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This might sound like a dumb question, but I want to start learning math from scratch — starting with arithmetic. I'm looking for a book that goes into good detail and explains why things work, not just how to do the steps.

If you know any solid books on basic arithmetic, or even more advanced stuff beyond that, drop them here.
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>>16798932
https://www.ulm.edu.pk/departments/admin/upload/downloads/202110030921.pdf
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>>16798932
You can just grab any introductory textbook on number theory or algebra. They will explain why things work: algebraic opertations, numbers.

If you are not satisfy by those you can try mathematical logic (Peano arithmetic).
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>>16798932
AOPS Prealgebra -> AOPS Introduction to Algebra -> AOPS Intermediate Algebra -> Spivak Calculus -> Axler's Linear Algebra Done Right -> Rudin's Principles of Mathematical Analysis -> Any abstract algebra text, they are all the same -> Conway's Functions of One Complex Variable -> Munkres Topology -> Any functional analysis book, they are all shit -> Loring Tu's Introduction to Manifolds

Those are the basics that every real math majors need to know.
Grind Hammack's Book of Proof and Zeitz's The Art and Craft of Problem Solving if you feel the need. Like if you're struggling with Spivak's Calculus or other serious intro math books.

Imo Serge Lang's Basic Mathematics is no good. It's too basic. It doesn't prepare you for a real proof-based calculus course. The smart students don't need it, and the retarded ones need more help.

Gelfand's books are the best alternative to AOPS' books. I personally think AOPS is more idiot-proof. But Gelfand are cheaper. Both Gelfand and AOPS are only available as less-than-perfect scans on annas, z-lib, other pirate websites. Unfortunate.
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>>16798932
>why things work, not just how to do the steps
Hung-Hsi Wu's Rational Numbers to Linear Equations and its sequels (precalc and calc)
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>>16798932

GDR (Eastern-German) maths books are in high demand among students in math-heavy subjects here (picrel is 12th grade).

They are thorough and come with clear examples while still being university level, i.e. made for the reader, not for the writer to display status or add a line to their academic CV.

The antiquarian bookshop in e.g. Berlin / Leipzig / Dresden know these customers well enough to dive into some decent recommendations if you ask them.

You can find some on vialibri. Even if you don't speak german, they might give you some examples on how to organize an actually good math book.

I wish someone would just bulk-translate them. There is likely no copyright to grab anyway.
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>>16801581
And yet France is still better at math.
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>>16801005
I am working through the first book now and its very good. One of my favorite math books so far.



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