文件名称:
A Problems Based Course in Advanced Calculus
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上传时间: 2018-12-10
详细说明： Some years ago at a national meeting of mathematicians, many of the conventioneers went about wearing pins which proclaimed, “Mathematics is Not a Spectator Sport”. It is hard to overemphasize the importance of this observation. The idea behind it has been said in many ways by many people; perhaps it was said best by Paul Halmos [Hal67]: The only way to learn mathematics is to do mathematics. In most respects learning mathematics is more like learning to play tennis than learning history. It is principally an activity, and only secondarily a body of knowledge. Although no one would try to learn tennis just by watching others play the game and perhaps reading a book or two about it, thousands of mathematics students in American universities every year attempt to master mathematical subjects by reading textbooks and passively watching their instructors do mathematics on a blackboard. There are, of course, reasons why this is so, but it is unfortunate nevertheless. This book is designed to encourage you to do mathematics. Perhaps the most important thing to know about the structure of this book is that, logically, the appendices come first. The appendices contain a summary of what is generally regarded as prerequisite information that, ideally, one should have before venturing into advanced calculus. In the real world, students’ backgrounds differ enormously. If, at one extreme, you are quite familiar with nearly all of the appended material, you are ready for Chapter 1. Use the appendices for reference and notation. At the other extreme, a very poorly prepared student may profit from spending considerable time working on these sections. In between, where most students find themselves, you have choices. For example, if you are unfamiliar with the distinction between “countable” and “uncountable” sets, you can master the concepts right away, knowing that you will use them later, or you can wait until one of the words crops up in your reading, and learn the concepts when you need them. xvii 英文原版 超清 ...展开详情收缩
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