I’m in the process of typing them up. In the meantime, the original handwritten notes are here.
Officially, Principles of Mathematical Analysis requires very little background material. Rudin explicitly mentions the axioms governing the arithmetic of the integers and familiarity of the rational number field . This means he is assuming the reader knows about:
- Associative, commutative, and distributive properties for the integers
- The greatest common divisiors and algorithm
- The unique factorization of integers into primes
- The binomial theorem/expansion
- How fractions (rational numbers) behave
- The well-ordering principle for the natural numbers