本课程是云南大学信息与计算科学专业数学专业的基础核心课程。本课程共4学分，每周4学时，共计72学时。
本课程主要介绍离散结构及其相互关系，为学生学习数据结构与算法、算法图论等后续数学课程做准备。旨在对学生进行系统的数学训练，提高学生的抽象思维和逻辑推理能力，掌握算法的本质，从而设计出高效的算法来解决数学问题，为学生今后在计算机科学领域的应用奠定坚实的理论基础。
离散数学包括许多重要的领域，如集合和集合上的运算、逻辑学、图论、代数系统、形式语言等。众所周知，离散数学是计算机科学、信息科学和计算科学的核心基础。实际上，离散数学在计算机科学的许多分支中随处可见。例如，当一个人想要学习和研究形式证明、密码学等时，理解形式证明的能力是必需的。图论中的许多概念已经广泛应用于计算机科学的各个领域，如数据处理、计算机网络、操作系统和编译器设计。集合论中的许多概念已经应用于软件工程和数据库系统中。在有限状态机的设计中，理解理论原理的能力是至关重要的，因此，代数系统和形式语言的思想被广泛应用。
随着计算机科学技术的发展，越来越多复杂的分析方法被应用到实践中。为了对未来的计算机科学有深入的理解，学生有必要掌握关于离散数学的基础知识。

Knowledge Objectives
1. To master the discretization and formalization of computational problems, including the application of basic knowledge such as mathematical logic, set theory, algebraic structures, and graph theory to formally describe computational issues.
2. To understand the mathematical description of discrete systems and appropriately apply these methods to the formal representation, logical calculation, logical reasoning, and construction of computational models.
3. To acquire comprehensive and systemic knowledge related to discrete mathematics and to analyze and design systems and models in information technology, including the formal proof of computational problems.
Skills Objectives
1. To construct correct direct and indirect proofs using mathematical terminology and symbols.
2. To employ proof strategies such as proof by cases and counterexamples.
3. To apply logical reasoning to solve various problems.
4. To work with propositional logic and predicate logic, including writing English sentences for logical expressions, completing and using truth tables, defining and using related terminology, and applying standard logical equivalences.
5. To solve problems involving elements of counting theory, such as even and odd integers, rational and irrational numbers, divisibility, etc.
6. To use mathematical induction, including stating the principle of mathematical induction and constructing inductive proofs involving sums, inequalities, and divisibility arguments.
7. To use set notation, prove propositions involving sets, and understand and use terms such as cardinality, finiteness, countable infinity, and uncountable infinity.
8. To solve counting problems by applying permutations, combinations, the addition rule, and the principle of inclusion-exclusion.
9. To define and use functions, domain, codomain, range, image, preimage, and composition, and to prove the one-to-one, onto, and bijective properties of functions.
10. To define and understand binary relations, reflexivity, symmetry, transitivity, equivalence relations, etc., and to demonstrate whether a binary relation on a set is an equivalence relation.
Ideological and Political Objectives
1. To emphasize the unity of knowledge imparting, ability enhancement, and value guidance, cultivating values such as the spirit of the Red Boat, etiquette, gratitude, social responsibility, and a commitment to continuous improvement and teamwork.
2. To foster a scientific spirit, dialectical thinking, and innovative consciousness.
3. To instill patriotism and establish a people-oriented philosophy of professional development.