[X] Chapter 1. Logic and Proof.
[X] Section 1. Logical Connectives
[X] Section 2. Quantifiers
[X] Section 3. Techniques of Proof: I
[X] Section 4. Techniques of Proof: II
[X] 2. Sets and Functions.
[X] Section 5. Basic Set Operations
[X] Section 6. Relations
[X] Section 7. Functions
[X] Section 8. Cardinality
[X] Section 9. Axioms for Set Theory(Optional)
[_] 3. The Real Numbers.
[X] Section 10. Natural Numbers and Induction
[X] Section 11 Ordered Fields
[X] Section 12 The Completeness Axiom
[X] Section 13 Topology of the Reals
[_] Section 14 Compact Sets
[_] Section 15 Metric Spaces (Optional)