What is the easiest way to learn high level maths by myself (I have textbooks but I think here I am asking for online resources). I completed my maths undergraduate degree in July 2020. Doing my degree was the best thing I ever did and it made me so happy. I really miss it.
I was planning to start a master's in Sept/Oct 2020, but was admitted to hospital and missed the first couple of months, so I thought I'd have to wait until Sept/Oct 2021. However, I was also in hospital then. In this admission I have been here for over a year (not the longest by a long shot, but I am absolutely desperate to get out!!)
So while I have been stuck here I have been working through my old notes from my UG and working through the problems again, so I don't get rusty.
I also like learning new things (in mathematics), that I am able to understand via books or online resources etc. Which is probably quite limited! There is an excellent resource from someone who I suppose still lectures at Lamar University (not sure where that is - I'm in the UK) and he has put up his notes for Calculus I, Calculus II, Calculus III, and Differential Equations. There are worked problems which are really easy to follow, and also you have to expand the solution so you can give it a good go first without it being spoilt by having the solution in front of them. In the calculus modules there are practice problems, again with worked solutions, should you need them. THere are homework questions too, but I am too scared to do that as I need to know if it's right or not. Some of the problems I could check by using Wolfram Alpha I know, but that just seems a bit too much.
Does anyone have any suggestions? Either on what resources are out there, or even just topics that I might enjoy and can watch videos about? I did a linear programming module in my second year and that was okay, and I found a lecture series from Penn State which I thought I could refresh my memory, but she teaches it slightly differently and I am concerned about getting confused doing it basically the opposite way. We'll see. I also when I am doom scrolling FB and Twitter (it is very boring here on the ward!!), I see maths videos, and last week they mentioned Lambert W Functions and I loved learning something that is new to me. I stayed up half the night trying to do more questions etc.
Sorry if I have written too much - my lecturers at uni used to keep telling me to write less, and said that when I publish in journals I will HAVE to be brief! I was just happy that he thought I might publish! I just love doing maths. As I write this, I have been doing maths for all but 6 hours of the past 36 hours. I haven't slept and I eat while doing maths. I call it doing maths for fun, partly because it is pretty pointless since I am not currently doing a course, and partly because I really DO find it fun, as perhaps you do if you are on this site!
Hoping to go back into education next autumn, as I am pretty certain I'll be out of hospital by then.
Thanks so much for reading. Feel free to moan about how long I have gone on for.
TL;DR Do you know of any resources I could use to study maths by myself at degree/postgrad level? Or can you recommend some interesting (and not too hard for me to learn without a tutor) topics that I could lose myself in going down a rabbit hole? Or where to look for something like a list of the different topics available, that I could then research myself.
Thanks!
 A: Here are some math subjects I enjoyed, and reference texts I found to be either insightful treatments of the subject, have challenging problems, or just fun to read:
Algebra: Lang - Algebra (dense with good problems), Dummit and Foote - Introduction to Abstract Algebra (in particular, easy to follow intro to Galois theory c.f. Ch. 13 and 14)
Differential Geometry: Lee - Introduction to Smooth Manifolds (this is THE book in my opinion)
Analysis: Rudin - Real and Complex Analysis (classic book, aka big Rudin), Marshall - Complex Analysis (read the exposition about the different possible approaches to the subject! Marshall emphasizes importance of power series), Stein and Shakarchi - Real Analysis (less terse than Rudin)
Topology: Hatcher - Algebraic Topology (classic book, albeit you're gonna bounce off it the first time you read it), Munkres - Topology (nice and readable! Doesn't go super far into the alg. top. though)
Misc.: MacLane - Categories for the Working Mathematician (if you like very abstract stuff!)
There are lots of good course notes online, but I prefer textbooks myself and I'm sure someone else can give better recommendations on course/lecture notes than I can. Finally, since the subjects listed have an obvious bias based on my grad studies, you can find a more comprehensive list (of mathematical sbujects) here.
