Discrete Mathematics and Proofs

模块目标

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

课程大纲

1. 01 Logic and quantifiers 15h

   学习结果 Negate a quantified statement correctly and explain the failure of a swapped quantifier.

   形成性检查 反例

2. 02 Direct proof, contradiction, induction 20h

   学习结果 Write one proof of each named type on a small number-theoretic or set claim.

   形成性检查 书面推导

3. 03 Sets, functions, relations 15h

   学习结果 Prove injectivity or surjectivity from the definition.

   形成性检查 书面推导

4. 04 Counting 15h

   学习结果 Apply a bijection or inclusion-exclusion with an explicit counting set.

   形成性检查 四选一检查

5. 05 Graphs (introduction) 20h

   学习结果 Prove a handshaking or path-existence fact from the definition of a graph.

   形成性检查 书面推导

6. 06 Synthesis 15h

   学习结果 Produce a short complete proof that a reader can mark without guessing omitted steps.

   形成性检查 书面推导

学习结果

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

学科技能

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

可迁移技能

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