Session 8C
Final portfolio assembly
45-75 min - work through lesson notes, practice, and the MCQ check.
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Session tips
- Finish the MCQ before marking complete.
- Check the answer outlines after trying on paper.
- Mark complete to update your certificate progress.
Lesson notes
- A proof portfolio is a set of polished proofs that demonstrate mastery of core methods. "Polished" means: correct logic, clear structure, minimal fluff, and explicit use of definitions. The portfolio should include a variety: at least one contrapositive proof, one contradiction proof, one induction proof, one set identity proof, one function property proof, and one modular or divisibility proof. This ensures you can move between styles and topics without relying on a single technique.
- When selecting proofs, choose ones you can explain out loud. If you cannot explain why each step is valid, it's not yet portfolio-ready. For each proof, aim for a clean beginning that sets variables and hypotheses, a middle that uses definitions and algebra or logic, and a crisp ending that restates the conclusion. The portfolio is less about difficulty and more about correctness and clarity, because those are the foundational skills proof-based math demands.
Practice
Core: even/odd proofs, set identities, bijection, induction, modular proofs.
- 1Stretch: sqrt(2) irrational, prime factorization, Pascal identity, odd/even subsets.
MCQ
How many polished proofs are required in the final portfolio?