Proofs are explanations that compel agreement from a skeptical but fair reader. This pathway builds habits rather than dumping formal logic all at once.
- Real analysis & proof habits — mindset and checklist.
- Epsilon-delta intuition — quantifier order in the wild.
- Write three proofs of increasing ambition: (a) $\lim_{x\to 2}(4x-1)=7$; (b) the sum of two continuous functions is continuous at a point; (c) a bounded monotone sequence converges (outline OK at first).
- Sequences and series — partial sums as the meaning of infinite addition.
- Keep a personal “counterexample notebook” for false converses and misplaced quantifiers.
Tone. Scratch work can be messy. Final write-ups should define terms, state assumptions, and end by naming what was proved.