Naive Set Theory

* The Art of Probability by Hamming. An opinionated, slightly quirky text on probability. Unlike the text used in my university course its explanations were clear and rigourous without being pedantic. The exercises were both interesting and enlightening. The only book in this list that taught skills I've actually used in the real world. * 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. Not sure how useful it would be for self-study though. * Measurement by Lockhart. I haven't read the whole thing, but have enjoyed working through some of the exercises. A good book for really grokking geometric proofs and understanding "mathematical beauty", rather than just cranking through algebraic proofs step by step.…

In order: 1. Book of Proof 1a. How to Prove It: A Structured Approach 2. Elements of Set Theory - Enderton 2a. Naive Set Theory - Halmos 3. Foundations of Analysis - Landau 4. Basic Mathematics - Lang 5. Principles of Mathematics - Allendoerfer & Oakley 6. A Transition to Advanced Mathematics 6a. Concept of Modern Mathematics - Stewart 7. Calculus - Apostol or Spivak Don't skip any

Set theory: You should definitely look at Naive Set Theory by Halmos. Despite the name, it's totally rigorous development of ZF set theory with discussion on the meaning and equivalent statements of AC.

Naive set theory by Paul Halmos

Set Theory is the building blocks of mathematics, and Halmos is a first-rate mathematician and teacher. Excellent recommendation Paul. I worked through Halmos 8 months into my mathematics self-study and loved it.

"Naive Set Theory" by Paul R. Halmos.