Beginning graduate students in mathematics and other quantitative subjects are expected to have a daunting breadth of mathematical knowledge. But few have such a background. This 2002 book will help students to see the broad outline of mathematics and to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential geometry, real analysis, point-set topology, probability, complex analysis, abstract algebra, and more. An annotated bibliography then offers a guide to further reading and to 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 who need to quickly learn some serious mathematics.
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短時間翻過用來復習基礎知識再順便看看證明的idea挺不錯,然而真的現在還需要看這本查漏補缺而不是一本本刷GTM的也不用考慮去北美讀數學phd,而是如我一般最多去讀個水碩然後考慮就業瞭吧= =
评分Excellent work...
评分以前讀的,實際每個章節講得超級簡單,也就給齣瞭基本定義。作為中學生科普或許比較閤適。
评分正在分辨不清雅可比矩陣與黑賽矩陣,或者一緻連續與逐點連續,或者散度與鏇度,或者測度與度量的時候,遇到瞭這本書。
评分理工科讀phd前暑假必讀書籍之一
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