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所在平台: Udemy |
课程主页: https://www.udemy.com/course/fundamental-concepts-of-mathematics-for-computer-science/
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**课程名称：** 计算机科学数学基础概念 **课程概述：** 本课程旨在教授计算机科学领域不可或缺的离散数学基本原理。离散数学关注离散而非连续的对象，是算法设计与分析、软件工程以及计算机系统设计与分析的数学基础。 **学习目标：** 完成课程后，您将能够： * **理解并应用** 离散数学的基本方法，包括集合论、逻辑、组合学和图论。 * **分析和解决** 与算法设计与分析、软件开发和计算机系统运行相关的问题。 * **提升** 解决问题和批判性思维能力，为计算机科学及其他领域的成功奠定坚实基础。 * **具备** 逻辑性和系统性思维能力，以应对复杂挑战并做出明智决策。 **具体能力培养：** * **数学推理能力：** 能够对计算机算法和系统中常用的基本数据类型和结构（如数字、集合、图和树）进行数学推理。 * **严谨性辨别：** 能够区分严格的定义和结论与看似合理的论断。 * **证明技巧：** 能够综合运用初等证明方法，特别是数学归纳法。 * **计算流程建模与分析：** 能够运用解析和组合方法对计算流程进行建模和分析。 * **离散概率应用：** 能够将离散概率原理应用于计算简单随机过程的概率和期望。 **学习内容：** 本课程将涵盖离散数学在计算机科学中的核心概念和应用，为您的技术生涯打下坚实的数学基础。
In this course, students will learn the fundamental principles of discrete mathematics as they relate to computer science. Discrete mathematics is a branch of mathematics that deals with discrete, rather than continuous, objects. It is an essential tool in computer science, as it provides the mathematical foundations for the design and analysis of algorithms, software engineering, and computer systems.Upon completing the course, students will be able to understand and apply the basic methods of discrete mathematics, including set theory, logic, combinatorics, and graph theory. These methods will enable them to analyze and solve problems related to the design and analysis of algorithms, as well as the development and operation of software and computer systems.In addition to acquiring a strong foundation in discrete mathematics, students will also develop skills in problem-solving and critical thinking, which are crucial for success in computer science and other fields. By learning to think logically and systematically, students will be better prepared to tackle complex challenges and make informed decisions in their future careers.In particular, students will be able to:Reason mathematically about basic data types and structures (such as numbers, sets, graphs, and trees) used in computer algorithms and systems; distinguish rigorous definitions and conclusions from merely plausible ones; synthesize elementary proofs, especially proofs by induction.Model and analyze computational processes using analytic and combinatorial methods.Apply principles of discrete probability to calculate probabilities and expectations of simple random processes.
