Baby Rudin
这周一直在读Baby Rudin (Principles of Mathematical Analysis by Walter Rudin). 当初心高气傲, 高考结束的那个暑假就买了这本书, 那时看第一章就晕了. 后来学了一遍工科的微积分, 想要捡起这本书, 但是缺乏勇气. 直到现在的”避震”生活, 每天无所事事, 就拿出来消磨时光. 昨天终于把Basic Topololy一章的所有证明读懂. 在这过程中想死的心都有, 难怪Volker Runde在他的A Taste of Topology的序言里, 开门见山的说: If mathematics is a language, then taking a topology course at the undergraduate level is cramming vocabulary and memorizing irregular verbs.
一般的, 大家写的东西都言简意赅, 深入浅出, 但为什么Rudin爷爷的书会是这般难读呢?? 可以肯定的一点是, Rudin不是没这种本事, 难道另有隐情? 我前几天一直想不明白, 现在琢磨出来了. Rudin晓得如果把数学写得如同肥皂剧一样, 学生读起来自然痛快, 但是学生也会像忘记剧情一样把概念定理都忘个一干二净. 所以一定要让学生痛苦挣扎一番, 他才长会记性. 而且读这样的书时, 读者不是被动的, 而是在使劲揣摩作者的意思, 这就达到了练习巩固的目的. 可以毫不夸张的说: Compact Sets小节中的每个证明的每一句话都能拿出来作一独立的证明题. 所以说人家Rudin就是高明.
全世界喜欢这本书的学生和老师特别多(Rudin的粉丝?), 许多老师都对书中难懂的地方做了解释, 这些解释给了我极大的帮助. 已故的Silvia教授的COMPANION NOTES – A Working Excursion to Accompany Baby Rudin干脆把Rudin的证明搬掉几句话, 然后让学生去添. 而Berkeley的一位老师把学生提的问题都集在一起放到网上, 只见师生一问一答十分有趣.
还有件旧事想说, 大概是高三时, 郭凯跟我说他十分喜欢拓扑学. 问其缘由, 此君答曰有趣… 凯妹情趣之高由此可见一斑!
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