Discrete Mathematics and Proofs

Module aims

Replace example-only reasoning with a written argument that quotes definitions and names the proof pattern.

Course outline

1. 01 Logic and quantifiers 15h

   Learning result Negate a quantified statement correctly and explain the failure of a swapped quantifier.

   Formative check Counterexample

2. 02 Direct proof, contradiction, induction 20h

   Learning result Write one proof of each named type on a small number-theoretic or set claim.

   Formative check Written derivation

3. 03 Sets, functions, relations 15h

   Learning result Prove injectivity or surjectivity from the definition.

   Formative check Written derivation

4. 04 Counting 15h

   Learning result Apply a bijection or inclusion-exclusion with an explicit counting set.

   Formative check Four-option check

5. 05 Graphs (introduction) 20h

   Learning result Prove a handshaking or path-existence fact from the definition of a graph.

   Formative check Written derivation

6. 06 Synthesis 15h

   Learning result Produce a short complete proof that a reader can mark without guessing omitted steps.

   Formative check Written derivation

Learning results

Prove a short numbered claim by a named method, and exhibit a failed proof when a quantifier is misplaced.

Subject skills

Propositional structure, quantifiers, induction, counting, elementary graph language.

Transferable skills

Choose a proof pattern on purpose; keep definitions before slogans.