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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大概高中生就能讀，沒有看最後幾章，感覺最難的是微分形式那章偷懶放下瞭，對本科數學各部分的核心做瞭介紹，想瞭解數學各個領域都是研究什麼可以從這本書開始
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。
评分科普書。
评分碾揪生 課程 良好 預備
评分理工科讀phd前暑假必讀書籍之一
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