伽罗瓦理论
Galois Theory

原始链接: https://golem.ph.utexas.edu/category/2024/08/galois_theory.html

Tom Leinster 为他在 2021 年至 2023 年间教授的本科伽罗瓦理论入门课程发表了全面且具有视觉吸引力的讲义。该出版物包括:详细的笔记、大约四十个教学视频、大量问题集、四百多个多项选择题,涵盖 无需先验知识或经验即可了解关键概念。 尽管以前公开教授过各种数学主题,但这些伽罗瓦理论笔记在学习者中非常受欢迎。 它们可能因其丰富多彩的设计(包括小图标)而有吸引力。 伦斯特认为,在新冠疫情封锁期间,学生的学习面临挑战,他特别注意提供明确的解释,以帮助弥合因缺乏课堂互动而造成的差距。 他希望这些资源能为那些有兴趣研究伽罗瓦理论的人们带来教育上的满足和享受。

用户对 ChatGPT 等人工智能模型表示不满,因为它们在回答复杂、专业的问题时经常出现错误和错误信息。 他们发现这些模型提供了错误的答案,通常会产生无意义的响应或混淆多个概念。 例如,他们提到提供的有关莱塞尔定理的信息不准确,其中 ChatGPT 提供了不同的几何关系而不是实际的定理。 尽管该模型能够提供一般知识,但用户必须彻底验证所有响应的准确性,然后才能将其视为事实。 用户还表示,该模型可能难以提供准确、专业的详细信息,特别是如果这些信息不容易在网上或在流行来源中获得的话。 总体而言,用户在依赖这些工具获取详细、准确的信息时需要谨慎,特别是在处理需要专家级理解的利基主题时。
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原文

Galois Theory

Posted by Tom Leinster

I’ve just arXived my notes for Edinburgh’s undergraduate Galois theory course, which I taught from 2021 to 2023.

I first shared the notes on my website some time ago. But it took me a while to arXiv them, because I wanted to simultaneously make public most of the other course materials. I now have, which means the following are now available to all:

  • Notes forming a complete, self-contained account of the part of Galois theory that we covered.

  • About 40 short explanatory videos.

  • A large collection of problems.

  • Nearly 500 multiple choice questions.

I’m a little bemused by the popularity of the Galois theory notes. I’ve made quite a few sets of course notes public before, e.g.:

But the Galois theory notes seem to have caught on in a way that none of the others have (except category theory — but that one, I made into a book).

It’s true that I probably took a bit of extra care on them: I first taught the course during full Covid lockdown, and I felt the students would need more guidance than usual, given that they were deprived of all opportunities for face-to-face interaction. But I wonder whether the real reason is that the Galois theory notes simply look nicer, with colour and little icons and so on.

In any case, I hope the notes, videos and questions bring people joy.

Posted at August 15, 2024 1:02 PM UTC

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