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© 2003

Reading, Writing, and Proving

A Closer Look at Mathematics

Textbook
  • 36k Downloads

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

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Pages 17-29
  3. Pages 53-62
  4. Pages 63-77
  5. Pages 79-87
  6. Pages 109-117
  7. Pages 119-127
  8. Pages 129-145
  9. Pages 175-189
  10. Pages 207-221
  11. Pages 223-235

About this book

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

  1. 1.Department of MathematicsBucknell UniversityLewisburgUSA

Bibliographic information

  • Book Title Reading, Writing, and Proving
  • Book Subtitle A Closer Look at Mathematics
  • Authors Ulrich Daepp
    Pamela Gorkin
  • Series Title Undergraduate Texts in Mathematics
  • DOI https://doi.org/10.1007/b97273
  • Copyright Information Springer-Verlag New York, Inc. 2003
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-00834-9
  • Softcover ISBN 978-1-4419-1840-6
  • eBook ISBN 978-0-387-21560-0
  • Series ISSN 0172-6056
  • Edition Number 1
  • Number of Pages XVI, 395
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Mathematical Logic and Foundations
    Analysis
    Number Theory
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking

Reviews

From the reviews:

U. Daepp and P. Gorkin

Reading, Writing, and Proving

A Closer Look at Mathematics

"Aids students in their transition from calculus (or precalculus) to higher-level mathematics . . . The authors have included a wide variety of examples, exercises with solutions, problems, and over 40 illustrations."

—L'ENSEIGNEMENT MATHEMATIQUE

"Daepp and Gorkin (both, Bucknell Univ.) offer another in the growing genre of books designed to teach mathematics students the rigor required to write valid proofs … . The book is well written and should be easy for a first- or second- year college mathematics student to read. There are many ‘tips’ offered throughout, along with many examples and exercises … . A book worthy of serious consideration for courses whose goal is to prepare students for upper-division mathematics courses. Summing Up: Highly recommended." (J.R. Burke, CHOICE, 2003)

"The book Reading, Writing, and Proving … provides a fresh, interesting, and readable approach to the often-dreaded ‘Introduction to Proof’ class. … RWP contains more than enough material for a one-semester course … . I was charmed by this book and found it quite enticing. … My students found the overall style, the abundance of solved exercises, and the wealth of additional historical information and advice in the book exceptionally useful. … well-conceived, solidly executed, and very useful textbook." (Maria G. Fung, MAA online, December, 2004)

"The book is intended for undergraduate students beginning their mathematical career or attending their first course in calculus. … Throughout the book … students are encouraged to 1) learn to understand the problem, 2) devise a plan to solve the problem, 3) carry out that plan, and 4) look back and check what the results told them. This concept is very valuable. … The book is written in an informal way, which will please the beginner and not offend the more experienced reader." (EMS Newsletter, December, 2005)