Because in fairness, it does do so many things right. It's kind of controversial[1] because of Axler's notation and de-emphasis on determinants. But it's an ideal book to give a student who has had a first, computational course in linear algebra (i.e. a course entirely devoted to solving systems of linear equations and drilling matrices). I think Hoffman & Kunze is really the best textbook for the arrangement of material I'm talking about, but it's outdated at this point and its exposition is strictly less pedagogical than Axler. My vision for the "perfect" linear algebra textbook would be…
I think Linear Algebra is traditionally recommended, since you can readily apply a lot of geometric intuitions while picking up the mathematical ones. The drawback is that you have to make sure you're not cheating yourself of the mathematics by over-relying on the geometry. Sheldon Axler's acclaimed "Linear Algebra Done Right" is freely available as a download [1] through July due to the pandemic. I've not read it (yet!), but I've heard so many good things about it I feel comfortable recommending it off the cuff. :) (Recommendation: try not to focus too hard on the matrices! They're just…
Speaking as one of the people who recommended it in this thread: I don't think math anxiety is the right focus for which textbook to choose. More precisely, I don't think you should try to solve that problem by getting a different linear algebra textbook. To put it bluntly, someone with math anxiety probably just doesn't have the mathematical maturity for linear algebra yet. In that case they'd be doing themselves a disservice by attempting the material using some sort of "more accessible" book; instead, they should focus on resolving that anxiety through developing a solid foundation in the…
Tips on Reading Mathematics[1]: - Be an active reader. Open to the page you need to read, get out some paper and a pencil. - If notation is defined, make sure you know what it means. Your pencil and paper should come in handy here. - Look up the definitions of all words that you do not understand. - Read the statement of the theorem, corollary, lemma, or example. Can you work through the details of the proof by yourself? Try. Even if it feels like you are making no progress, you are gaining a better understanding of what you need to do. - Once you truly understand the statement of what…
I've been waiting for this for 6th months. Thanks to Sheldon Axler for making it available for free. This is intended to be a second book on Linear Algebra. For a first book I suggest "Linear Algebra: Theory, Intuition, Code" by Mike X Cohen. It's a bit different than a typical math textbook, it has more focus on conversational explanations using words, although the book does have plenty of proofs as well. The book also has a lot of code examples, which I didn't do, but I did appreciate the discussions related to computing; for example, the book explains that several calculations that can be…
> This is actually why I feel that mathematical texts tend to be not rigorous enough, rather than too rigorous. On the surface the opposite is true - you complain, for instance, that the text jumps immediately into using technical language without any prior introduction or intuition building. My take is that intuition building doesn't need to replace or preface the use of formal precision, but that what is needed is to bridge concepts the student already understands and has intuition for to the new concept that the student is to learn. If you read the book in the original post you may find…
I agree with the basic thrust of your comment, which as I interpret it boils down to saying it's unhelpful to throw book titles at a person without any context or guidance. However, I disagree with this point: > If some 2-minute video gives you something actionable to do rather than going through a 2-hour chapter in textbook there is no point of going through 2-hour chapter. Knowledge is all about applying not learning the facts and saying it around to your friends I know it feels good but nothing comes out of it in real life. There are optimal and suboptimal ways to learn things, sure. But…
I was in a very similar situation. The thing that helped me the most was getting an understanding of what it is mathematicians are trying to do and what their methods are. "What is Mathematics?" ended up being pretty pivotal (as another poster mentioned), though the topics did seem pretty random to me when going through it at first. The introductory material to "The Princeton Companion to Mathematics" is an excellent compass for orienting yourself. That introductory portion is about 120 pages, though it's a huge book (well over 1000 pages) and the rest of it probably won't be too useful to…
There is no royal road to mathematics[1], and it's incredibly arrogant to think that any person can provide a single optimal path. For me for example the next steps are Axler, Abbott and Herstein[2]. That's where I am at the moment, and it's way earlier than the books listed here. It would be far from optimal for me to try to bang my head stubbornly on this list. Mathematics demands you put in the work to build a foundation - you cant just skip steps. For some people those books I listed are very rudimentary. For others they are definitely too advanced for where they are and they'll…
Upvoting this because I think it's really important that we start getting more open source textbooks which specialize in exposition[1]. That being said, I'd make a different arrangement of the material. Here are a few thoughts: 1. This book embraces the modern take on a rigorous course in linear algebra, which I disagree with. That is to say, it covers vector spaces front and center in the first chapter. Conversely, systems of linear equations (Gaussian elimination) and corresponding notions like row reduction of coefficient/augmented matrices are pushed back several chapters. You see this…