back in the day. I can remember doing differential equations (and being good at doing them, as well as enjoying doing them), but I can't remember how or why one would solve a differential equation. So anything which could briefly give me pointers on that kind of thing would also be good.
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