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.

“弱”其实是一种强大的力量
“暗”其实是一股巨大的存在
“美丽”其实是科学照进现实后爆发的诗意
他是科学家，他是诗人，他是音乐发烧友，他跨过肉身，飞向“终极”
【内容简介】
婚姻原来是“四年之痒”？
宇宙的秘密都在气泡巧克力里？
暗宇宙给了我一双黑色的眼睛，我却用它寻找光明
评王朔如何荒腔走板混搭《金刚经》与《时间简史》
林黛玉看似弱不禁风，实则“弱”是一股强大的力量！
……
本书从生活的最细微处开始着手，用生动有趣的语言为我们揭开了物质世界中那些简洁又美丽的法则。本书从宇宙到人心，从牛顿到王朔，从热巧克力到命运，涉及的知识领域广阔得惊人，用科学来解释生活的可能性和多元化，既严谨又八卦，带你发现科技人文交融之美，探索精神生活的多维空间。

作者从生活情景中的事物和人类文明发展史的观点切入，提出独特的科学观点，丰富科学的意义。其风趣、机智、富含创意的笔锋，以及字里行间流露出的对科学的热情，令读者感同身受。他努力传达的是： 科学本是很人文，可以很动人，应该很美丽，必须很浪漫。