离散数学 课程安排:
Week 1: 命题逻辑与真值表
Propositional logic, connectives, truth tables
Week 2: 谓词逻辑与量词
Predicate logic, quantifiers, logical equivalences
Week 3: 集合论基础
Set theory, set operations, subsets, power sets
Week 4: 关系与函数
Relations & their properties, functions, injective/surjective
Week 5: 证明技巧
Proof methods: direct, contraposition, contradiction, induction
Week 6: 组合原理
Counting principles: permutations, combinations, pigeonhole
Week 7: 中期复习与考试
Midterm exam on Weeks 1–6 material
Week 8: 递推与生成函数
Recurrence relations, characteristic equations, generating functions
Week 9: 数论基础
Number theory: divisibility, primes, gcd, modular arithmetic
Week 10: 图论 I
Graphs, paths, connectivity, trees, spanning trees
Week 11: 图论 II
Euler & Hamilton paths, graph coloring, planar graphs
Week 12: 复习 + 期末考试
Review session + final exam