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在数学的殿堂中,伽罗瓦理论一直以其深奥的抽象性著称,挑战着无数大学本科生的智慧。近日,一份来自英国爱丁堡大学的图解版伽罗瓦理论课程笔记公开,为学习者提供了全新的学习资源。

数学家的浪漫与悲剧:伽罗瓦的传奇人生

埃瓦里斯特・伽罗瓦,这位19世纪的法国数学天才,短暂的生命中充满了浪漫与悲剧。在决斗前夜,他奋笔疾书留下了数学的宝贵遗产,却因腹部中弹不幸离世。他的理论在死后由数学家刘维尔发表,开启了群论的篇章,对现代数学产生了深远影响。

爱丁堡大学教授的创新教学实践

爱丁堡大学数学家Tom Leinster教授,以其独特的教学方式,将伽罗瓦理论以图解的形式呈现,使得这一抽象主题变得更为直观易懂。他的课堂笔记涵盖了2021年至2023年间的教学内容,包括域扩展、伽罗瓦群的基本定理,以及与尺规构造、可解多项式和有限域分类相关的讨论。

课程资源丰富,助力学习者深入理解

Leinster教授提供的学习资料不仅包括详尽的笔记,还有大约40个简短的解释视频、大量练习题和近500道多项选择题,旨在帮助学生全面掌握伽罗瓦理论的核心概念。

公开教材反响热烈,图解助力数学普及

这些资料在arXiv上公开后,迅速引起了广泛关注,Leinster教授对此表示惊讶。这份详细且生动的图解教材,降低了伽罗瓦理论的学习门槛,有望激发更多学生对抽象代数的兴趣。

学习资源链接

这一创新教学实践不仅为爱丁堡大学的本科生带来了福利,也对全球范围内对伽罗瓦理论感兴趣的学者提供了宝贵的自学材料。

【source】https://www.jiqizhixin.com/articles/2024-08-26-12

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