Beginning graduate students in mathematics and other quantitative subjects are expected to have a daunting breadth of mathematical knowledge ,but few have such a backgroud .This book will help stedents see the broad outline of mathematics and to fill in the gaps in their knowlegde.
The author explains the basic points and a few key results of the most important undergradute topics in mathematics ,emphasizing the intutions behind the subject.The topics include linear algebra,vector calculus,differential geometry,real analysis ,point-set topology,differential equations,probability theory,complex analysis,abstract algebra,and more.An annotated biliography offers a guide to further reading and more rigorous foundations.
This book will be an essential resource for advanced undergraduate and beginning graduate students in mathematics,the physical sciences,engineering,computer science,statistics,and economics,and for anyone else who needs to quickly learn some serious mathemaics.
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1，2章全部+部分散篇 号称休闲读物
评分differential forms 那块还是不会啊不会啊
评分很多原创的思想隐藏在初次证明里面。线性代数的关键在于不同的可逆条件的等价性，解方程等价于算子的核元素。复分析的关键是不同的解析函数的定义的等价性。计算复杂性问题本质是可构造性和存在性证明的区别。粒子的运动和曲线（波）的运动是过程和对象之间的类比；Lewy's Example本质是解存在依赖于几何条件
评分不像教材，像教辅。
评分这是一本真正想帮助初入数学殿堂的人的武林秘籍。想写一本炫耀式的专著对“数学家”来说并不难，但如何用三百页写一本实用的数学丛林生存指南恐怕是一般数学家不愿意做也做不好的。如果你以后的职业生涯中会大量的涉及到数学方面的知识，在研究生阶段把这本书读完吧。
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