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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适合美国高年级本科生看,研究生偶尔也可以回头看看入门下没学过的领域。这本书的缺点和优点是一样的:面面俱到但是每个点都没办法细说。不是说每个领域都要完全cover,但是离五星的差距就是没足够的insight和高观点。当然,it does a pretty good job on what it is supposed to do。然而靠这本书是没办法考过中等以上美国学校的phd资格考试的,不过光想靠这本就混过去那也没读phd的必要了。
评分查漏补缺...可怕的PhD life已经来了
评分Excellent work...
评分It's similar to having dinner with a mathematician who can't stop talking about the topics they love.
评分科普书。
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