>>9735907it's a list likely made by an undergrad based on things that undergrad did or recommendations that undergrad found on /sci/.
actually, looking closer, it's garbage. if you're recommending something like velleman, then an "optional" first chapter of some set theory book, then you clearly haven't read one of those books. many tracks just outright skip bridge books like velleman or discrete math books, and cover all necessary set theory within the first chapter or appendix of their linear algebra book.
>although ideally one would like to study algebra first, linear algebra is so important...what? this is either poor writing or just stupidity, as is everything else in this paragraph. linear algebra comes first because it's easy, well-known, and very useful (so easy ti motivate). it has nothing to do with helping you understand examples in later algebra books and there is no smart idealist out there saying algebra should come first.
>recommending dummit and foote>before you encounter these structures, you want to be able to identify themno, you don't have to. it's entirely unnecessary. jump into analysis if that's what you want, you have a time harder in any notable way than those who took algebra first. there are more concise and interesting algebra books to recommend than dummit and foote's, not to say it's a bad book.
>real analysis after analysis, and Tao's books no lessTao is an amazing mathematician. however, his books for undergrads aren't anything special and a bit too easy, so i personally find them overrated. i think his reputation, not the quality of the book, is what's made them popular.
also, picking up a hard, more general analysis text (like rudin) completely sidesteps the need for an undergrad real analysis course.
there's more to say but i need to poop
