Calculus

The canonical text for this topic is Calculus by Michael Spivak. It's what I used in my first year, and most importantly, comes with a solution manual :)

on HN, 2019

Reading Spivak's Calculus, with the way that it starts off its path of inquiry by showing that, beginning with the basis of a totally-ordered field, the axioms at hand don't suffice to demonstrate the existence of e.g. a number that satisfies x^2 = 2, made me feel right at home again.

on HN, 2019

Calculus by Spivak. This was used in my intro calculus course in university. It's very much a bottom-up, first-principles construction of calculus. Very proof-based, so you have to be into that. Tons of exercises, including some that sneakily introduce pretty advanced concepts not explicitly covered in the main text. This book, along with the course, rearranged by brain.

on HN, 2023

This gives you a rigorous treatment of calculus, which hopefully you have some familiarity with. After this you can move on to real analysis.

on HN, 2019

However, I personally would never learn it this way--I prefer Spivak, during my read through I learned more than I could ever learn in a class.

on HN, 2020

Spivak’s Calculus is an introductory real analysis book pitched at undergraduates who have gone through a computational calculus course already and want to study the subject more formally and rigorously; it has many difficult problems and would generally benefit greatly from the structure and expert feedback of a university course.

on HN, 2018