Any pointers on useful textbooks in this space? I seem to have difficulties finding one that is at the right level (not too easy, not too hard) or that provides a way to gauge your level and start accordingly at a later chapter or whatever.
I decided start with Calculus I on MathAcademy because that was the last thing I did in High School. MathAcademy disagreed and told me to do PreCalculus and even bits of Algebra II first, but I knew better (MathAcademy was right and in hindsight I should’ve just started the Foundation courses to build up my pretty weak algebra skills again).
For Calculus I simply use the textbook that’s recommended at the link above. As far as I can tell, it’s good. I don’t do the problems, though - for that I use MathAcademy.
I took college algebra three times - not because I failed, but because I had a couple multi-year breaks in my college career and didn't do much math during them. It was definitely worth it - each time I took the class I picked up on things I had missed previously.
If I went back for my master's, I'd probably take it again.
I'm biased, but very fond of the open-access introductory textbooks used where I studied. The department was very much pure maths, but the intro classes were accessible to general liberal arts students. I think the texts are relatively unique in that they're very proof oriented, yet with a pedagogical style that doesn't assume the reader is a future graduate student.
For linear algebra, we used the relatively standard Friedberg Insel and Spence [2], but I hear good things about https://hefferon.net/linearalgebra/.
[1] Link is off university domain, since apparently it was at some point turned into a bit more hardcore textbook oriented towards those going onto graduate studies in mathematics. If curious: https://www.amazon.com/Calculus-Analysis-Euclidean-Undergrad...
Not a textbook, but https://betterexplained.com is an awesome resource for gaining intuition, its author's approach is very unlike others I've encountered.
Just checking out a few of these will change your concept of what it means to understand something in math and cause you to seek out better explanations beyond the textbook one. You can also refresh yourself on a topic in a way that's fun.
For proofs and introductory real analysis, I highly recommend Prof. Jay Cummings' books at the awesome price of about $20 on Amazon for freaking 400 page books. If anything, just buy it to support the guy.
