离散数学专业级 Certification
逻辑、结构与计算的数学基础
Key facts
- Level: Professional
- Field: Mathematics
- Estimated study time: about 32 hours
- Credential price: $213
- Exam: 88 questions · 140 minutes · pass mark 75%
About the 离散数学专业级 certification
一项专业级离散数学认证——计算机科学、密码学、网络与形式推理的严密数学基础。你将掌握命题逻辑与谓词逻辑，包括联结词、真值表、逻辑等价、量词与推理规则；主要证明方法——直接证明、逆否证明、反证法，以及普通数学归纳法与强归纳法；集合论及其运算、幂集、笛卡尔积、基数与可数/不可数的区分；函数与关系，包括单射/满射/双射映射、等价关系与划分、偏序关系与Hasse图；组合数学——加法原理与乘法原理、排列与组合、鸽巢原理、容斥原理、二项式系数及生成函数入门；递推关系及如何求解线性递推，以及主定理入门；数论——模运算、求最大公因数的欧几里得算法、素数、同余，以及RSA背后的思想；图论——术语、路径与回路、连通性、树与生成树、欧拉回路与哈密顿回路、平面性、图着色、同构与最短路径；布尔代数与逻辑电路；以及使用大O记号的算法分析，以及P与NP等复杂度类、有限自动机与形式语言入门。每个主题均配以逐步解析的例题、图示与清晰的讲解，使你最终能够读懂、书写并验证严谨的数学论证——这是专业计算机科学与数学的工作语言。
What you will learn
The official 离散数学专业级 study course covers:
- Logic & Proof — Propositions, connectives, quantifiers and the rules of inference that make arguments valid.
- Methods of Proof — Direct, contrapositive and contradiction proofs, plus ordinary and strong induction.
- Sets, Functions & Relations — Set operations and cardinality, the three function types, and equivalence relations and orders.
- Combinatorics — Counting principles, permutations and combinations, pigeonhole, inclusion-exclusion and the binomial theorem.
- Number Theory & Recurrences — Modular arithmetic, the Euclidean algorithm, primes and RSA, plus solving recurrence relations.
- Graphs, Logic Circuits & Computation — Graph theory and spanning trees, Boolean algebra and circuits, Big-O and the P vs NP question.
- 动手实验——逻辑、计数与图 — Google Colab 中的离散数学顶点项目：构建真值表并测试逻辑等价性，用排列组合计数，进行模运算和递推，遍历并着色图。纯 Python，免费运行。
Prerequisites
Frequently asked questions
- Is the 离散数学专业级 certificate verifiable?
- Yes. Every issued Hootix Academy certificate carries a unique credential code that anyone can verify online.
- How is the 离散数学专业级 exam structured?
- It is a 140-minute ID-verified multiple-choice exam of 88 questions; you need 75% to pass.
- Do I need to buy the course to take the exam?
- Each certification is sold three ways: the exam on its own, the online course on its own, or both together as a Course + exam bundle (the bundle price is the course price plus the exam price).
- How long does the 离散数学专业级 course take?
- About 32 hours of self-paced study.