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