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所在平台: Udemy |
课程主页: https://www.udemy.com/course/settheory/
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**课程名称：** 数学证明与逻辑入门 **课程概述：** 本课程旨在帮助学习者从“为什么”的角度重新审视数学，通过证明来解答数学概念的“为什么”。课程强调数学证明的绝对真理性和不可否认性，将数学提升到科学和其他学科都可探讨的“真理”层面。 与高中几何课程中格式化的证明方式不同，本课程将引导学习者掌握更灵活、更实用的证明方法。通过学习，你将能够证明以下数学事实： * $\sqrt{2}$ 是无理数 * 偶数加偶数等于奇数（此处为笔误，应为偶数） * 某些函数的连续性 * 存在无穷多个素数 * 理解无穷的概念 * 理解等式与不等式 课程将展示证明过程的趣味性，即使是证明“1+1=2”这样的基本事实，也需要严谨的逻辑和方法。 **核心内容：** * **数学证明的本质：** 探索“为什么”是真理，而非仅仅接受“它是这样”。 * **证明的多种方法：** 学习超越格式化证明的技巧。 * **证明经典数学命题：** 学习如何证明无理数、函数连续性、素数等重要数学概念。 * **理解数学概念：** 深入理解无穷、等式与不等式。 * **享受证明的乐趣：** 体验逻辑推理带来的乐趣。 **目标受众：** 对数学证明和逻辑感兴趣的初学者。 **行动号召：** 不要犹豫，立即加入，开启你的数学证明之旅！
When we grow up and take math courses, we tend to ask: "Why is that true?" Most of the time, the teacher tells you something like "because that's the way it is." In this course, we reintroduce all of mathematics in the perspective that we should have. We answer and PROVE the "why" in our lives. The greatest part is that we are dealing with truth - something that science or any other subject can talk about. Everything proven in this course is absolute truth and cannot be denied. Many students get their first exposure to mathematical proofs in a high school course on geometry. Unfortunately, students in high school geometry are usually taught to think of a proof as a numbered list of statements and reasons, a view of a proof that is too restrictive to be very useful. Learn How To Prove It Today! In this course, we learn how to prove amazing mathematical facts: The square root of 2 is irrationalAn even number plus an even number is an odd numberProve that certain functions are continuousProve that there are infinitely many prime numbersUnderstand infinity!What is equality and inequality? The proofs in this course may sound extremely simple, but if I were to ask you to prove 1+1=2, could you do it? It takes 362 pages to prove this fact! Well, there are better methods today, but the process of proving things is more fun than you can imagine! What Are You Waiting For? Sign Up Today!
