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所在平台: Udemy |
课程主页: https://www.udemy.com/course/linear-algebra-with-applications/
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**课程名称：** 线性代数 **课程概述：** 本课程旨在向学习者介绍线性代数的概念及其广泛的应用，尤其是在机器学习和数据科学等热门领域。线性代数作为一门重要的数学分支，在工程、科学、经济学、信号处理等多个领域都有着不可或缺的地位。 **课程特色：** * **全面性：** 涵盖了标准线性代数教材中的主要内容，并着重讲解了许多在本科线性代数课程中较少涉及的主题，如最小二乘法、奇异值分解和数值线性代数。 * **实践性：** 强调“实践出真知”，课程中会通过逐步演示手动计算过程，解释每一步的原理，并针对过于复杂的问题，提供使用 Python 编程语言编写的程序演示，以及包含详细解答的练习题。 * **应用性：** 为每个主要主题都配有实际应用案例，帮助学习者理解线性代数在现实世界中的价值。 * **启发性：** 鼓励学习者从“线性代数有哪些用途”的疑问出发，在课程结束后能体会到“线性代数几乎无处不在”的认识。 **学习目标：** * 理解线性代数的核心概念和理论。 * 掌握线性代数的基本运算和求解方法。 * 认识线性代数在不同领域的广泛应用。 * 培养利用线性代数解决实际问题的能力。 **推荐理由：** 本课程借鉴了 Gilbert Strang（MIT 线性代数教授）的观点，强调线性代数在21世纪数学教育中的核心地位。通过严谨的理论讲解、细致的实践操作和丰富的应用案例，帮助学习者深入理解并熟练掌握线性代数这门重要的数学工具。
I believe that linear algebra is the most important area of math that most people have never heard of. While it has long been important in engineering and the sciences, it is also widely used in the currently popular fields of machine learning and data science.To give you an idea of how widely it is used, check out the titles of these books:An Introduction to Wavelets Through Linear AlgebraFundamentals and Linear Algebra for the Chemical EngineerGraph Algorithms in the Language of Linear AlgebraIntermediate Dynamics: A Linear Algebraic ApproachIntroduction to Linear Algebra: A Primer for Social ScientistsIntroduction to Linear Algebra in GeologyIntroduction to Matrix Methods in OpticsLinear Algebra and Optimization for Machine LearningLinear Algebra for EconomistsLinear Algebra for Signal ProcessingMatrix Algebra From a Statistician's PerspectiveTheory of Matrix Structural AnalysisMy goal in this course is to introduce you to linear algebra in such a way that you not only understand the purpose of the various topics, but that you also see how you can apply the material. I hope that if you begin the course thinking "what is linear algebra used for?" that you end the course thinking "what can't you use linear algebra for?"We will cover standard topics of linear algebra that you can find in any linear algebra textbook, but I also spend a lot of time on topics that are less common in an undergraduate linear algebra course: least squares, singular value decomposition, and numerical linear algebra.I am a big believer that in order to learn to do something, you have to actually practice doing it. Therefore, I do the following: work problems by hand, explaining the steps used and promoting understanding of why we are doing it in a few cases the problems are too large or complex to do by hand, so I wrote a computer program in the Python programming language to do the work or plot the values provide practice problems with solutions, showing my work for obtaining the answers It is also easy to claim that linear algebra is useful but then not back it up. Therefore, for each major topic I include practical applications. Finally, let me leave you with a quote from Linear Algebra: A Happy Chance to Apply Mathematics by Gilbert Strang, who teaches linear algebra at MIT: "I believe that linear algebra is the most important subject in college mathematics. Isaac Newton would not agree! But he isn't teaching mathematics in the 21st century (and maybe he wasn't a great teacher, we will give him the benefit of the doubt). Certainly Newton demonstrated that the laws of physics are best expressed by differential equations. He needed calculus: quite right. But the scope of science and engineering and management (and life) is now so much wider, and linear algebra has moved into a central place."
