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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

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closed as primarily opinion-based by Daniel Fischer Feb 22 '17 at 16:24

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ I don't see how you could possibly find out what book you like without looking at a bunch of books and picking the one you like. $\endgroup$ – MJD Dec 17 '14 at 18:27
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    $\begingroup$ I always choose the books required in the corresponding course of MITOCW, especially the ones with the solution available online or at the end of the book. For the level beyond that, I just pick the book most highly recommended by the experts in Math Overflow. $\endgroup$ – Math.StackExchange Dec 17 '14 at 18:29
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    $\begingroup$ Take a book. Read it. Work some problems. If you hate it, make a note of it and set it aside. Find a different book, and iterate until you find one you like. After you have finished the book you like, ask yourself why you hated the other books. Go back to them. See if your newfound knowledge gives you a different opinion. $\endgroup$ – Emily Dec 17 '14 at 18:51
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    $\begingroup$ Aran Komatsuzaki's suggestion is very good. Pick a course taught in a great math dept that you could in theory take and follow, and get the book that course uses. This is of course a first approximation, and sometimes it won't be appropriate --- look through it to see if it looks good for you and/or generally gets terrible reviews --- but it's better than "too many books" paralysis. $\endgroup$ – aes Dec 17 '14 at 18:56
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    $\begingroup$ This is a good question, why close it? $\endgroup$ – user45220 Dec 18 '14 at 16:05
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For a list of great books, see The Mathematics Autodidact’s Aid.

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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

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  • $\begingroup$ @AnalysisIncarnate that's a nice mistake to have happen, I almost used Bererbian for my linear algebra course next semester, however, I decided to use Damiano and Little since there are solutions to the exercises at the end. $\endgroup$ – James S. Cook Dec 18 '14 at 0:14
  • $\begingroup$ I discovered Berberian only recently and I quite like it. How was your course using Damiano and Little going? Was the text effective? $\endgroup$ – user1551 Jan 15 at 11:15
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    $\begingroup$ @user1551 the book is good. I enjoyed it. However, the homework for which there are no solutions given was a bit odd in places. I recall an eigenvalue which was something along the lines of $\lambda = 1+\sqrt{17}$. Of course, this is not an error, but, I don't want my students to deal with that when integer e-values do just fine. That said, I am still using other exercises gleaned from the text. Now I use my own notes which stem from D & L and a half-dozen other things. No book is perfect. $\endgroup$ – James S. Cook Jan 16 at 0:50

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