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Comment by ghufran_syed | Hacker News Reader

I went from only having done high school math 10 years ago to completing an MS in math and statistics at my local state university while working in an unrelated field. I would recommend NOT starting with calculus if you haven’t done it, instead, just learn how to do proofs - I used Chartrand “Mathematical proofs” - You don’t need to know any math beyond algebra in order to do that most of this book. If you need to revise or learn Algebra, then I would do Stroud “engineering math” first which is designed for self-learners with lots of solutions and feedback.

At some point, it would be good to get a a copy of Lyx and start to learn to write math in LaTeX - Then you can get feedback on your proofs online at math.stackexchange.com if you don’t know any math people locally.

Feel free to get in touch with me if you want to discuss further, happy to help!

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I looked up the Chartrand Mathematical Proofs book and it's been a while since I had to buy a textbook, but $175 for hardcover and $75 for paperback or ebook? That's nuts. If I were a student today, I'd pirate that and feel absolutely no remorse for doing so.

you mean sites like libgen.rs and b-ok.cc ?

I should also have mentioned this completely free book by richard hammack as an alternative: https://www.people.vcu.edu/~rhammack/BookOfProof/

Maybe, but this is not so bad, if you realize that the time and the effort you would spend on learning the material from such textbook is in some ways incomparable with the price of a couple of dinners at a restaurant.

Thing is that I just can't read PDFs.

If you have the means, try printing them little by little: chapter by chapter plus any back-of-the-book material. This way you can focus on one thing at a time, tactile paper in hand, without expending money on topics you don't yet need. You can annotate it, solve problems in the margins, file it, and reserve it for reference if/when you move on to successive chapters.

Sigh. I miss having a printer.

Try borrowing a good e-ink reader to see if it helps. If so, get a good one with larger screen if you'll be using more for textbooks.

Use an iPad, or any tablet, rather than smartphones.

I also read PDFs full-screen on my high-res, high-dpi laptop.

Try these two.

I have read tens of thousands of pages in PDF. (Yes, I checked)

Almost the same thing imo. It's a screen and I already sit so much in front of screens... all the more now that Elden Ring is out.

Yes! Combinatorics, graph theory, linear algebra, and even some parts of theory of computation and grad-level abstract algebra and algebraic number theory can be learned without calculus (I think!).

N.b. This is not to say that these are all easier than calculus, and I wouldn’t even really recommend learning say Galois theory before calculus, I’m just saying it seems that one could.

How old were you when you started into maths past the highschool level, and how many hours a week were you working in the unrelated field? I’m 29 and have a sincere interest in math, but I’m relegated to self-learning because I earned on.y a 2.3 GPA in undergrad. I’ve been working threough Hammond’s proof book as well as some vector calculus, and while I seem to completely understand the material as I read about it, the exercises leave me pretty bruised up.

I don’t know anyone who knows or values math much past algebra. “I don’t need it for my career, so why would I spend tome on it?” I don’t plan to switch to engineering, so I often find myself distracted & wondering what value math will add to my life other than making my interests more obscure and distant from the everyday people I meet. All I have to go on is “I’m interested & I trust that I’ll find it helpful once I know it. Also some people who are good at math make pretty good money.” But when I get 60% on a set of exercises, it’s challenging to keep faith.

Well,

I feel like one can easily get a bunch of "Really you should start with X" statements concerning math. Really you should start with proofs, really you should start with problems, really you should start with these concepts. I started with concepts rather than proofs or problem and I too went to a MA and various study. I tackled both proofs and problems but I don't think I'd have done as well if I'd jumped on these immediately.

So, altogether for someone wanting to get into advanced math, I'd say to look at the variety of advice out there and follow the kind that seems to help your progress.

On the other hand I sometimes wonder why Calculus is made a big deal out of. It was probably the easiest among all the parts of maths. You just have to imagine an small unit and how to extrapolate for integration and imagine how to break it down to small parts for differentiation. When I originally learnt Calculus in high school it was couple of days of learning the concepts and the a week of deriving everything from that and move on!

Did you multivariable calc in that week? Very impressive.

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