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I'd honestly spend my energy on finding a platform which gets you closest to a mentor. Books are good, but in no way, shape, or form a substitute for a mentor. Mentoring is two-way communication, a books is almost always a one-way. Forums, chat groups/channels, pen pal, whatever it takes.
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No. Books can't understand how you think and learn and help guide you. There is no substitute for a good teacher. Is there a best book for that student? Probably, but who is that student? We don't know! Beyond just learning mathematics, seeing the art and beauty in it is also best taught by someone who knows the subject and the student. Without the beauty, it's just what could be in a textbook, assuming you found the right book. If you're asking if you can find a good book to teach someone, that depends on your style and theirs . . . We will almost certainly have good student-focused AI teachers during our lifetimes for things like math and languages. Will AI be able to show us the art? I can't say for sure, but I bet so . . .
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I really like Arthur Benjamin's work on mental mathematics. I'm not savant-level, doing division in the thousands or huge floating points in my head yet but I sure am a lot sharper than I was coming out of high school from studying his work, and I guarantee you will just have fun with expanding your capability to think about numbers. [1] I got a copy of this book from the 1920s which is really cool because it teaches you math lessons you have to actually go out and physically do stuff with like pegs and strings in a field, from the perspective of the history of mathematics where people were limited to such devices in order to do stuff like trigonometry. Very very different approach, probably not for everyone, but for me I just think it's pretty cool. It definitely was written in the 1920s though so you better get used to that particular writing style if you plan on digesting it like a course. It's designed that way, though, and it's got great reviews. Just keep in mind maybe some of the history is subject to have changed over the years. [2] Ultimately I've self-taught myself a lot more than I ever learned in school for sure but a wide variety of sources is probably more what you're after in terms of getting a grip on what's interesting enough to pursue further for your own means and ends. I think exploring what fascinates you the most and then just going and finding things from that point is a pretty good start as long as you've got elementary understandings up to a point where the fascination actually happens. [1] https://www.goodreads.com/book/show/83585.Secrets_of_Mental_... [2] https://www.goodreads.com/book/show/66355.Mathematics_for_th...
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It's going to very much depend on which field you are interested in. The subject is huge. If you want to study statistics or number theory, you're going to be looking at very different skills and knowledge, with only basically high school maths in common.
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What type of mathematics? What level? I taught myself all of A-level maths and further maths here in the UK from the standard text books at the time (Bostock and Chandler) before I started in the sixth form and then maybe about half of the first year university material before I went. Still better when you have somebody to teach you but not impossible. I did have access to somebody whom I could ask questions but didn't really use that.
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The question reminds me of Susan Rigetti's recommendations for math self-study. If your goal is to self-study the equivalent of a university undergraduate mathematics degree, this is one approach: https://www.susanrigetti.com/math
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his recommendation is quite useful, I've read most of it and found most of them are approachable
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Nothing can replace a teacher, much less a good one, but I recently stumbled upon an introduction book on calculus from 1910 (yes last century) that had a really nice way to explain things. I just read the beginning so I don't know how far it goes but anyway here the link https://calculusmadeeasy.org/
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Spivak's Calculus! (It's really a book about real analysis.) It's extremely well written and starts by rebuilding your understanding of your fundamental mathematical building blocks, only using things you can prove. It also teaches you how to prove them.
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Do you have specific mathematical topics you're interested in? I have tried reading textbooks a few times to teach myself but found it hard to stay motivated, so I found a tutor on Upwork to assign and grade homework problems and answer my questions. Along with math textbooks and YouTube videos, this has been super helpful for fleshing out my knowledge of college-level math that I never learned properly. It's also great because they can go at the pace you want and focus on topics you find challenging, interesting, or useful.
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Do you have favorite YT channels that you can recommend?
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I believe Richard Feynman has mentioned in interviews that he learned calculus from "Calculus Made Easy". IIRC there might have been other books in a "Made Easy" series about math, but I'm not sure.
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That's one of the books my grandpa had that I wish I had managed to get before that whole collection got dispersed because I remember him reading it over like a ten year time period. He just liked repeating variations on the exercises I think
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I had two acceptable maths teachers in my life. Good teachers seem so rare.
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J.Steward's "Calculus: Early Transcendentals" is pretty on point for calculus. Mathematics is more than calculus though.
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Burn Math Class by Jason Wilkes is interesting.
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It is a long time since I learned, so I dont have specific book, but dont underestimate exercises. Whatever math topic you are learning, look for one of those books with only exercises in them and solutions in the end.
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And an active author/publisher who still posts corrections, or on older book. Maths books tend to have errors in the solutions.
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