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所在平台: Udemy |
课程主页: https://www.udemy.com/course/advanced-math-for-computer-science-mastery/
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课程名称：计算机科学高级数学精通课程 课程概述： 本课程全面讲解了软件开发者所需的数学基础，涵盖线性代数、现代分析、数学逻辑、数论和离散数学等多个数学概念。完成本课程后，您将具备分析和阐明计算机科学领域中原理和技巧的能力，为在编程中深入理解计算机系统的复杂运行提供了绝佳机会。 具体的课程目标包括： - 掌握将证明技巧应用于计算机程序的艺术。 - 通过数论获得加密和解密信息的专业能力。 - 探索软件开发与离散数学和数字电子之间的相互联系。 - 培养利用数学工具灵活分析任何计算机算法的能力。 - 在计算任务中运用微积分、概率论和线性代数的强大力量。 - 理解λ演算在函数式编程中的应用。 离散数学的核心在于研究本质上具有离散性的数学结构，而非连续性。与呈平滑变化的实数不同，离散数学关注的是像整数、图形和逻辑陈述等不具平滑过渡的实体，因此排除了“连续数学”领域的内容，如微积分或欧几里得几何。离散对象通常可以通过整数计数。简而言之，离散数学专注于可计数的集合，包括有限集合或与自然数具有相同基数的集合。然而，“离散数学”一词并没有确切的定义，更准确地说是通过排除的方式来描述，特别是排除连续变化的量及相关概念的领域。
This course comprehensively addresses the mathematical foundations essential for aspiring software developers. It delves into a diverse range of mathematical concepts, including Linear Algebra, Modern Analysis, Mathematical Logic, Number Theory, and Discrete Mathematics. Upon completing this course, you will possess the skills to scrutinize and elucidate principles and techniques within the realm of computer science. It offers a remarkable opportunity to acquire a profound grasp of the intricate workings of computer systems during programming. The specific objectives of the course encompass the following:Master the art of applying proof techniques to your computer programs. Gain proficiency in encrypting and decrypting messages through Number Theory. Explore the interconnectedness of software development with Discrete Mathematics and Digital Electronics. Develop a keen aptitude for utilizing mathematical tools to adeptly analyse any computer algorithm. Harness the power of Calculus, Probability Theory, and Linear Algebra in computational tasks. Grasp the application of Lambda Calculus in the realm of Functional Programming. Discrete mathematics, in essence, centres around the study of mathematical structures that exhibit a fundamental discreteness rather than continuity. Unlike real numbers, which exhibit smooth variations, discrete mathematics revolves around entities like integers, graphs, and logical statements, which do not exhibit such smooth transitions but instead feature distinct and separated values. Consequently, discrete mathematics excludes topics encompassed by "continuous mathematics," such as calculus or Euclidean geometry. Discrete objects are often countable through integers. To succinctly put it, discrete mathematics focuses on countable sets, which may include finite sets or sets with a cardinality analogous to the natural numbers. Nonetheless, the term "discrete mathematics" lacks a precise definition and is more accurately characterized by what it omits, specifically the domain of continuously varying quantities and related concepts.
