19世纪牛津大学的本科生代数

Joseph Gage
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摘要

19世纪对于牛津数学和代数来说都是一个重要的时期。虽然当时牛津大学有大量的数学研究文献,但教学却并非如此。这门课程的内容呈现了一幅不同的画面:它展示了那些设置这门课程的人认为对一个年轻数学家来说最有价值的东西,也许表明了他们对数学未来发展方向的期望。为了弄清楚本科生都学了些什么,我查阅了1828年至1912年间的试卷,重点是代数和辅助材料。在本文中,我将介绍我的发现。我将给出一张19世纪末牛津大学本科生代数课程的图片,并讨论我自己的结论,为什么它会采取这种形式。
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Undergraduate algebra in nineteenth-century Oxford
The nineteenth century was an important period for both Oxford mathematics and algebra in general. While there is extensive documentation of mathematical research in Oxford at this time, the same cannot be said of the teaching. The content of the course presents a different picture: it shows what those who set it felt was most valuable for a young mathematician to learn, perhaps indicating what direction they expected mathematics to take in the future. To find out what undergraduates were taught, I have looked through examination papers of the years between 1828 and 1912 with a focus on algebra, as well as supporting material. In this paper I will present my findings. I will give a picture of what an Oxford undergraduate's course in algebra looked like by the end of the nineteenth century and discuss my own conclusions as to why it took such a form.
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