Here we delve a bit into the realm of topology, adding a notion of "closeness" to our sets and seeing how that helps us understand the real numbers.

1. Problem Solving 101
2. Introduction to Proofs
3. Propositional Logic
4. Proof Techniques
5. Set Theory
6. Predicate Logic
7. More Proof Techniques
8. Relations
9. Functions
10. Number Theory
11. Modular Arithmetic
12. Infinity
13. Construction of the Real Numbers
14. Topology
15. Sequences and Functions
16. Group Theory
17. Rings and Fields
18. Morphisms
19. Epilogue & Fields of Mathematics

This is a friendly introduction to important concepts in higher mathematics, including analysis, set theory, proofs, group theory, rings, and graph theory.