Have to rep for my favorite math text that pretty much no one else has heard of: Ray Mayer's Introduction to Analysis [1]. It's rigorous, compellingly readable, and accessible to college freshmen. It was never published commercially, but decades of students where I went to school have been delighted by it, tortured by it, or both.
> The worst calculus book ever written. This was the 150s text in 1994–95; it tries to give a Spivak-style rigorous presentation in colorful mainstream-calculus-book format and reading level. Horrible. Take a look at it to see how badly written a mathematics book can be.
I think this list could use some updating. Most books on the list are super old. Also, from cursory look, there appears to be only one book on discrete math in Intermediate. There are tons of discrete math books that should serve as stepping stones for the one listed. For example, Discrete Intro to Math by Edward Scheinerman and Discrete Math by Susanna Epp.
Old books aren't bad, in fact, it's rare that new books are much better than the very best of the old books.
The Reddit discussion linked in another comment yields an updated Github repository, but a cursory glance didn't come up with any big changes.
Re: your Discrete Math complaint; if the author (and his friends, there were very few reviewers involved) didn't specialize in Discrete Math, then it's not surprising that somethign is missing. In fact the author actually explicitly says that the list is incomplete and which his specialties were.
I am not really complaining about Discrete Math. The book listed in Intermediate is fairly/horrendously difficult for someone who hasn't seen elementary treatment of the subject before.
Also, there are newer books of comparable quality to old classics like Algebra by Birkhoff/Maclane. If nothing, they have updated prose. Chapter 0 by Aluffi is phenomenal, for example.
Of the fields I know well, this book is pretty good. It would certainly not hurt to add new topics (high but finite dimensional vector spaces, computational harmonic analysis, statistics), but for the specific topics covered this list is excellent.
Recommending Maclane as the only book on Category Theory is a bit rough. I would add «Conceptual Mathematics» by Lawvere to the elementary list to be prepared.
