How to select the right books?

Question

As the saying goes, "Give a man a fish, feed him for a day. Teach a man how to fish, feed him for life." I've always had a problem with selecting appropriate books. It could be a problem that I'm a perfectionist, but it's starting to take over my life. I recently made a huge list of linear algebra books which I found in various "book-recommendation" type threads on different website (e.g. reddit, stackexchange, etc), and then proceeded by elimination to cross out books that were obviously too advanced for me or just plain rubbish. I'm fed up of this; every time I need to learn a new topic, the same thing happens, and it kills my initial enthusiasm. What I'm trying to find is a quicker and more efficient way of choosing math books. If you could also post your experience with this problem (or non-problem, depending on your personality), it would really help.

Thanks

Answer 1

For a list of great books, see The Mathematics Autodidact’s Aid.

Answer 2

There is no one answer to your question. It depends where you are in your mathematical journey. Take linear algebra for example. Perhaps one should begin with: (this may be too silly for some of us, not me)

The Manga Guide to Linear Algebra

Easy reading, fun, maybe good for highschool. A bit later, say after you've had some calculus at the university, you might look at a book like that by Anton, Strang, Larson or Lay. The list of these standard university texts for the Sophomore/Junior level linear course is endless. Almost certainly you should buy an edition from circa 1970-1980 as those have a bit more content and a bit less pandering to the slothful student. Two nice examples, recently published by Dover,

A Course in Linear Algebra by David B. Damiano, John B. Little

or, at a bit higher level,

Linear Algebra by Sterling K. Berberian

But, at some point, you realize you need more, then you start reading things like Halmos, Curtis, Insel-Spence-Friedberg. Yet, still, something is missing, so, you move on to the relevant chapters in Dummit and Foote or Roman's Advanced Linear Algebra. But, even then, you will still have questions. This is the great part of it all, it's endless.

Back to your original question: I don't think there is an efficient answer. In some sense, knowing the answer to "what is the right book on X" amounts to knowing what you know and what you don't know about X. But, how can you know that unless you know X? That said, you can get approximate knowledge by reading the reviews on various websites and seeing the recommendations made in answers such as

what are the best books on linear algebra