u/RemoteDot2128

Hi everyone, I've just started with proof-based mathematics (I'm self-taught) and I made the mistake of starting with linear algebra done right.

The book is really good, but I can't do almost any of the end-of-chapter exercises (actually, the same thing happens to me with real analysis too). So, since I'd like to understand it 100%, and since the author himself says to use it as a second course, I need an intermediate book to use. Now, I hate non-proof-based books (I don't like recipe books), so I'd like one like this.

I'm undecided between linear algebra done wrong and linear algebra by Friedberg, Insel, and Spence. What are your opinions on these two? Is Friedberg's book practically a duplicate of Axler's book in terms of difficulty, or does it really make sense in my situation? I repeat, I'm really bad at non-mechanical exercises on proofs.

(One advantage of Friedberg's Linear Algebra is that it comes in paperback, which is a huge plus for me as I prefer physical books. By the way, if the answer is Friedberg, what are your thoughts on the Pearson International Edition of the book? I mean, the Indian one. Is it any good, or should I go for the classic fourth edition?)

Hi everyone, I'm trying to learn real analysis, but books like "Analysis 1" by Terence Tao or "Understanding Analysis" by Abbott are really too hard for me. So I was browsing "Elementary Analysis, The Theory of Calculus" by Ross online, and it seems to be much easier than those two. Is that really the case? The exercises, however, seem almost stupid. After reading it, will my mathematical maturity be much greater, or will I still have the same problem with the other two books? Is it a deep enough book? in general I mostly have big problems with the exercises that involve proofs.

Hi everyone, I'm in high school and wanted to start with formal mathematics (I already have an informal understanding of the topics, mainly from Khan Academy), so I tried reading Analysis 1 by Terence Tao: chapter 2 is very enlightening and doable, but after chapter 3 it became incomprehensible, then I tried Linear Algebra Done Right: I understand the theory but the exercises are impossible, then I tried Calculus by Spivak; same situation as Tao, and after spending all this money I feel really guilty, I have 3 books that I don't understand, I'm not too bad because sooner or later I know I'll read them, but in practice now they are all incomprehensible, how to unblock the situation? Do books like How to Prove It make sense or not in this situation? What advice do you have? I absolutely don't want to read non-formal books like Linear Algebra by Anton or the counterpart for Calculus

Hi everyone, I am an aspiring research scientist in deep learning, I already have some engineering experience with models, but I wanted to learn formal mathematics for research, I'm in high school and I'm reading Linear Algebra Done Right by Sheldon Axler (after dopping analysis 1 by terence tao) and although I was able to solve almost all the problems in the first chapter, the book became extremely cryptic and ambiguous by page 30. I'm also annoyed by the use of Calculus topics as examples (I know Calculus, but not very formally, that's why I wanted to do real analysis). I'm not blaming Axler, on the contrary, the problem is clearly my lack of mathematical maturity, so I wanted to ask you: which books do you consider the most formative in this sense? I mean, besides those boring books like How to Prove It or Book of Proof (nothing against them, but they're too boring, it's just me), in this sense I've heard good opinions about Spivak's Calculus, is it really that good? How much transfer learning is there in mathematics? Will learning to do proofs in one area of ​​mathematics make me better at doing them in another area?

ciao, scusate per la domanda forse sciocca ma non conosco per niente le dinamiche universitarie, finito il liceo prenderò matematica alla sapienza, e mi chiedevo: siccome preferisco di gran lunga i libri in inglese, se lo chiedo al professore me li farà usare al posto di quelli del corso? (ovviamente se l'argomento trattato è lo stesso, tipo usare calculus di Spivak/analysis di Rudin invece di analisi di Giusti o quel che sia italiano), dovrei chiedere a un ricevimento o in altre occasioni? verrei visto in modo strano/ambiguo?