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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很多原創的思想隱藏在初次證明裏麵。綫性代數的關鍵在於不同的可逆條件的等價性，解方程等價於算子的核元素。復分析的關鍵是不同的解析函數的定義的等價性。計算復雜性問題本質是可構造性和存在性證明的區彆。粒子的運動和麯綫（波）的運動是過程和對象之間的類比；Lewy's Example本質是解存在依賴於幾何條件
评分好吧，其實我不打算讀
评分不像教材，像教輔。
评分感覺除瞭列齣書目之外並沒有太大用...
评分據說很經典 下次再看
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