My username comes to mind. Spivak's Calculus is hands down the best intro Calc book if you want to learn math for its own sake. His book on manifolds is also amazing but definitely not intro.

If you want stats I highly recommend Statistical Inference by Casella & Berger -- it's extremely dry but so many stats books out there try to "make it easy" but the simplification means that you can't actually grok what's really going on. HOWEVER if you want to actually apply anything in this book you'll need to grab something more practical as well. Going through an applied stats book after having done SI is like having superpowers.

Spivak’s Calculus is hands down an excellent book for a first course in real analysis, and I’ll die on that hill(it’s only real competition is Analysis 1 by Tao, in my opinion).

Anyone that says “it’s just a calculus book; it’s not good for introductory real analysis” is invited to go solve every problem in, for example, the chapter which defines integration, and compare the difficulty with problems in “traditional” analysis books.

If they know how to do (rigorous) proofs, then Spivak would be good. Otherwise it would be far too advanced. It's essentially an introduction to analysis.

That's fair. I don't really know what counts as advanced anymore. There just aren't that many books on theoretical math that aren't "graduate level" (which is way scarier than it sounds) -- Spivak was my Real Analysis 101 book as a freshman math major.

Spivak at least has the nice property that it doesn't assume you know much.

No one can have an enjoyable and helpful reading experience by picking a textbook or applying for a random course. Instead, reading the history of mathematics to learn about topics and their background would be a great way to capture the idea and a good starting point to find your favorite area. I recommend searching for Paul Lockhart's books, Mathematics in Western Culture by Morris Kline, and Famous problems of geometry and how to solve them by Benjamin Bold.

I've made it a hobby of reading beginner Calculus texts. I believe it to be a fascinating thing to explain and teach. Recently, the Teach Yourself series re-released their 1992, Calculus: A Complete Introduction. It isn't clever like Things Better Explained, with the visualizations, but does share excellent examples you already understand as unusual and then provides a pathway to using the integral. Like most good Calc books, just bring algebra!

I'd like to augment request one step further: Is there anything that kinda goes through the fundamentals all over again, but is programming aware?

I constantly assert that I'd have actually been successful with mathematics throughout school if I were able apply it in code (which was not a thing in my educational environment); not with my broken brain where I fuck up numbers on paper and use my fingers for arithmetic.

Graphics programming where applied linear algebra is built from the ground up

http://billsix.github.io/modelviewprojection/intro.html

Most of it is done but I’m updating the content in web form weekly

I have, but have not yet read, this one. It appears to claim to be something like what you're looking for.

https://www.manning.com/books/math-for-programmers

There is also the coding based Linear Algebra course that is available online (there's an accompanying print book).

https://codingthematrix.com/

And somebody who posts here on HN recently published a book with a title something like "Mathematics for Computer Programmers" or something to that effect. I forget the username and the exact title though. If you search around you can probably find it.

Edit: here's that last one. A Programmer's Introduction to Mathematics

https://www.amazon.com/gp/product/B088N68LTJ/

> I'd like to augment request one step further: Is there anything that kinda goes through the fundamentals all over again, but is programming aware?

This is the second time today I'm recommending Knuth's "The Art of Computer Programming". It really is a math book, and it includes answers to ALL the exercises. For example, the last 150 pages of Volume 1 are solutions to the exercises.

Not a book. But I'd recommend this website :- https://www.mathsisfun.com/ website. Everything is broken down into to smaller chunks. I stumble upon it when I was looking to revise my algebra concepts. But now I'm learning physics on it.

There are multiple entry points, depending on your goals.

However, if your goal is to learn mathematics for the sake of art, I recommend Kolmogorov's Elements of the Theory of Functions and Functional Analysis.