# Reading, Writing, and Proving

## A Closer Look at Mathematics

• Ulrich Daepp
• Pamela Gorkin
Book

Part of the Undergraduate Texts in Mathematics book series (UTM)

1. Front Matter
Pages i-xvi
2. Pages 1-15
3. Pages 17-29
4. Pages 31-38
5. Pages 39-52
6. Pages 53-62
7. Pages 63-77
8. Pages 79-87
9. Pages 89-96
10. Pages 97-108
11. Pages 109-117
12. Pages 119-127
13. Pages 129-145
14. Pages 147-161
15. Pages 163-173
16. Pages 175-189
17. Pages 191-205
18. Pages 207-221
19. Pages 223-235
20. Pages 237-250

### Introduction

This book, which is based on Pólya's method of problem solving, aids students in their transition from calculus (or precalculus) to higher-level mathematics. The book begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics. It ends by providing projects for independent study.

Students will follow Pólya's four step process: learn to understand the problem; devise a plan to solve the problem; carry out that plan; and look back and check what the results told them. Special emphasis is placed on reading carefully and writing well. The authors have included a wide variety of examples, exercises with solutions, problems, and over 40 illustrations, chosen to emphasize these goals. Historical connections are made throughout the text, and students are encouraged to use the rather extensive bibliography to begin making connections of their own. While standard texts in this area prepare students for future courses in algebra, this book also includes chapters on sequences, convergence, and metric spaces for those wanting to bridge the gap between the standard course in calculus and one in analysis.

### Keywords

Algebra Arithmetic Cantor Cauchy–Bunyakovsky–Schwarz inequality Countable set Finite Problem solving Problem-solving calculus function mathematical induction mathematics proof theorem

#### Authors and affiliations

• Ulrich Daepp
• 1
• Pamela Gorkin
• 1
1. 1.Department of MathematicsBucknell UniversityLewisburgUSA

### Bibliographic information

• DOI https://doi.org/10.1007/b97273
• Copyright Information Springer-Verlag New York, Inc. 2003
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-00834-9
• Online ISBN 978-0-387-21560-0
• Series Print ISSN 0172-6056