Reading, Writing, and Proving: A Closer Look at Mathematics / Edition 2

Hardcover (Print)
Rent from
(Save 80%)
Est. Return Date: 12/19/2014
Buy New
Buy New from
Used and New from Other Sellers
Used and New from Other Sellers
from $52.41
Usually ships in 1-2 business days
(Save 30%)
Other sellers (Hardcover)
  • All (9) from $52.41   
  • New (8) from $52.41   
  • Used (1) from $63.67   


This book, which is based on Polya'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 Polya'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.

Read More Show Less

Editorial Reviews

From the Publisher
From the reviews of the second edition:
“This is at heart a fairly conventional transition text, but it has a number of features that encourage students to practice and improve their mathematical reading, writing, and proving skills. … The book is primarily concerned with an exposition of those parts of mathematics in which students need a more thorough grounding before they can work successfully in upper-division undergraduate courses. … a mathematically-conventional but pedagogically-innovative take on transition courses.” (Allen Stenger, The Mathematical Association of America, September, 2011)
Read More Show Less

Product Details

  • ISBN-13: 9781441994783
  • Publisher: Springer New York
  • Publication date: 6/29/2011
  • Series: Undergraduate Texts in Mathematics Series
  • Edition description: 2nd ed. 2011
  • Edition number: 2
  • Pages: 378
  • Sales rank: 854,638
  • Product dimensions: 6.20 (w) x 9.30 (h) x 1.10 (d)

Meet the Author

Ueli Daepp is an associate professor of mathematics at Bucknell University in Lewisburg, PA. He was born and educated in Bern, Switzerland and completed his PhD at Michigan State University. His primary field of research is algebraic geometry and commutative algebra.

Pamela Gorkin is a professor of mathematics at Bucknell University in Lewisburg, PA. She also received her PhD from Michigan State where she worked under the director of Sheldon Axler. Prof. Gorkin’s research focuses on functional analysis and operator theory.

Ulrich Daepp and Pamela Gorkin co-authored of the first edition of “Reading, Writing, and Proving” whose first edition published in 2003. To date the first edition (978-0-387-00834-9 ) has sold over 3000 copies.

Read More Show Less

Table of Contents

1 The How, When, and Why of Mathematics 1
2 Logically Speaking 17
3 Introducing the Contrapositive and Converse 31
4 Set Notation and Quantifiers 39
5 Proof Techniques 53
6 Sets 63
7 Operations on Sets 79
8 More on Operations on Sets 89
9 The Power Set and the Cartesian Product 97
10 Relations 109
11 Partitions 119
12 Order in the Reals 129
13 Functions, Domain, and Range 147
14 Functions, One-to-One, and Onto 163
15 Inverses 175
16 Images and Inverse Images 191
17 Mathematical Induction 207
18 Sequences 223
19 Convergence of Sequences of Real Numbers 237
20 Equivalent Sets 251
21 Finite Sets and an Infinite Set 261
22 Countable and Uncountable Sets 271
23 Metric Spaces 283
24 Getting to Know Open and Closed Sets 297
25 Modular Arithmetic 313
26 Fermat's Little Theorem 331
27 Projects 343
28 Appendix 379
References 383
Index 389
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)