This material is now organized into four chapters. Follow the sequence below, or use the questions to find the topic you need. This original address remains the study-guide entry point.

Reading route

  1. Naive Set Theory: What belongs to a set, how do we construct sets, and how do we prove set identities?
  2. Functions and Mappings: What does a mapping specify, when is it injective or surjective, and when does an inverse exist?
  3. Sequences and Series: How do indices and initial data determine a sequence, and how do terms differ from partial sums?
  4. Finite Sums and Summation Techniques: How can we transform finite sums without losing terms, changing bounds, or counting twice?

The first chapter uses elementary, informal set constructions and puts comparisons of ZF, ZFC, and NBG in optional explorations. Relations and Order later develops classes and relations. Calculus handles detailed real-function properties and infinite-series convergence.

After these chapters, Number Systems, Algorithms, and Recursion applies countability to integers, rationals, and reals, then connects integer arithmetic to algorithm invariants and structural induction.