[tgb]

As a math grad student, I can say that this Chicago list has primarily books that mathematicians know. The one posted here has primarily books that I am unfamiliar with. If one were to follow that one, other people trained in math would have a hard to judging what you've done (it's common to say things like "I've learned algebra at the level of Dummit and Foote" but this only works if people know the book you're referring to).

On the other hand, books written for mainstream math majors and graduate students are not necessarily the ones best suited for an autodidact. Perhaps the author of this post has selected those that are more appropriate, but I can't judge. Also, Springer is a great name in math books and you generally don't go too far wrong by sticking with them, but I've never seen their undergraduate series before. Perhaps they're more common in the UK than the US?

[ryanmonroe]

An added benefit to learning from a book that's more popular is that if you hit a wall and have a specific question about the material as it's presented in your book, you're more likely to find your question answered online. You might even be able to find course material that follows the book, whether from an official online course or just because the professor at some university didn't bother to make the course page blocked off from non-students.

[mafribe]

   book that's more popular 

Yet another benefit of popular books is that they won't be first edition, so a lot of mistakes that make it into the first edition will have been ironed out.

Don't underestimate how much a strategically placed typo can confuse a learner.

Rule of thumb: avoid first edition maths books.

[_asummers]

I once had an analysis book that began the chapter "There exists epsilon < 0", which I found very amusing.

[chestervonwinch]

I've found this to be a big plus in my experience. Additionally, if you're question has not been answered, you at least have the benefit of widespread familiarity with the text you are using. This means friendly internet folk will have less mental overhead due to notation, etc., and less of a barrier to answering your question if you ask.

[Ntrails]

> Perhaps they're more common in the UK than the US?

I can't speak for all universities over here, but my undergrad had a single textbook from what I recall. The rest were all printed notes or simply lecturers writing with astonishing speed on the blackboards.

There was certainly extra reading we could do, and I'm sure someone did. But most of the learning was from attending lectures and watching someone go through things step by step.

I'd be interested to know if other courses are more textbook based - although I know which I would choose.

[tgb]

That's sounds typical for a graduate course in the US and atypical for an undergraduate, even an advanced undergraduate course. Most assign problems from texts and will have one or two texts that are required or possibly strongly suggested to have. On the other hand, many students don't really read the texts except for the questions. In graduate courses there are usually just a few suggested books you could use if you wanted to.

[FabHK]

> Perhaps the author of this post has selected those that are more appropriate [for autodidacts]

The Springer SUMS series (which appears on this list a couple of times) is very nice for autodidacts, so your conjecture could well be correct.