数学分析、线性代数、解析几何、泛函、拓扑、抽象代数、实变、微分几何是最重要的课
以几何直观做启发,大胆想象,严密论证.
可以从多角度思考问题.
勤动手算,勤动手推导,在算例中发现规律.
注重一题多解.
重视练习自己的举反例能力,平时多看些数学上有名的反例.
见多识广,博览百家之长!
学数学应该包括数学发现和数学证明两部分!
注重不同分支之间的联系.
http://vdisk.weibo.com/u/3587740491?page=5
http://www.cnblogs.com/scicalweb/p/3984152.html
http://www.douban.com/group/topic/11638537/
General Mathematics
The Princeton Companion to (Applied) Mathematics
數學辭海
數學大辞典
高觀點下的初等數學
“大学基础数学自学丛书”
赵慈庚, 朱鼎勋, “大学数学自学指南”
Weyl, “Symmetry”
Diacu, Holmes, “Celestial Encounters: The Origins of Chaos and Stability”
Aleksandrov, “Mathematics: Its Content, Methods and Meaning”
Kline, “Mathematical Thought from Ancient to Modern Times”
Lars Gårding, “Mathematics and Mathematicians”
Courant, “What Is Mathematics?”
Halmos, “I want to be a mathematician”
Rudin, “The way I remember it”
华罗庚, “数论导引”
汪芳庭, “数学基础”
Serendipities 