真实数据分析：数学入门教材 英文原版 Real Analysis: A Long-Form Mathematics Textbook

基本信息/Product Details

出版社 ‏ : ‎ Independently published; 第 2nd 版 (2019年7月15日)

语言 ‏ : ‎ 英语

平装 ‏ : ‎ 445页

ISBN-10 ‏ : ‎ 1077254547

ISBN-13 ‏ : ‎ 978-1077254541

商品重量 ‏ : ‎ 1.03 kilograms

尺寸 ‏ : ‎ 21.59 x 2.57 x 27.94 cm

页面参数仅供参考，具体以实物为准

书籍简介/Book Description

这本教科书是为学生设计的。本书不是典型的定义-定理-证明-重复的风格，而是包括更多的评论、动机和解释。证明并不简明扼要，目的是为了理解而不是省钱。此外，几十个证明之前都有 "笔记"或证明草图，以便给学生一个大局观，并解释他们如何自己想出这个证明。例子常常推动叙述，挑战读者的直觉。该书的目的还在于使观点清晰可见，并包含200多幅插图。文章写得很轻松，包括有趣的历史说明、周期性的幽默尝试，以及偶尔转移到数学的其他有趣领域。该书包括实数、基数、序列、数列、实数的拓扑学、连续性、微分、积分以及函数的序列和数列。每一章最后都有习题，而且几乎都包括一些开放性问题。第一个附录包含了一个关于实数的构造，第二个附录收集了分析学中额外的奇特和病态的例子。作者认为大多数教科书的价格都非常高，并努力帮助改变这种情况。提示和精选练习的解决方案可以在官网上找到。

This textbook is designed for students. Rather than the typical definition-theorem-proof-repeat style, this text includes much more commentary, motivation and explanation. The proofs are not terse, and aim for understanding over economy. Furthermore, dozens of proofs are preceded by "scratch work" or a proof sketch to give students a big-picture view and an explanation of how they would come up with it on their own. Examples often drive the narrative and challenge the intuition of the reader. The text also aims to make the ideas visible, and contains over 200 illustrations. The writing is relaxed and includes interesting historical notes, periodic attempts at humor, and occasional diversions into other interesting areas of mathematics. The text covers the real numbers, cardinality, sequences, series, the topology of the reals, continuity, differentiation, integration, and sequences and series of functions. Each chapter ends with exercises, and nearly all include some open questions. The first appendix contains a construction the reals, and the second is a collection of additional peculiar and pathological examples from analysis. The author believes most textbooks are extremely overpriced and endeavors to help change this.

作者简介/Author

Jay Cummings is a professor in the Department of Mathematics and Statisticsat California State University, Sacramento. He received his Ph D. from UC San Diego under Ron Graham. Most of his published work is in various areasof combinatorics. He believes that learning math has become far too expensiveand is striving to write textbooks which are enjoyable to read, highlight thebeauty in mathematics, and are significantly more affordable than the othersthe market