Apply Discrete Mathematics Through Formal Proofs
8 weeks · 0 milestones
Produce written solutions to 30+ proof exercises spanning propositional logic, mathematical induction, graph theory, and combinatorics — not just correct answers, but proofs with valid structure (base case, inductive step, conclusion) that a mathematician would accept. Each proof must show your reasoning, not just the result. Proof: the submitted exercise set reviewed by a CS lecturer or maths researcher who also presents 2–3 unseen claims during the review and asks you to prove or disprove them live — the live reasoning is what demonstrates understanding rather than memorisation.
Milestone map
Milestone map
3 milestones
Study propositional logic (truth tables, logical equivalences), predicate logic (quantifiers), set theory (operations, power set), and four proof techniques: direct proof, contrapositive, contradiction, and proof by cases. Complete at least twenty proof exercises — not just read about them.
Proof required
Submit: a typed proof portfolio containing at least twenty completed proofs — at least five each of: direct proof, proof by contrapositive, proof by contradiction, and set identity proofs. Each proof must be fully written out with every step justified. A mathematician, CS lecturer, or logician must review the portfolio and confirm in writing that the proofs are formally valid.
What gets checked
- Portfolio contains at least twenty typed proofs — fully written out with every step justified
- All four technique categories have at least five proofs each
- A mathematician or CS lecturer has confirmed the proofs are formally valid