Robert B. Ash 的一些当作教材的书。 [推广有奖]

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universecn 发表于 2017-2-11 11:54:04 |只看作者 |坛友微信交流群|倒序 |AI写论文

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Robert B. Ash可能在发表文章上不是那么有名，但是他写的书很不错，可以说是devoted himself to write good textbooks.我读他的第一本书是2000的Probability and Measure Theory,是我转向stochastic calculus及financial math时系统看的第一本书，感觉非常好，concise, intuitive, to the point, and rigorous at same time。
下面是他写书时的一些观点（免费）

Robert_Ash_Remarks on Expository Writing in Mathematics.pdf (160.53 KB)
A Pari/GP Tutorial - collection of definitions/explanations of basic concepts（免费）

Robert_Ash_GPTutorial.pdf (337.47 KB)

Successful graduate students in mathematics are able to reach an advanced level in one
or more areas. Textbooks are an important part of this process. A skilled lecturer is able
to illuminate and clarify many ideas, but if the pace of a course is fast enough to allow
decent coverage, gaps will inevitably result. Students will depend on the text to fill these
gaps, but the experience of most students is that the usual text is difficult for the novice
to read. At one extreme, the text is a thousand page, twenty pound encyclopedia which
cannot be read linearly in a finite amount of time. At the other extreme, the presentation
in the book is essentially a seminar lecture with huge gaps.

He offers six main recommendations
1. "Adopt a linear style"
2. "Include solutions to exercises"
3. "Discuss the intuitive content of results"
4. "Replace abstract arguments by algorithmic procedures if possible"
5. "Use the concrete example with all the features of the general case," and
6. "Avoid serious gaps in the reasoning."

He concludes,
I hope to see a change in the reward structure and system of values at researchoriented
universities so that teaching and expository writing become legitimate as a
specialty. This will help to improve the current situation in which many advanced areas
of mathematics are inaccessible to most students because no satisfactory exposition
exists. I hope to see more mathematicians write lecture notes for their courses and post
the results on the web for all to use.

下面的书他写的比较受欢迎的一些当作教材的书。