Discrete Mathematics
离散数学是计算机科学的理论基础课程，主要研究离散对象的数学结构。核心内容包括集合论、命题逻辑与谓词逻辑、关系与函数、图论、组合数学、布尔代数以及初等数论。课程旨在培养学生的抽象思维与形式化推理能力，为后续算法分析、数据结构、编译原理、数据库等课程提供必要的数学工具。通过严格证明训练，学生将掌握数学归纳法、反证法等基本证明技巧。
Discrete Mathematics is the theoretical foundation of computer science, focusing on mathematical structures over discrete objects. Topics include set theory, propositional and predicate logic, relations and functions, graph theory, combinatorics, Boolean algebra, and elementary number theory. The course cultivates abstract thinking and formal reasoning, providing mathematical tools for algorithms, data structures, compilers, and databases. Students master proof techniques such as induction and contradiction.
学生需选择一个实际场景（如社交网络、交通路径、任务调度），抽象为图模型并完成建模与分析。要求使用邻接矩阵或邻接表表示图，实现最短路径、最小生成树或拓扑排序等核心算法，并撰写报告说明算法选择依据与复杂度分析。交付物包括源代码、测试数据及不少于2000字的实验报告。
Students select a real-world scenario such as social networks, routing, or scheduling, model it as a graph, and perform analysis. Deliverables include adjacency matrix or list representation, implementation of shortest path, minimum spanning tree, or topological sort algorithms, source code, test data, and a report of at least 2000 words explaining algorithm choice and complexity.