作者:
Raffi Grinberg 出版社: Princeton University Press 副标题: All the Tools You Need to Understand Proofs 出版年: 2017-1-17 页数: 208 定价: USD 27.95 装帧: 平装 丛书:Princeton Lifesaver Study Guides ISBN: 9780691172934
Real analysis is difficult. For most students, in addition to learning new material about real numbers, topology, and sequences, they are also learning to read and write rigorous proofs for the first time. The Real Analysis Lifesaver is an innovate guide that helps students through their first real analysis course while giving them the solid foundation they need for further stu...
Real analysis is difficult. For most students, in addition to learning new material about real numbers, topology, and sequences, they are also learning to read and write rigorous proofs for the first time. The Real Analysis Lifesaver is an innovate guide that helps students through their first real analysis course while giving them the solid foundation they need for further study in proof-based math.
Rather than presenting polished proofs with no explanation of how they were devised, The Real Analysis Lifesaver takes a two-step approach, first showing students how to work backwards to solve the crux of the problem, then showing them how to write it up formally. It takes the time to provide plenty of examples as well as guided "fill in the blanks" exercises to solidify understanding.
Newcomers to real analysis can feel like they are drowning in new symbols, concepts, and an entirely new way of thinking about math. Inspired by the popular Calculus Lifesaver, this book is refreshingly straightforward and full of clear explanations, pictures, and humor. It is the lifesaver that every drowning student needs.
•The essential "lifesaver" companion for any course in real analysis
•Clear, humorous, and easy-to-read style
•Teaches students not just what the proofs are, but how to do them--in more than 40 worked-out examples
•Every new definition is accompanied by examples and important clarifications
•Features more than 20 "fill in the blanks" exercises to help internalize proof techniques
•Tried and tested in the classroom
作者简介
· · · · · ·
Raffi Grinberg is an entrepreneur and former management consultant. He graduated with honors from Princeton University with a degree in mathematics in 2012.
目录
· · · · · ·
Preliminaries 1
1 Introduction 3
2 Basic Math and Logic* 6
3 Set Theory* 14
Real Numbers 25
4 Least Upper Bounds* 27
· · · · · ·
(更多)
Preliminaries 1
1 Introduction 3
2 Basic Math and Logic* 6
3 Set Theory* 14
Real Numbers 25
4 Least Upper Bounds* 27
5 The Real Field* 35
6 Complex Numbers and Euclidean Spaces 46
Topology 59
7 Bijections 61
8 Countability 68
9 Topological Definitions* 79
10 Closed and Open Sets* 90
11 Compact Sets* 98
12 The Heine-Borel Theorem* 108
13 Perfect and Connected Sets 117
Sequences 127
14 Convergence* 129
15 Limits and Subsequences* 138
16 Cauchy and Monotonic Sequences* 148
17 Subsequential Limits 157
18 Special Sequences 166
19 Series* 174
20 Conclusion 183
Acknowledgments 187
Bibliography 189
Index 191
· · · · · · (收起)
remember that it all comes back to the basics. Everything relies on real numbers, topology, and sequences. If you can master those topics, the rest will be a breeze! Really. (查看原文)
In the future, whenever you encounter a problem that uses a new definition, you should first try to fully internalize the definition before applying it to the problem. Write out what it means in both words and symbols, play with some basic examples, understand how it works in R or R^k , and draw pictures.
In the future, whenever you encounter a problem that uses a new definition, you should first try to fully internalize the definition before applying it to the problem. Write out what it means in both words and symbols, play with some basic examples, understand how it works in R or R^k , and draw pictures.
In the future, whenever you encounter a problem that uses a new definition, you should first try to fully internalize the definition before applying it to the problem. Write out what it means in both words and symbols, play with some basic examples, understand how it works in R or R^k , and draw pictures.
層云
人民邮电出版社2020版
小艾的名义
人民邮电出版社2020版
1 有用 grantpanda 2023-03-04 23:12:38 上海
神作，这本书宝贵在它不光讲证明过程，他还讲了从一无所知，怎么想到推理的证明过程
0 有用 任平生 2020-02-06 23:08:47
过年期间也算是看完一本书了。
0 有用 自由度 2023-04-02 17:41:36 山东
还行吧，不如understanding analysis
0 有用 D I P 2021-09-29 22:48:24
顿时感觉baby rudin能看了
0 有用 Veto 2024-05-27 22:19:29 浙江
无痛上手Baby Rudin